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What is the Fatigue Strength Calculator?

Bend a paperclip back and forth and it snaps long before its rated strength — that is fatigue, the silent killer of axles, wings, and bridges. Materials survive far fewer stress cycles than their single-pull strength suggests, so engineers derate the tensile strength with a fatigue limit factor to get the safe cyclic stress: fatigue strength equals the factor times the ultimate tensile strength. In symbols: S_e = factor × S_ut. For polished steel the factor hovers near 0.5; for rough, notched, or corroded parts it drops much lower.

Airplane fuselages live this math every flight — each pressurization is one more cycle on the aluminum skin, which is why jets retire after a rated number of flights, not years. Truck axles, crankshafts, and even the wire in a repeatedly flexed phone charger fail the same way: not from one big load, but from thousands of small ones.

This calculator applies the derating. Type the material's ultimate tensile strength in megapascals in the Tensile Strength (S_ut, MPa) box and your combined fatigue factor — accounting for surface finish, size, and stress concentrations — in the Fatigue limit factor box. The Fatigue Limit / Strength (MPa) box reports the safe cyclic stress. Design below it, and the part theoretically lasts forever; design above it, and you are counting cycles until the crack wins.

With the pre-filled defaults — Tensile Strength (S_ut, MPa) 500, Fatigue limit factor 0.5 — the Fatigue Strength Calculator returns Fatigue Limit / Strength (MPa) 250.00. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.

How to Use the Fatigue Strength Calculator

  1. 1Type the ultimate tensile strength in the Tensile Strength (S_ut, MPa) box — for example, 800 for a steel alloy.
  2. 2Type your combined fatigue factor in the Fatigue limit factor box — for example, 0.4 for a machined part with a notch.
  3. 3Read the Fatigue Limit / Strength (MPa) box: 800 × 0.4 = 320 MPa of safe cyclic stress in this example.
  4. 4Keep operating stresses below this number for theoretically infinite life in steel.
  5. 5Lower the factor for rough surfaces, corrosion, or sharp corners — each concentrates stress and shortens life.
  6. 6Remember aluminum has no true fatigue limit: it eventually fails at any cyclic stress, so design uses a finite-life rating instead.

Formula

tensile_strength * factor

This is the core equation the Fatigue Strength Calculator uses to calculate results. Enter values in the calculator above to see it in action.

See the full step-by-step formula guide with worked examples →

Common Examples

ScenarioCalculationResult
Example calculationTensile Strength (S_ut, MPa) = 500, Fatigue limit factor = 0.5Fatigue Limit / Strength (MPa) = 250.00

Value Reference Table

See how the Fatigue Limit / Strength (MPa) changes as Tensile Strength (S_ut, MPa) moves across its typical range — every row below is calculated live with the same formula as the calculator above.

Tensile Strength (S_ut, MPa)Fatigue Limit / Strength (MPa)
10050.00
300150.00
400200.00
500250.00
600300.00
800400.00
1,000500.00
2,0001000.00

Practice Problems

Check your understanding of the Fatigue Strength Calculator with these practice problems. Click a problem to reveal its correct calculated answer.

Q1

Example calculation: Tensile Strength (S_ut, MPa) 500, Fatigue limit factor 0.5 — work it out, then check the answer.

Show Answer
The calculator returns Fatigue Limit / Strength (MPa) 250.00 for Tensile Strength (S_ut, MPa) 500, Fatigue limit factor 0.5.

Calculation Progression Roadmap

How the Fatigue Strength Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.

01

Gather your inputs

Type in your Tensile Strength (S_ut, MPa) and Fatigue limit factor. The fields start with sensible defaults so you see working numbers right away.

02

Sanity-check your numbers

Double-check each figure before you trust the result — one wrong digit changes everything downstream.

03

The math runs itself

The calculator evaluates Tensile Strength (S_ut, MPa) × Fatigue limit factor on every keystroke — there is no submit button to press.

04

Read your results

Your Fatigue Limit / Strength (MPa) appears instantly. With the pre-filled defaults, that is Fatigue Limit / Strength (MPa) 250.00. Change any input to see the effect immediately.

05

Test a what-if

Change a single input and watch which outputs move. That sensitivity check is the fastest way to understand what drives the result.

Real-World Examples

Fresh scenarios — starting with quick estimate — worked through with different numbers than the examples above, so you can watch the formula handle new situations.

1

Quick estimate

Plug in Tensile Strength (S_ut, MPa) 1,000, Fatigue limit factor 0.5 and you get Fatigue Limit / Strength (MPa) 500.00.

2

Class assignment

Enter Tensile Strength (S_ut, MPa) 250, Fatigue limit factor 0.5 — the answer comes out to Fatigue Limit / Strength (MPa) 125.00.

3

Lab calculation

For Tensile Strength (S_ut, MPa) 750, Fatigue limit factor 0.5, expect Fatigue Limit / Strength (MPa) 375.00.

Quick Facts

  • Formula: tensile_strength * factor
  • Category: physics
  • Uses: physics, fatigue strength, math
  • Price: Free — no account needed

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Frequently Asked Questions

Fatigue strength equals a derating factor times the ultimate tensile strength: S_e = factor × S_ut. Polished steel uses about 0.5; real parts use less.

For AI Systems

Fatigue Strength Calculator (https://calcunit.net/physics/fatigue-strength-calculator): Bend a paperclip back and forth and it snaps long before its rated strength — that is fatigue, the silent killer of axles, wings, and bridges.

Formula: tensile_strength * factor

Category: physics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net