# Fatigue Limit Calculator (Goodman / Gerber / Soderberg)

Mean-stress fatigue correction under cyclic loading. Given stress amplitude σ_a, mean stress σ_m, and material σ_uts / σ_-1 (endurance limit) / σ_y, compute safety factors from three classical criteria: Modified Goodman (linear, conservative), Gerber (parabolic, better for ductile metals), and Soderberg (uses σ_y, most conservative). Reports the governing (smallest) value and whether the operating point lies inside the Goodman line.

> Canonical page: https://elysiatools.com/en/tools/fatigue-limit-calculator

- **Category:** Math & Numbers

- **Keywords:** fatigue, fatigue limit, endurance limit, Modified Goodman, Gerber, Soderberg, mean stress correction, Haigh diagram, sigma_a, sigma_m, cyclic loading, mechanical design

## Overview

The Fatigue Limit Calculator estimates fatigue safety factors under cyclic loading using the Modified Goodman, Gerber, and Soderberg criteria. Enter stress amplitude, mean stress, and the applicable material strengths to compare criteria, identify the governing minimum safety factor, and check the operating point against the Goodman line.

## Inputs

- **Stress Amplitude σ_a (MPa)** (number): Alternating stress amplitude σ_a = (σ_max − σ_min)/2 in MPa. Must be > 0 (zero amplitude means no cycling).
- **Mean Stress σ_m (MPa)** (number): Mean stress σ_m = (σ_max + σ_min)/2 in MPa. Tensile (>0) reduces fatigue life; compressive (<0) is beneficial but unusual in textbook problems.
- **Ultimate Strength σ_uts (MPa)** (number): Ultimate tensile strength of the material in MPa. Required by Goodman and Gerber.
- **Fatigue Limit σ_-1 (MPa)** (number): Fully reversed fatigue (endurance) limit σ_-1 in MPa, typically for 10⁶ cycles or more. Must not exceed σ_uts.
- **Yield Strength σ_y (MPa)** (number): Yield strength in MPa. Required by Soderberg to prevent first-cycle yielding.
- **Decimal Places** (number)

## When to use

- Evaluate fatigue safety under cyclic loading with a known stress amplitude and mean stress.
- Compare Goodman, Gerber, and Soderberg mean-stress correction criteria during mechanical design.
- Check whether an operating point falls inside the Goodman line and identify the most conservative criterion.

## How it works

- Enter the alternating stress amplitude σ_a in MPa; this value must be greater than zero.
- Enter the mean stress σ_m and the material properties required for the selected calculations: ultimate strength σ_uts, endurance limit σ_-1, and yield strength σ_y.
- The calculator computes Goodman, Gerber, and Soderberg safety factors when their required inputs are available.
- The result reports the smallest, governing safety factor and whether the point is inside or outside the Goodman line.

## Use cases

- Preliminary fatigue checks for shafts, brackets, fasteners, and other cyclically loaded components.
- Comparison of conservative and less conservative mean-stress correction methods for material selection and design review.
- Screening operating points before detailed fatigue testing or a broader mechanical design analysis.

## Frequently asked questions

### What does the stress amplitude represent?

Stress amplitude is σ_a = (σ_max − σ_min) / 2, expressed in MPa. It must be greater than zero.

### What does mean stress represent?

Mean stress is σ_m = (σ_max + σ_min) / 2. Tensile mean stress generally reduces fatigue safety.

### Which material inputs are needed?

Goodman and Gerber require ultimate strength σ_uts and endurance limit σ_-1. Soderberg also requires yield strength σ_y.

### What is the governing safety factor?

It is the smallest safety factor among the available Goodman, Gerber, and Soderberg results.

### What does a safety factor below 1 mean?

A value below 1 indicates that the calculated operating condition does not meet that criterion.

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