The FE Mechanical exam is broad, but it is not random. Most points come from recognizing familiar setups in thermodynamics, fluids, dynamics, statics, mechanics of materials, heat transfer, and design, then finding the right equation or property quickly enough to stay on pace. This guide gives you the topic map, the highest-return study order, and a 12-week plan that keeps practice tied to real exam decisions.
FE Mechanical Exam at a Glance
| Questions | 110 multiple-choice |
| Time | 5 hours 20 minutes (~2.9 min/question) |
| Format | Computer-based at Pearson VUE centers, year-round |
| Topic areas | 14 knowledge areas — 6 high-weight topics dominate |
| Reference | NCEES FE Reference Handbook (provided digitally) |
| Cost | $225 NCEES fee (full cost breakdown) |
| Pass rate | 69% first-time, 37% repeat (NCEES Squared 2025) |
| Study time | About 110 hours within a year of school, up to about 185 at 12+ years out |
Practice Coverage by Topic
The weights above come from the NCEES specification. The table below is ours: how many questions our FE Mechanical bank actually carries for each official topic, how many distinct subtopics they cover, and what share are rated hard.
| Official topic | NCEES questions | Practice questions | Per exam question | Subtopics | Rated hard |
|---|---|---|---|---|---|
| Mathematics | 6–9 | 197 | shared pool | 25 | 23% |
| Probability and Statistics | 4–6 | 142 | shared pool | 64 | 21% |
| Ethics and Professional Practice | 4–6 | 82 | shared pool | 20 | 20% |
| Engineering Economics | 4–6 | 120 | shared pool | 24 | 25% |
| Electricity and Magnetism | 5–8 | 32 | 4.9 | 16 | 16% |
| Statics | 9–14 | 78 | 6.8 | 21 | 17% |
| Dynamics, Kinematics, and Vibrations | 10–15 | 92 | 7.4 | 35 | 16% |
| Mechanics of Materials | 9–14 | 82 | 7.1 | 40 | 26% |
| Material Properties and Processing | 7–11 | 57 | 6.3 | 24 | 5% |
| Fluid Mechanics | 10–15 | 91 | 7.3 | 39 | 18% |
| Thermodynamics | 10–15 | 88 | 7 | 31 | 19% |
| Heat Transfer | 7–11 | 58 | 6.4 | 16 | 21% |
| Measurements, Instrumentation, and Controls | 5–8 | 35 | 5.4 | 13 | 14% |
| Mechanical Design and Analysis | 10–15 | 94 | 7.5 | 44 | 17% |
Electricity and Magnetism has the thinnest coverage relative to its weight. Mechanics of Materials has the largest share tagged hard among Mechanical-specific topics at 26%; Engineering Economics, shared across FE exams, has a lower share at 25%. These are bank difficulty tags, not a measured exam-difficulty comparison.
Counts are from the live FE Mechanical bank (1248 questions) as of 2026-10-05, matched to the official topic names in the current NCEES specification. Mathematics, ethics, and economics questions come from a pool shared across all FE disciplines, so no per-exam-question ratio is shown for them. Difficulty ratings are ours, not NCEES.
Worked Examples
Four problems spanning the mechanical core - dynamics, mechanics of materials, heat transfer, and machine design - each worked end to end: the setup, the arithmetic, the calculator keystrokes, and the handbook section the relation lives on.
Show the answer and worked solution
Answer: C. 95.6 m
Worked solution
- vy = v0 sin 60° = 50(0.8660) = 43.30 m/s
- At maximum height, vy = 0: h = vy2/(2g) = 43.302/(2 × 9.81) = 1874.9/19.62 = 95.6 m
Why other options are wrong: Option A (127.4) uses v02/(2g). Option B (31.9) uses v0 cos 60°. Option D (63.7) uses v02 sin 60°/(2g).
On the TI-36X Pro:
Step 1: Set angle mode to degrees; Step 2: 50 × sin(60) enter 43.30 m/s; Step 3: 43.30 x² enter 1874.9; Step 4: 1874.9 ÷ (2 × 9.81) enter 95.6 m.
Handbook: Mechanical Engineering > Dynamics
Show the answer and worked solution
Answer: D. 25 kip·ft
Worked solution
- Identify: Simply supported beam, UDL w = 2 kip/ft, L = 10 ft
- Apply: Mmax = wL2/8
- Calculate: Mmax = 2(102)/8 = 25 kip·ft
Why other options are wrong: Option A (20 kip-ft) uses wL instead of wL2/8, omitting the length-squared dependence. Option B (50 kip-ft) uses wL2/4, which is double the correct value and corresponds to no standard beam formula. Option C (10 kip-ft) uses wL/2, which equals the maximum shear force rather than the maximum moment.
On the TI-36X Pro:
Step 1: 10 x² enter 100; Step 2: 2 × 100 enter 200; Step 3: 200 ÷ 8 enter 25 kip*ft.
Handbook: Mechanics of Materials > Beam Diagrams
Show the answer and worked solution
Answer: D. 7,750 W
Worked solution
- Cylindrical conduction: Q = 2π k L(Ti - To)/ln(ro/ri) = 2π(50)(1)(10)/ln(1.5)
- With ln(1.5) = 0.4055: Q = 3,141.6/0.4055 = 7,748 ≈ 7,750 W
Why other options are wrong: Option B applies the flat-wall formula with mean radius; Option C uses (ro - ri) in the denominator.
On the TI-36X Pro:
Step 1: 0.075 ÷ 0.05 enter 1.5; Step 2: ln 1.5 enter 0.4055; Step 3: 2 × π × 50 × 1 × 10 enter 3141.6; Step 4: 3141.6 ÷ 0.4055 enter 7750 W.
Handbook: Mechanical Engineering > Heat Transfer
Show the answer and worked solution
Answer: B. 20.4 MPa
Worked solution
- J = π d4/32 = π(0.050)4/32 = π × 6.25 × 10-6/32 = 6.136 × 10-7 m4
- τmax = Tc/J = 500 × 0.025/6.136 × 10-7 = 12.5/(6.136 × 10-7) = 20.4 × 106 Pa = 20.4 MPa
Why other options are wrong: Option A uses J = π d4/16 with diameter instead of radius; Option C doubles the result; Option D uses polar moment for hollow shaft.
On the TI-36X Pro:
Step 1: π × 50 xʸ 4 ÷ 32 enter 613592 mm^4; Step 2: 500000 × 25 ÷ 613592 enter 20.4 MPa.
Handbook: Mechanical Engineering > Machine Design
These are FE Mechanical practice questions from our bank, not official NCEES items. Keystrokes are for the TI-36X Pro; the Casio fx-115ES PLUS differs in the memory and solver keys. Handbook references point at FE Reference Handbook 10.6 — confirm the version assigned to your exam date.
What Is the FE Exam and Why Does It Matter?
NCEES runs FE Mechanical as a computer-based exam at Pearson VUE centers: 110 questions in 5 hours and 20 minutes, with the digital FE Reference Handbook on screen for every one of them. Treat that handbook as part of the test, not a backup plan: the faster you can recognize a cycle, beam, pump curve, vibration setup, or heat-transfer mode, the easier it is to choose the right formula and move.
A pass gets you the Engineer Intern (EI) or Engineer in Training (EIT) title, depending on your state, and starts the clock toward the PE: most boards want the required years of experience, typically four under a licensed PE, before you can sit for the PE exam and earn full licensure.
Career Benefits of Passing the FE Exam
- PE licensure pathway: A PE license is required to offer engineering services directly to the public, hold certain senior positions, and sign and seal engineering documents. In many industries — HVAC, power generation, manufacturing, and consulting — PE licensure is a significant differentiator.
- Competitive advantage: Many mechanical engineering firms expect new hires to have passed the FE or to pass it within their first year.
What Are the 14 Topic Areas on the FE Mechanical Exam?
The FE Mechanical exam draws from 14 distinct knowledge areas. The first four topics are shared across all FE disciplines, while topics 5 through 14 are specific to the mechanical engineering exam. NCEES publishes an exam specification (effective July 2020) that gives each topic a range for the number of questions out of 110; the weight column is that range divided by 110 and rounded. Below is a summary table, largest areas first, followed by a detailed look at each topic.
| Topic Area | NCEES Questions | Weight | Priority |
|---|---|---|---|
| Dynamics, Kinematics, and Vibrations | 10–15 | 9–14% | HIGH |
| Fluid Mechanics | 10–15 | 9–14% | HIGH |
| Thermodynamics | 10–15 | 9–14% | HIGH |
| Mechanical Design and Analysis | 10–15 | 9–14% | HIGH |
| Statics | 9–14 | 8–13% | HIGH |
| Mechanics of Materials | 9–14 | 8–13% | HIGH |
| Material Properties and Processing | 7–11 | 6–10% | MEDIUM |
| Heat Transfer | 7–11 | 6–10% | MEDIUM |
| Mathematics | 6–9 | 5–8% | LOW |
| Electricity and Magnetism | 5–8 | 5–7% | LOW |
| Measurements, Instrumentation, and Controls | 5–8 | 5–7% | LOW |
| Probability and Statistics | 4–6 | 4–5% | LOW |
| Ethics and Professional Practice | 4–6 | 4–5% | LOW |
| Engineering Economics | 4–6 | 4–5% | LOW |
Where to Review the Highest-Return FE Mechanical Topics
Mechanical prep gets easier when you group topics by workflow instead of studying every chapter equally. Use this map to decide when to use the handbook, when to practice, and when an outside refresher is worth your time.
Treat loads, reactions, stress, and deflection as one chain.
A beam problem may start as statics and end as stress or deflection. Build the habit of finding reactions first, then moving to internal loads and material response.
- Handbook move: mark section properties, stress equations, torsion, and beam-deflection tools.
- Practice move: keep sign conventions visible on every beam and shaft problem.
Choose the model before choosing the equation.
Mechanical dynamics questions often hinge on whether the problem is particle motion, rigid-body rotation, work-energy, impulse-momentum, or one-degree vibration.
- Handbook move: separate kinematics, kinetics, and vibration references in your review notes.
- Practice move: draw the coordinate system and positive direction before calculating.
Write the system boundary and energy balance first.
Cycles, compressors, turbines, nozzles, heat exchangers, conduction, convection, and radiation all become cleaner once the control mass or control volume is clear.
- Handbook move: know where property tables, cycles, and heat-transfer relationships start.
- Practice move: track state numbers and units before using table values.
Identify pressure, energy, momentum, or loss before solving.
Fluids questions reward classification. Decide whether the problem is statics, Bernoulli, pipe loss, pump power, dimensional analysis, or momentum before opening the calculator.
- Handbook move: mark fluid-property, head-loss, pump, and dimensionless-number lanes.
- Practice move: convert all pressures and elevations into a consistent energy form.
Look for failure mode and material behavior first.
Design and materials questions often ask whether stress, fatigue, safety factor, material property, or manufacturing behavior controls the answer.
- Handbook move: connect design factors, material properties, and failure criteria.
- Practice move: state the failure mode before substituting values.
Source note: topic names and question ranges should be checked against the current NCEES FE exam page. Mechanics Map, LibreTexts and Khan Academy are optional refreshers that go deeper than FE Mechanical does; use them to rebuild a concept, then return to the handbook for exam-style lookups.
Each topic below lists what the exam actually asks for, which is often narrower than the course you took.
Part 1: Shared Topics (All FE Disciplines)
1. Mathematics (6–9 questions)
Covers calculus (derivatives and integrals), differential equations, linear algebra, vector operations, and analytic geometry. You will encounter problems involving partial derivatives, solving first- and second-order ordinary differential equations, matrix operations, and vector cross and dot products. The handbook gives you the steam tables, Moody diagram, and fatigue curves. What it cannot tell you is which of them a question is asking for, and that recognition is what separates a 3-minute solve from a 6-minute one. Math on the FE Mechanical exam carries more weight than on some other disciplines because it underpins thermodynamics, dynamics, fluid mechanics, and heat transfer. Numerical methods (approximations, error propagation, Taylor series, Newton’s method) and algorithm and logic development (flowcharts, pseudocode) also sit in this area; there is no separate computational tools area in the current specification.
2. Probability and Statistics (4–6 questions)
Expect questions on probability distributions (normal, binomial, Poisson), measures of central tendency and dispersion, linear regression, hypothesis testing, and confidence intervals. Mechanical engineers use statistics extensively in quality control, reliability engineering, and experimental analysis. Most problems are straightforward if you understand when to apply each distribution and how to use the standard normal table in the reference handbook.
3. Ethics and Professional Practice (4–6 questions)
Four to six conceptual questions on the NCEES Model Rules of Professional Conduct, public safety obligations, and licensure requirements. Expect short scenarios that ask for the correct ethical course of action rather than a calculation. Read the ethics section in the reference handbook carefully; it is a compact topic area where focused review can pay off.
4. Engineering Economics (4–6 questions)
Topics include time value of money, present and future worth analysis, annual cost comparisons, benefit-cost analysis, rate of return, breakeven analysis, and depreciation methods. Practice the six factor formulas (P/F, F/P, A/P, A/F, P/A, F/A) on equipment comparisons, such as a cheaper pump with higher running costs against an efficient one that costs more up front. Mechanical engineers routinely use economic analysis to compare equipment alternatives and justify capital expenditures.
Part 2: Mechanical Engineering–Specific Topics
5. Electricity and Magnetism (5–8 questions)
The only knowledge area on the Mechanical exam devoted to circuits and electrical machines, and it carries as many questions as Measurements, Instrumentation, and Controls. The specification lists electrical fundamentals, DC circuit analysis, AC circuit analysis with resistors, capacitors, and inductors, and motors and generators. Subtopics include:
- Electrical fundamentals: charge, current, voltage, resistance, power, energy, and magnetic flux
- DC circuits: Ohm’s law, Kirchhoff’s laws, series and parallel combinations
- AC circuits with resistors, capacitors, and inductors
- Motors and generators
6. Statics (9–14 questions)
One of the most heavily tested topics on the exam. Covers resultants of force systems, concurrent and non-concurrent forces, equilibrium of rigid bodies, analysis of trusses (method of joints and method of sections), frames and machines, centroids and moments of inertia, and friction. You must be able to draw free body diagrams confidently and solve equilibrium equations. This is a foundational topic — weaknesses here will cascade into Mechanics of Materials, Dynamics, and Mechanical Design. Subtopics include:
- Two- and three-dimensional force systems
- Equilibrium of particles and rigid bodies
- Truss analysis (method of joints, method of sections)
- Frames and machines
- Centroids and area moments of inertia
- Static and kinetic friction
7. Dynamics, Kinematics, and Vibrations (10–15 questions)
A major topic area that goes well beyond what other FE disciplines test. Covers particle and rigid body kinematics (rectilinear, curvilinear, and relative motion), kinetics using Newton’s second law, work-energy methods, impulse-momentum methods, impact (elastic and inelastic collisions), and vibrations (free, damped, and forced). Subtopics include:
- Rectilinear and curvilinear motion of particles
- Rotation and general plane motion of rigid bodies
- Newton’s second law for translation and rotation
- Work-energy theorem and conservation of energy
- Linear and angular impulse-momentum
- Free vibration: natural frequency, period, amplitude
- Damped vibration: underdamped, overdamped, critically damped
- Forced vibration: resonance and transmissibility
8. Mechanics of Materials (9–14 questions)
Another high-weight topic. Includes stress and strain (normal and shear), axial loading, torsion of circular shafts, bending stresses in beams, shear stresses in beams, combined loading, Mohr’s circle for stress and strain, beam deflections, statically indeterminate members, pressure vessels, and column buckling (Euler’s formula). Subtopics include:
- Stress-strain diagrams and material properties
- Axial deformation and thermal expansion
- Torsion of circular and thin-walled shafts
- Beam bending: flexure formula and shear formula
- Shear and bending moment diagrams
- Mohr’s circle for plane stress and plane strain
- Combined loading and principal stresses
- Thin- and thick-walled pressure vessels
- Euler column buckling and effective length
- Beam deflections (double integration, superposition)
9. Material Properties and Processing (7–11 questions)
Covers mechanical properties of metals, polymers, ceramics, and composites. Expect questions on the stress-strain curve (yield strength, ultimate strength, modulus of elasticity, ductility), hardness testing, fatigue life, creep, phase diagrams (iron-carbon), heat treatment processes (annealing, quenching, tempering), and corrosion mechanisms. Subtopics include:
- Mechanical properties: yield, ultimate, elastic modulus, Poisson’s ratio
- Iron-carbon phase diagram and heat treatments
- Fatigue, creep, and fracture mechanics fundamentals
- Material selection for engineering applications
- Manufacturing processes: casting, forming, machining, joining
10. Fluid Mechanics (10–15 questions)
Covers fluid properties (density, viscosity, surface tension, compressibility), fluid statics and manometry, buoyancy, the Bernoulli equation, the continuity equation, pipe flow with friction losses (Darcy-Weisbach and Moody diagram), Reynolds number, dimensional analysis, external flow (drag and lift), and turbomachinery. Subtopics include:
- Fluid statics: pressure variation, manometers, forces on submerged surfaces
- Buoyancy and stability of floating bodies
- Conservation equations: continuity, momentum, energy
- Bernoulli’s equation and its assumptions
- Internal flow: laminar vs. turbulent, Darcy-Weisbach, Moody diagram
- Minor losses: valves, fittings, expansions, contractions
- Pump and turbine performance: head, power, efficiency, NPSH
- External flow: drag coefficient, boundary layers
- Dimensional analysis and similitude
11. Thermodynamics (10–15 questions)
The most formula-dense section on the exam. Covers the first and second laws, properties of pure substances (steam tables, ideal gas), power cycles (Rankine, Brayton, Otto, Diesel), refrigeration cycles (vapor-compression), psychrometrics, gas mixtures, and entropy. Subtopics include:
- Thermodynamic properties and state postulate
- First law: closed systems (Q − W = ΔU) and open systems (SFEE)
- Second law: Carnot efficiency, entropy, irreversibility
- Ideal gas behavior and processes (isothermal, isentropic, polytropic)
- Steam tables: compressed liquid, saturated mixture, superheated vapor
- Vapor power cycles: Rankine with reheat and regeneration
- Gas power cycles: Brayton, Otto, Diesel with air-standard analysis
- Refrigeration: vapor-compression cycle and coefficient of performance
- Psychrometrics: humidity ratio, dew point, wet-bulb, psychrometric chart
12. Heat Transfer (7–11 questions)
Covers conduction (Fourier’s law, thermal resistance, composite walls, fins), convection (Newton’s law of cooling, forced and natural convection correlations, dimensionless numbers), radiation (Stefan-Boltzmann law, emissivity, view factors), and heat exchangers (LMTD and effectiveness-NTU methods). Subtopics include:
- Steady-state conduction: plane wall, cylinder, sphere, thermal circuits
- Fins: effectiveness, efficiency, and heat dissipation
- Forced convection: internal and external flow correlations (Re, Nu, Pr)
- Natural convection: Rayleigh number, Grashof number
- Radiation: blackbody, graybody, view factors, radiation exchange
- Heat exchangers: LMTD method, effectiveness-NTU method, fouling
13. Measurements, Instrumentation, and Controls (5–8 questions)
Covers measurement uncertainty, sensor types (thermocouples, strain gauges, pressure transducers, flow meters), signal conditioning, data acquisition basics, and feedback control systems (block diagrams, transfer functions, stability, PID controllers). Subtopics include:
- Measurement accuracy, precision, and uncertainty analysis
- Sensors for temperature, pressure, flow, and strain
- Block diagrams and transfer functions
- Open-loop and closed-loop systems
- PID control: proportional, integral, derivative actions
- System response: first-order and second-order systems
- Stability criteria
14. Mechanical Design and Analysis (10–15 questions)
Ties together statics, mechanics of materials, and material properties into real-world design problems. Covers stress analysis, fatigue (S-N curves, endurance limit, Goodman diagram), failure theories (von Mises, Tresca, maximum normal stress), bolted and welded connections, springs, bearings, gears, shafts, power transmission, and fits and tolerances. Subtopics include:
- Static failure theories: maximum shear stress, distortion energy (von Mises)
- Fatigue failure: endurance limit modifications, Goodman and Soderberg lines
- Shaft design: combined bending and torsion, critical speed
- Bolted joints: preload, proof load, fatigue of bolted connections
- Welded joints: fillet welds, butt welds, allowable stresses
- Springs: helical compression, extension, torsion springs
- Rolling-element bearings: load-life relationships
- Gears: spur, helical, bevel — force analysis and terminology
- Power transmission: belts, chains, couplings
- Fits, tolerances, and surface finish
Which Topics Should You Prioritize?
Not all 14 topics carry equal weight. Mechanical splits almost evenly between thermal-fluids and mechanical design, so the usual mistake is over-investing in whichever half you enjoyed more at university. Weight your plan by the NCEES question counts below, not by comfort.
The Big Six (58–88 questions, ~53–80% of the exam)
- Dynamics, Kinematics, and Vibrations (10–15) — the broadest mechanics topic with vibrations as a unique sub-area
- Fluid Mechanics (10–15) — heavily tested with multi-step pipe and pump problems
- Thermodynamics (10–15) — the most formula-dense topic that rewards thorough preparation
- Mechanical Design and Analysis (10–15) — failure theories, fatigue, and machine elements, built on statics and mechanics of materials
- Statics (9–14) — the foundational topic that everything mechanical builds upon
- Mechanics of Materials (9–14) — formula-driven, and directly connected to statics and design
Together, these six topics account for roughly 58 to 88 questions — approximately 53% to 80% of the entire exam. If you can consistently answer these correctly, you are well on your way to passing.
After mastering those, move to the mid-weight topics: Material Properties and Processing (7–11 questions) and Heat Transfer (7–11 questions). These collectively represent another 14–22 questions. Material Properties is the quieter win: it is factual and rarely revised, and it carries as many questions as Heat Transfer.
Finally, review the foundational and lighter-weight topics: Mathematics (6–9), Electricity and Magnetism (5–8), Measurements, Instrumentation, and Controls (5–8), Probability and Statistics (4–6), Ethics and Professional Practice (4–6), and Engineering Economics (4–6). While they carry fewer questions individually, together they still account for roughly 28–43 questions — and many of these are among the easiest to score well on. Ethics and Economics reward light prep on this exam. Do not skip Electricity and Magnetism: it is the only circuits area on the Mechanical exam.
Worked Examples: Five Problems from the Big Six
Here are five short worked examples, one each from Statics, Mechanics of Materials, Dynamics, Fluid Mechanics, and Thermodynamics: five of the six highest-weight areas. Work each on paper before reading the solution; the Carnot result in Example 5 doubles as an upper-bound check on any cycle-efficiency answer.
Example 1 — Statics: Reaction on a Beam with UDL and Point Load
Problem: A simply supported beam spans 8 m between supports A (left) and B (right). It carries a uniformly distributed load of 3 kN/m over the full length plus a 12 kN concentrated load located 2 m from A. Determine the reaction at A.
Solution: Replace the UDL by its resultant (3 kN/m × 8 m = 24 kN at mid-span, x = 4 m) and sum moments about B to eliminate RB.
ΣMB = 0: RA(8) − 12(6) − 24(4) = 0
RA(8) = 72 + 96 = 168
RA = 21 kN
Why it matters: Nearly every Statics item on the FE Mechanical exam reduces to one smart moment-sum. Pick the support that eliminates the most unknowns and the rest is arithmetic.
Example 2 — Mechanics of Materials: Euler Buckling of a Pin-Ended Column
Problem: A pin-ended aluminum column has a circular cross-section of diameter 50 mm and a length of 3 m. With E = 70 GPa, determine the critical (Euler) buckling load.
Solution: Use I = πd4/64 for a solid circular section and Pcr = π2EI / Le2 with Le = L for pin-pin ends.
I = π(0.050)4/64 ≈ 3.07 × 10−7 m4
Pcr = π2(70 × 109)(3.07 × 10−7) / (3)2
Pcr ≈ 23.6 kN
Why it matters: Euler buckling is sensitive to effective length. Know the four standard end-condition factors (pin-pin = L, fixed-free = 2L, fixed-pin ≈ 0.7L, fixed-fixed = 0.5L) or you will get the right formula with the wrong answer.
Example 3 — Dynamics: Natural Frequency of a Mass-Spring System
Problem: A spring with stiffness k = 200 N/m supports a 2 kg mass in an undamped mass-spring system. What is the natural frequency in Hz?
Solution: For undamped free vibration, ωn = √(k/m) and fn = ωn / (2π).
ωn = √(200/2) = √100 = 10 rad/s
fn = 10 / (2π) ≈ 1.59 Hz
Why it matters: Vibrations questions almost always start with ωn = √(k/m) or ωn = √(g/δst). Get the natural frequency right and the rest (damping ratio, transmissibility, resonance) falls out quickly.
Example 4 — Fluid Mechanics: Drag on a Sphere
Problem: A sphere of diameter 100 mm moves through water (ρ = 1000 kg/m3) at 2 m/s. Assuming a drag coefficient CD = 0.5, what is the drag force on the sphere?
Solution: Use FD = ½ ρ V2 CD A, with frontal area A = πr2.
A = π(0.050)2 ≈ 7.85 × 10−3 m2
FD = 0.5(1000)(2)2(0.5)(7.85 × 10−3)
FD ≈ 7.85 N
Why it matters: The external-flow drag equation is a one-line plug once you have the projected area. Most mistakes happen when candidates use surface area instead of frontal area, or forget the factor of ½.
Example 5 — Thermodynamics: Carnot Efficiency
Problem: A Carnot heat engine operates between a high-temperature reservoir at 500 K and a low-temperature reservoir at 300 K. What is its thermal efficiency?
Solution: Carnot efficiency depends only on absolute temperatures: η = 1 − TL / TH.
η = 1 − 300 / 500
η = 0.40 = 40%
Why it matters: Carnot sets the theoretical upper bound for any heat engine operating between two reservoirs. It is also the fastest sanity check—if a Rankine or Brayton problem’s answer exceeds the Carnot efficiency at the same temperatures, something is wrong.
For more worked problems across every FE Mechanical topic, see our FE Mechanical practice problems with step-by-step solutions.
How Should You Structure Your 12-Week Study Plan?
Budget about 110 hours within a year of school, rising to about 145 at 5 years out and 185 at 12 or more (hand-checked study-hour reports from 41 FE passers, 2024–2026, plus NCEES pass-rate data). At 10 hours a week the 12-week version below fits a recent graduate; further out, stretch the relearning weeks. It puts Statics and Mechanics of Materials right after the diagnostic, because Mechanical Design and Dynamics build on both; reorder the relearning weeks by exam weight × your diagnostic weakness:
| Weeks | Focus Areas | What to Do |
|---|---|---|
| 1 | Diagnostic, handbook and calculator setup | Take a placement diagnostic to identify weak areas. Start 10-minute handbook and calculator warm-ups (handbook fluency takes 2–6 hours in all; the calculator 2–3, about 6 if you are new to the TI-36X Pro), and warm up with Math, Probability & Stats and Engineering Economics. |
| 2–4 | Statics, Mechanics of Materials, Thermodynamics | Free body diagrams, equilibrium, trusses, stress/strain, beam bending, Mohr’s circle, torsion, and column buckling; then ideal gas problems, steam tables, power cycles (Rankine, Brayton, Otto, Diesel), refrigeration cycles, and psychrometrics. Blocked and untimed: about 12 problems per 90-minute session. |
| 5 | First full simulation + Dynamics & Vibrations | Take a full 110-question timed simulation (about 40% of the way through) and review it, about 8.5 hours in all. Then practice kinematics, work-energy, impulse-momentum, and vibration problems. |
| 6–7 | Fluid Mechanics, Mechanical Design, Heat Transfer, then the smaller areas | Pipe flow, Bernoulli, pump performance, and dimensional analysis; fatigue analysis, failure theories, shaft design, bolted joints; composite wall conduction, convection correlations, and heat exchangers; then Material Properties, Controls, Electricity and Magnetism, and Ethics. Hold about 20% of each topic’s time for 2–3 spaced revisits. |
| 8–10 | Mixed timed sets | Mixed sets at exam pace; note which cycle and pipe-and-pump problems run long. About a quarter of your attempts should re-work earlier misses. Take a second full simulation; the official NCEES practice exam is about as hard as the real FE. |
| 11 | Hard and challenge sets + final simulation | Hard and challenge sets on your weakest high-weight topics. Take the final full simulation at the end of the week, about 7 days before the exam. |
| 12 | Repair and taper | Review every question you missed on the final simulation early in the week, then 3 days of light review with no new material. |
What Study Tips Will Help You Pass?
- Practice under timed conditions: The budget is roughly 2.9 minutes per question, and multi-state cycle problems and pipe-and-pump problems are the ones most likely to overrun it. Time mixed sets, note which problem types run long, and practice flagging them instead of grinding.
- Focus on units and reasonableness: Mechanical engineering problems frequently involve unit conversions (SI and US customary). Carry your units through every calculation to catch errors. If your answer has unreasonable units or magnitude, recheck your work before moving on.
Test-Day Strategy and Common Mistakes
Thermodynamics and fluid mechanics are two of the four largest areas on this exam (10–15 questions each), and both punish unit slips harder than concept gaps — a correct approach in the wrong unit system still scores zero. FE Mechanical was 69% first-time pass / 37% repeat in the NCEES Squared 2025 table — roughly two in three first-timers pass, so the margin usually comes down to pacing and a few avoidable errors.
What to do on test day
- Get there 30 minutes early. Pearson VUE check-in takes time, and it needs valid, unexpired ID.
- Manage time aggressively. 320 minutes for 110 questions leaves under 3 minutes each, and a multi-state Rankine or pump-and-pipe problem can easily run longer. Flag anything past 4 minutes and come back once the one-line Carnot and drag problems are banked.
- Answer every question. Wrong answers cost nothing, so a blank throws away the 25% a four-option guess would earn. Eliminate impossible magnitudes, then pick something.
- Work the obvious physics first. Dynamics, fluids, heat transfer, and thermo problems usually announce their model through the diagram, process, or given properties. Solve the recognizable ones before a longer machine-design or controls question.
- Use the break to reset sign conventions. Mechanical questions punish stale assumptions about work, heat, acceleration direction, and stress sign. Restart with fresh sketches and coordinate choices.
- Don't over-study one machine element. If a detail is unfamiliar, find the handbook table, eliminate impossible magnitudes, and move on. Time lost on one gear or bearing question is stolen from solvable thermo and fluids points.
The most common mistakes to avoid
- Ignoring low-weight topics entirely. Ethics, Engineering Economics, and Probability and Statistics are easy points with light prep, and together are 12–18 questions.
- Not practicing with the reference handbook. The mechanical sections — steam tables, Moody diagrams, fatigue curves, gear formulas — are extensive. Make the handbook your primary reference in every practice session.
- Memorizing instead of understanding. Especially for Thermodynamics (which cycle model applies) and Mechanical Design (which failure theory the material calls for).
- Underestimating Dynamics and Vibrations. Dynamics fades fastest for engineers a few years out of school, yet it carries up to ~15 questions and includes vibrations. Budget extra time here.
- Neglecting calculator proficiency. Solving a thermodynamic state or a two-equation statics system by hand costs time and invites arithmetic slips; the approved calculator's solver handles both.
- Cramming the night before. Last-minute cramming raises anxiety and cuts sleep. If you review at all, skim where the steam tables and the Moody diagram sit in the handbook, then stop.
What Study Materials Do You Need?
Two resources carry most of the weight here: the handbook itself, and enough timed practice that steam-table lookups stop costing you a minute each.
- NCEES FE Reference Handbook — the same searchable reference you get on exam day. Practise finding the property tables specifically; Mechanical examinees open them more than any other section.
- TI-36X Pro Calculator — The most popular NCEES-approved calculator. Master its equation solver, matrix functions, and unit conversions before exam day.
- Lindeburg FE Mechanical Review Manual — The most broad review book, covering all 14 topic areas with practice problems and detailed explanations.
For a full comparison of prep books, calculators, and other resources, see our best FE exam prep books guide and exam day checklist.
Final Thoughts
Focus on the high-weight topics first — Dynamics, Fluid Mechanics, Thermodynamics, Mechanical Design, and Statics/Mechanics of Materials — then build outward to the remaining areas. Rehearse the steam-table and Moody-diagram lookups until they are reflexes, sit at least two timed full-length exams, and hold the 4-minute flag rule on exam day. Most people who fail this exam did not run out of ability; they ran out of time on thermal-fluids problems they could have solved.
FE Mechanical FAQ
How many questions are on the FE Mechanical exam?
FE Mechanical gives you 110 multiple-choice questions and a 5-hour, 20-minute time limit. That gives you about 2.9 minutes per question. The exam is computer-based and offered year-round at Pearson VUE centers.
What are the highest-weight topics on the FE Mechanical exam?
Four areas carry 10–15 questions each: Dynamics, Kinematics, and Vibrations; Fluid Mechanics; Thermodynamics; and Mechanical Design and Analysis. Statics and Mechanics of Materials follow at 9–14 each. Together these six account for 58–88 of the 110 questions. Focus your study time on these areas first for the highest return.
How long should I study for the FE Mechanical exam?
Budget about 110 hours if you are within a year of school, rising to about 125 at 2 years out, 145 at 5, 170 at 8 and 185 at 12 or more, based on hand-checked study-hour reports from 41 FE passers (2024–2026) plus NCEES pass-rate data. At 10 hours a week a recent graduate needs about 12 weeks. Start with the six high-weight topics where your diagnostic is weakest and work outward to the remaining 8 subject areas. Hours are a budget, not a guarantee of a pass.
What calculator can I use on the FE Mechanical exam?
Only NCEES-approved models are allowed. The TI-36X Pro and Casio fx-115ES PLUS are the top choices. Master your calculator’s equation solver, unit conversion, and statistics functions before exam day to save time on calculations.
Which TI-36X Pro functions help most on FE Mechanical?
The TI-36X Pro is on the official NCEES approved calculator list, and four of its functions earn their keep on this exam: the equation solver (statics reactions and thermodynamic states), numerical integration, the polynomial root finder, and the statistics functions. For a side-by-side comparison with the Casio fx-115ES PLUS, see our FE exam calculator guide.
Is the FE Reference Handbook provided during the exam?
Yes, as a searchable PDF on the exam computer, and it is the only reference you get: no notes or printed copies. Study with the handbook daily so you know exactly where each formula lives—especially in Thermodynamics and Fluid Mechanics where the tables and property charts are critical.
Is the FE Mechanical exam harder than FE Civil or FE Electrical?
Difficulty depends on your background. FE Mechanical is more computational than FE Civil and tends to lean heavily on Thermodynamics, Fluid Mechanics, and Heat Transfer—three formula-dense topics that together can make up more than a third of the exam. Candidates from mechanical engineering programs generally find the content familiar; candidates from adjacent disciplines often need extra time on thermo and heat transfer.
Is there a passing percentage for FE Mechanical?
Not a fixed one. Results are reported as pass/fail only, based on a psychometric cut score set by a committee of licensed professional engineers. Historically, candidates who can correctly answer roughly 70% of high-quality practice problems tend to pass. For scale, 69% of first-time FE Mechanical takers passed in the NCEES Squared 2025 table.
How often can I retake FE Mechanical?
Up to three attempts in any 12-month period, at least two months apart, with no lifetime cap. If you do not pass, the NCEES diagnostic report breaks your result down by knowledge area, so a weak Thermodynamics or Fluid Mechanics line tells you where the next study cycle starts.
When should I take the FE Mechanical exam?
The best time is your senior year of an ABET-accredited mechanical engineering program or within one year of graduating. That is when coursework material—especially thermodynamics, dynamics, and heat transfer—is freshest in your memory. The FE is offered year-round, so pick a date that gives you enough lead time for your budget: about 110 hours within a year of school, or about 12 weeks at 10 hours a week.
Is the FE Mechanical exam worth it if I don’t plan to become a PE?
For most mechanical engineers, yes. Passing earns you the Engineer Intern (EI) or Engineer in Training (EIT) designation, which employers widely recognize as a signal of technical competence. It also keeps the PE path open, which often matters later for senior design, HVAC, power, or consulting roles where a PE license is required. The FE is considerably easier to pass right out of school than years later.
Disclaimer: This guide is an independent educational resource and is not affiliated with, endorsed by, or sponsored by NCEES. The “Fundamentals of Engineering” exam, “FE” exam, and “NCEES” are trademarks of the National Council of Examiners for Engineering and Surveying. Exam specifications and content are subject to change; always refer to the official NCEES website for the most current information.
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