Miner’s Rule Cumulative Fatigue Damage Calculator

Understanding the Miner's rule fatigue damage calculator — concept and principle

Most machine parts and structures do not see one constant stress level; they see a mix of small, medium and large cycles. Miner's rule (the Palmgren–Miner linear damage rule) adds up the fatigue damage of each stress level to estimate how much of the part's life has been used. This calculator takes a list of applied cycle counts and the matching cycles to failure and returns the total damage and the remaining life.

How it is calculated

• Damage: D = Σ nᵢ/Nᵢ, where nᵢ is the number of cycles applied at stress level i and Nᵢ is the number of cycles to failure at that level, read from the material's S–N curve.
• Remaining life: (1 − D) × 100%.

Enter the lists separated by commas, in the same order; both lists must have the same length.

The principle

The rule assumes every cycle consumes a fixed fraction of life: one cycle at a level where the part would last N cycles uses up 1/N. Damage from different levels simply adds, regardless of order, and failure is predicted when the sum reaches 1. It was proposed by Palmgren for ball bearings (1924) and by Miner for aircraft structures (1945), and it remains the standard starting point because it is simple and needs only the S–N curve.

Worked example

1. Inputs: n = 10,000 and 50,000 cycles; N = 100,000 and 1,000,000 cycles.
2. First level: 10,000 ÷ 100,000 = 0.10.
3. Second level: 50,000 ÷ 1,000,000 = 0.05.
4. Damage: 0.10 + 0.05 = 0.15.
5. Remaining life: (1 − 0.15) × 100 = 85%.

How to read the result

D = 0.15 means 15% of the predicted fatigue life has been used. If the same load block keeps repeating, the part is predicted to survive 1 ÷ 0.15 ≈ 6.7 blocks in total, about 5.7 more. A value of D near 1 means failure is expected; many design standards require D to stay well below 1 to cover scatter.

Common mistakes

• Counting cycles incorrectly from an irregular load history; use a proper method such as rainflow counting.
• Reading Nᵢ from an S–N curve that is not corrected for notches, surface finish or mean stress.
• Ignoring cycles below the endurance limit; once cracks start they can become damaging.

Frequently asked questions

Does the order of loads matter?

In reality yes, but Miner's rule assumes it does not. That is one of its main limitations.

Where do the Nᵢ values come from?

From an S–N (Wöhler) curve for the material and detail, often in Basquin form N = C·S⁻ᵐ, taken from tests or a design standard.

Can D exceed 1?

The formula can give D greater than 1; it means the predicted life has already been exceeded.

Sources: M. A. Miner, "Cumulative Damage in Fatigue", Journal of Applied Mechanics 12 (1945) · A. Palmgren, "Die Lebensdauer von Kugellagern", VDI-Zeitschrift 68 (1924) · ASTM E1049, Standard Practices for Cycle Counting in Fatigue Analysis