Fatigue Life Calculator (S-N Curve)
Estimate the number of cycles to failure from an S-N curve built from ultimate tensile strength, the corrected endurance limit, and the applied stress amplitude.
📉 What is Fatigue Life (S-N Curve)?
Fatigue life is the number of stress cycles a component can withstand before fatigue failure, and the S-N curve (stress-number of cycles curve) is the standard way engineers plot it, applied stress amplitude on one axis and cycles to failure on the other, typically on log-log scales. On log-log axes the high-cycle region of the curve for many metals is close to a straight line, which lets it be described by just two numbers: a coefficient a and an exponent b.
This calculator builds that two-point S-N line the way it is taught in mechanical design courses, anchored at N = 1000 cycles (using the fatigue strength fraction f times the ultimate tensile strength Sut) and at N = 10^6 cycles (using the corrected endurance limit Se). Engineers use this model to size shafts under rotating bending, check bolted brackets under vibration, estimate the life of a spring under repeated loading, or sanity-check a fatigue-critical weld against a target service life.
A common point of confusion is the difference between the uncorrected endurance limit Se' (measured on a small polished lab specimen) and the corrected endurance limit Se used here, which already accounts for the real part's surface finish, size, loading type, temperature, and reliability requirement through Marin factors. Entering the uncorrected value here will overstate the predicted life.
This calculator solves the two-point S-N line for you, reports the coefficient a and exponent b, and plots the full curve with your operating point marked, so you can see at a glance whether a given stress amplitude sits in the finite-life region or beyond the endurance limit.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Steel Rotating Shaft
A steel shaft with Sut = 700 MPa, Se = 350 MPa, f = 0.9, under Sa = 450 MPa
Example 2 — Stress Below the Endurance Limit
A part with Sut = 500 MPa, Se = 250 MPa, f = 0.9, under Sa = 200 MPa
Example 3 — High-Strength Steel Bracket
A bracket with Sut = 900 MPa, Se = 400 MPa, f = 0.85, under Sa = 600 MPa
❓ Frequently Asked Questions
🔗 Related Calculators
What is an S-N curve?
An S-N curve (stress-number of cycles curve) is a plot of applied stress amplitude against the number of cycles to failure, on log-log axes it typically appears as a straight line down to the endurance limit, where many materials show an apparent infinite life.
What is the formula for fatigue life from an S-N curve?
N = (Sa / a)^(1/b), where Sa is the applied stress amplitude, and a and b are the S-N line's coefficient and exponent, found from b = -(1/3) log10(f Sut / Se) and a = (f Sut)^2 / Se.
What is the fatigue strength fraction f?
f is the ratio of the fatigue strength at 1000 cycles to the ultimate tensile strength Sut. For many steels with Sut under about 1400 MPa, f is approximately 0.9, it is read from a standard f-vs-Sut chart for other materials or strength ranges.
What is the corrected endurance limit Se?
Se is the endurance limit after applying Marin correction factors, surface finish, size, load type, temperature, and reliability, to the uncorrected rotating-beam endurance limit Se'. Always enter the corrected Se here, not the raw lab value.
What does it mean if the calculator shows infinite life?
If the applied stress amplitude Sa is at or below the corrected endurance limit Se, the two-point S-N model predicts the part will never fail from fatigue under fully-reversed loading, this is shown as infinite life (a runout).
Is this formula valid for any number of cycles?
No. The two-point log-log S-N line is only intended for the high-cycle fatigue region, roughly 10^3 to 10^6 cycles. Predictions below 1000 cycles fall in the low-cycle fatigue region, where strain-based methods are more appropriate.
Does this calculator handle mean stress (non-zero R ratio)?
No, this calculator assumes fully-reversed loading (R = -1, mean stress = 0). A non-zero mean stress requires an additional correction, such as the Goodman, Gerber, or Soderberg criteria, applied to the stress amplitude before using this S-N model.
How is the endurance limit Se typically estimated for steel?
A common rule of thumb for steel is Se' is approximately 0.5 x Sut (uncorrected), capped near 700 MPa for very high-strength steels, then Marin factors are applied to get the corrected Se used in this calculator.
What happens if I enter a stress amplitude above Sut?
The formula will still return a numeric N, but a stress amplitude at or above the ultimate tensile strength is physically unrealistic for a real component, in that case failure would be expected on the first cycle, well outside the model's valid range.
Why does a higher stress amplitude reduce the predicted cycles to failure?
The S-N line has a negative slope (negative exponent b), so as Sa increases, N = (Sa/a)^(1/b) decreases. Physically, higher cyclic stress accumulates fatigue damage faster, shortening the life to crack initiation and final fracture.