FE Mechanical

Statics, dynamics, mechanics of materials, fluids, thermodynamics, heat transfer, and machine design.

Practice questions: 2,400+
Study topics: 14
Study topics: …
Study concepts: 66
Difficulty levels: 3
Mock exams: Unlimited

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What's inside

14 study topics, weighted to the NCEES blueprint — tap any topic to drill it.

Mathematics

Analytic geometry, single- and multivariable calculus, differential equations and Laplace transforms, linear algebra, and numerical methods.Probability and Statistics

Probability distributions, central tendency and dispersion, confidence intervals, expected value in decisions, and regression and curve fitting.Ethics and Professional Practice

NCEES Model Law and codes of ethics, public health, safety, and welfare, intellectual property, and societal and sustainability considerations.Engineering Economics

Time value of money and annuities, cost types and breakdowns, and economic analyses including cost-benefit, break-even, and life cycle.Electricity and Magnetism

Electrical fundamentals and magnetic flux, DC circuit analysis, AC circuits with R, L, and C, and motors and generators.Statics

Resultants and concurrent force systems, equilibrium of rigid bodies, frames and trusses, centroids and moments of inertia, and static friction.Dynamics, Kinematics, and Vibrations

10%

Kinematics and kinetics of particles and rigid bodies, work-energy and impulse-momentum, kinematics of mechanisms, and free and forced vibrations.Mechanics of Materials

Axial, bending, torsion, shear, and thermal stress and strain, shear-moment diagrams, stress transformation and Mohr's circle, deformations, buckling, and indeterminate systems.Material Properties and Processing

Mechanical, thermal, and electrical properties, stress-strain behavior, ferrous and nonferrous metals and engineered materials, phase diagrams and heat treating, corrosion, and failure mechanisms.Fluid Mechanics

10%

Fluid properties and statics, energy and momentum, internal and external flow, compressible flow and normal shock, and pump, fan, and compressor performance and scaling laws.Thermodynamics

10%

Ideal gases and pure substances, the laws of thermodynamics, processes and component performance, power and refrigeration cycles, gas mixtures, psychrometrics, HVAC processes, and combustion.Heat Transfer

Conduction through walls and cylinders, convection and Newton's law of cooling, radiation, transient (lumped) processes, and heat exchangers.Measurements, Instrumentation, and Controls

Sensors and transducers, signal conditioning and data acquisition, feedback control and block diagrams, dynamic system response, and measurement uncertainty.Mechanical Design and Analysis

10%

Stress analysis of machine elements, static and fatigue failure theories, springs, pressure vessels, bearings, power screws, power transmission, and joining methods.

See a real question

Straight from the FE Mechanical bank — 2,400+ questions, every one with a full worked solution.

medium

A. Machine-element stress, failure theories, springs & deflection

At the critical point of a loaded machine element the plane-stress components are

\sigma_x=80\,\text{MPa}

\sigma_y=30\,\text{MPa}

, and

\tau_{xy}=25\,\text{MPa}

(see the stress element). The distortion-energy (von Mises) effective stress is most nearly:

74.3 MPa
82.3 MPa (correct answer)
95.8 MPa
108 MPa

Worked solution

The FE Handbook's distortion-energy theory (Mechanical Engineering — Static Loading Failure Theories, p. 452) gives the effective (von Mises) stress for a biaxial state as

\sigma'=\sqrt{\sigma_x^2-\sigma_x\sigma_y+\sigma_y^2+3\tau_{xy}^2}=\sqrt{80^2-(80)(30)+30^2+3(25)^2}=\sqrt{6775}

= 82.3 MPa. Distractors: dropped the factor

3

on the shear term (

+\tau_{xy}^2

), 74.3 MPa; dropped the cross term

-\sigma_x\sigma_y

(used

\sigma_x^2+\sigma_y^2+3\tau_{xy}^2

), 95.8 MPa; and added the cross term (

+\sigma_x\sigma_y

) instead of subtracting it, 108 MPa.

Difficulty mix

How this bank splits by our own difficulty rating, from quick wins to multi-step problems.

Easy29%
Medium48%
Hard24%

Study handbook

66 concepts — worked theory, key equations, and common pitfalls for every topic.

Sample concept

Single- and Multivariable Calculus

Limits, derivatives and optimization, the chain rule, integration and the fundamental theorem, partial derivatives and the gradient, and series — the workhorse mathematics of FE Mechanical.

Calculus is not a topic you study for the FE so much as a language you must already speak, because it lives inside almost every other chapter. A velocity is a derivative of position, an acceleration a derivative of velocity; the work done by a varying force is an integral; a maximum bending stress i…

f'(x)=\lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}

Open the study handbook

The FE Mechanical exam at a glance

Sourced from NCEES — the numbers, not the folklore.

Questions: 110; scored and pretest, one sitting
Exam time: 5h 20m; in a 6h appointment · about 2.9 min per question
First-time pass rate: 69%; 37% for repeat takers · NCEES Squared 2025 (FY2024-25)
NCEES fee: $225; per attempt, paid to NCEES; your state board's fees are separate
Retakes: 3 per 12 months; at most one attempt per testing window
Reference on screen: FE Reference Handbook 10.6; closed book: no notes or references of your own

What NCEES says is on it

Every knowledge area in the official FE Mechanical specification, with the number of questions NCEES says each one gets. The four heaviest are about 40% of the exam. Share is our arithmetic, not an NCEES figure: each range's midpoint as a percentage of all the midpoints.

Knowledge area	Questions	Share
Dynamics, Kinematics, and Vibrations	10–15	10%
Fluid Mechanics	10–15	10%
Mechanical Design and Analysis	10–15	10%
Thermodynamics	10–15	10%
Mechanics of Materials	9–14	9%
Statics	9–14	9%
Heat Transfer	7–11	7%
Material Properties and Processing	7–11	7%
Mathematics	6–9	6%
Electricity and Magnetism	5–8	5%
Measurements, Instrumentation, and Controls	5–8	5%
Engineering Economics	4–6	4%
Ethics and Professional Practice	4–6	4%
Probability and Statistics	4–6	4%

Sources: NCEES FE Mechanical exam specification (Effective beginning with the July 2020 examinations) · pass rate: NCEES Squared 2025 (FY2024-25) · fee and retake policy: ncees.org, read 2026-09-15. Your state board sets its own fees and deadlines.

How to prepare for FE Mechanical

Four steps, in the order that pays off — each one built from this exam's own blueprint.

1
Study to the blueprint, not the textbook
Dynamics, Kinematics, and Vibrations; Fluid Mechanics; Mechanical Design and Analysis; and Thermodynamics are about 40% of the exam. Give them that share of your hours — Probability and Statistics is only 4–6 questions.
See every area's question range
2
Practice one area at a time, then mix
Work a knowledge area until its worked solutions stop surprising you, then switch to mixed sets so recognizing the problem type becomes the skill.
Practice FE Mechanical questions
3
Sit timed mock exams at the real pace
The real exam gives you about 2.9 minutes per question. Full-length timed mocks are the only way to find out whether you can hold that pace for 5h 20m.
Take a mock exam (with a pass)
4
Read what the exam actually asks
The highest first-time pass rate of the seven FE disciplines, at 69%. Why that is less reassuring than it sounds, and which knowledge areas mechanical engineers reliably underestimate.
How hard is the FE Mechanical exam?

Questions, answered

How hard is the FE Mechanical exam?

NCEES reports a 69% pass rate for first-time takers of FE Mechanical and 37% for repeat takers in NCEES Squared 2025 (FY2024-25). It is 110 questions in 5h 20m, about 2.9 minutes per question, so pacing matters as much as knowledge. The heaviest areas are Dynamics, Kinematics, and Vibrations; Fluid Mechanics; Mechanical Design and Analysis; and Thermodynamics.

What topics are on the FE Mechanical exam?

NCEES's FE Mechanical specification lists 14 knowledge areas with a question range for each. The heaviest are Dynamics, Kinematics, and Vibrations (10–15 questions); Fluid Mechanics (10–15 questions); Mechanical Design and Analysis (10–15 questions); and Thermodynamics (10–15 questions) — together about 40% of the exam. The full list is in the exam-at-a-glance table on this page.

How long is the FE Mechanical exam?

The FE Mechanical exam is 110 questions in 5h 20m of exam time, inside a 6h appointment that also covers the nondisclosure agreement, the tutorial and a scheduled break. It is a closed-book, computer-based test offered year-round at Pearson VUE test centers.

What reference material do you get on FE Mechanical exam day?

The FE Mechanical exam is closed book. NCEES provides an electronic reference on screen (FE Reference Handbook 10.6). No notes, books or references of your own come into the room; you may bring one NCEES-approved calculator, and an on-screen TI-30XS calculator is also available during the exam. Practicing with that same reference in front of you, so you already know where each method lives, is half the preparation.

How much does the FE Mechanical exam cost, and can you retake it?

The NCEES fee for the FE Mechanical exam is $225, paid per attempt when you register through your MyNCEES account; some state licensing boards also charge their own application fee. NCEES allows one attempt per testing window and no more than three attempts in a 12-month period.

What do I get with FE Mechanical on FE → PE Prep?

2,400+ FE Mechanical practice questions, every one with a step-by-step worked solution; unlimited full-length timed mock exams weighted to the NCEES blueprint; a 66-concept study handbook, 600+ flashcards, and an AI tutor. Access is a one-time pass for 1, 3, 6 or 12 months — no subscription, no auto-renew — and the free sample questions need no account. Within 7 days, with little or no paid content used, you can ask for a refund, which we consider under the Refund Policy.

Free reading for FE Mechanical

No account needed — pass rates, worked problems, and what the exam actually asks.

Free FE Mechanical practice problemsReal questions from the bank, with the figures and full worked solutions.Free FE Mechanical formula sheet134 key equations by exam topic, each with what it is for and its handbook reference.Which FE exam should you take? Other Disciplines vs your majorFE Other Disciplines ties for the lowest first-time pass rate of the seven FE exams, not the highest, and half of it is mechanics. All seven compared on the published specifications.How hard is the FE Mechanical exam?The highest first-time pass rate of the seven FE disciplines, at 69%. Why that is less reassuring than it sounds, and which knowledge areas mechanical engineers reliably underestimate.FE Mechanical practice problems: one dropped factorThree FE Mechanical practice problems worked in full (von Mises, Fourier conduction, bending stress), and why each of the nine wrong answers traces to one mishandled term, constant or quantity.

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