Soderberg fatigue criterion calculator
Check whether a cyclic load stays inside the Soderberg line: 120 alternating and 80 mean against a 300 endurance limit and 500 yield give a utilization of 0.56, a margin of 0.44 and a safe result. Free in your browser.
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Worked example
- Alternating stress
- 120
- Mean stress
- 80
- Endurance limit
- 300
- Yield strength
- 500
- Alternating ratio
- 0.4
- Mean ratio
- 0.16
- Soderberg utilization
- 0.56
- Safety factor
- 1.7857142857
The Soderberg fatigue criterion calculator assesses a fluctuating tensile stress state using alternating stress, mean stress, the corrected endurance limit, and material yield strength. It evaluates the conservative linear relation between those quantities, reports each normalized contribution, and returns utilization, margin, safety factor, and a clear safe or unsafe result. Use consistent stress units throughout; megapascals, pascals, ksi, and psi all work reliably when every value uses the same unit.
What the Soderberg line measures
A cyclic load can damage a component even when its peak stress is below the static yield strength. The Soderberg diagram separates a fluctuating stress history into alternating stress, which represents the cycle amplitude, and mean stress, which represents its tensile offset. The criterion normalizes alternating stress by the corrected endurance limit and mean stress by tensile yield strength, then adds the two contributions.
Values below one lie inside the conservative safe region; one is exactly on the boundary; values above one cross the line. This calculator reports the two ratios separately so you can see whether cyclic amplitude or tensile mean loading consumes more of the allowance. It also reports utilization and the remaining margin, making the result easier to audit than a bare pass or fail.
The model is intended for non-negative tensile mean stress and does not silently reinterpret compressive mean stress.
How to enter data and interpret the result
Enter alternating stress as a non-negative amplitude, not as the full peak-to-peak range. If a stress cycle varies from a minimum to a maximum, its alternating stress is half of that range and its mean stress is the midpoint. Supply a corrected component endurance limit rather than an unmodified laboratory specimen value whenever surface finish, size, temperature, reliability, stress concentration, or loading mode matters.
Yield strength must be the tensile yield strength for the material condition being assessed. All four values must use one consistent stress unit, although the particular unit cancels in the ratios. The Soderberg utilization is the sum of the alternating and mean ratios.
A utilization of 0.80 means the point consumes eighty percent of the criterion allowance, has a margin of 0.20, and gives a safety factor of 1.25 when both applied stress components scale together. A safety factor below one corresponds to an unsafe result. Zero applied stresses produce an unbounded safety factor because division by zero utilization has no finite numerical result.
Scope, assumptions, and engineering use
Soderberg is deliberately conservative because it connects the endurance-limit intercept to the yield-strength intercept. That makes it useful for preliminary screening, teaching, design checks that prioritize yielding avoidance, and automated review of many load cases. It is not a complete fatigue-life analysis.
The calculation assumes that the supplied alternating and mean stresses already represent the critical local stress state and that the endurance limit has already been corrected for the real component. It does not calculate stress concentration or notch sensitivity, combine multiaxial stresses, estimate finite life from an S-N curve, apply cumulative damage, account for residual stress, or model plastic cyclic behavior. Compare its conclusion with the design code, material data, loading spectrum, and required reliability for the actual application.
Goodman, Gerber, ASME elliptic, strain-life, or fracture-mechanics methods can be more appropriate depending on the material and failure mode.
What you can do with it
Screen a shaft load case
Check whether bending amplitude and steady tensile stress place a preliminary shaft design below the conservative Soderberg boundary.
Audit a fatigue worksheet
Recalculate normalized alternating and mean contributions, utilization, margin, and safety factor with a deterministic reference result.
Compare material choices
Hold the applied stresses fixed and compare corrected endurance limits and yield strengths for candidate material conditions.
FAQ
Can I use MPa, psi, or ksi?
Yes. Use any stress unit as long as all four inputs use exactly the same unit; the normalized ratios and safety factor are dimensionless.
Should alternating stress be the full stress range?
No. Alternating stress is the amplitude, equal to half the difference between maximum and minimum stress. Mean stress is their midpoint.
Does this accept compressive mean stress?
No. This contract targets the standard tensile-mean Soderberg line and requires non-negative mean stress rather than applying an undocumented compression correction.
What does a safety factor above one mean?
It means proportionally scaling both entered stress components by that factor would place the point on the Soderberg line. It does not replace code-required factors or uncertainty analysis.
How do I get alternating and mean stress from a minimum and a maximum?
The alternating stress is half the range between the maximum and the minimum, and the mean stress is the midpoint between them. Enter the amplitude, not the full peak-to-peak range.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/eng/soderberg-fatigue \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"alternating_stress":120,"mean_stress":80,"endurance_limit":300,"yield_strength":500}'const res = await fetch("https://api.kit.forhosting.com/eng/soderberg-fatigue", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"alternating_stress": 120,
"mean_stress": 80,
"endurance_limit": 300,
"yield_strength": 500
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/soderberg-fatigue",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"alternating_stress": 120,
"mean_stress": 80,
"endurance_limit": 300,
"yield_strength": 500
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/soderberg-fatigue", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"alternating_stress":120,"mean_stress":80,"endurance_limit":300,"yield_strength":500}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"alternating_stress":120,"mean_stress":80,"endurance_limit":300,"yield_strength":500}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/soderberg-fatigue", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"alternating_stress": 120,
"mean_stress": 80,
"endurance_limit": 300,
"yield_strength": 500
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.soderberg_fatigue",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
What the Soderberg line measures
A point on the diagram is acceptable when sigma_a divided by Se plus sigma_m divided by Sy is no greater than one.
Technical questions
What equation does the calculator use?
It evaluates sigma_a / Se + sigma_m / Sy <= 1, where sigma_a is alternating stress, sigma_m is tensile mean stress, Se is corrected endurance limit, and Sy is tensile yield strength.
How much does an API calculation cost?
Each successful API item uses the published base price of $0.002. The same deterministic calculation can run in the browser for an immediate check.