Calculate stress range, cycles to failure, or material constants K and m for an S-N fatigue curve using known points and stress units.

Fit two known S-N points, then evaluate a cycle count.

Two-point power-law fit only. Use matching stress ranges and test conditions; no endurance limit, mean-stress correction or design safety factor is included.

SN Curve Formula

The following formula is used to calculate the SN Curve. 

N = K × S⁻m

Variables:

  • N is the number of cycles to failure
  • S is the stress range 
  • K is the fitted coefficient, dependent on the stress unit and test conditions
  • m is the positive fitted exponent for a decreasing stress-life curve

The calculator fits two known points using S = A × Nb, with b = ln(S₂/S₁) / ln(N₂/N₁). The equivalent form above uses m = -1/b and K = Am. Supply matching stress ranges and complete cycles, not mixed amplitude/range or cycle/reversal data. The fitted curve has no endurance plateau, mean-stress correction, fatigue-scatter allowance or design safety factor.

How to Calculate SN Curve?

The following steps outline how to calculate the SN Curve.

  1. First, obtain two positive known stress-range and cycle-count pairs from matching material and test conditions.
  2. Enter both known points; their cycle counts must differ and stress must decrease as cycles increase.
  3. Select the stress-range or cycles solve and enter the corresponding positive target.
  4. The calculator fits b and A, then reports equivalent K and m using point 1’s selected stress unit.
  5. Select Calculate and distinguish interpolation within the known cycle counts from extrapolation beyond them.
  6. After inserting the variables and calculating the result, check your answer with the calculator above. 

Example Problem:

Use the following variables as an example problem to test your knowledge.

stress range S = 400. To reproduce this illustrative curve in the calculator, use known points (N₁ = 1,000,000, S₁ = 400) and (N₂ = 2,000,000, S₂ = 25) in one consistent stress unit, then solve cycles at S = 400.

material constant K = 4.472136×106 (cycles · [stress unit]m)

material constant m = 0.25

N = K * S^-m = 4.472136×106 * 400^-0.25 ≈ 1,000,000 cycles