True strain calculator
A 10% stretch, an engineering strain of 0.1, is a true strain of about 9.53%, and doubling a length gives about 0.693, not 1. Enter the engineering strain as a ratio to get the true strain and the stretch ratio. Free in your browser.
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Run — free
Worked example
- Engineering strain
- 0.1
- True strain
- 0.0953101798
- Stretch ratio
- 1.1
True strain is the logarithmic deformation measure used in large-strain solid mechanics, metal forming, and tensile-test analysis when engineering strain no longer tracks the current geometry of a specimen. Given a finite engineering strain, this calculator returns the dimensionless true strain defined as the natural logarithm of one plus that engineering value. The conversion exists only when engineering strain is strictly greater than minus one: at minus one the current length would vanish, and below that the stretch ratio is negative so a real logarithm does not exist. Zero engineering strain maps to zero true strain. Modest extensions produce a true strain slightly smaller than the engineering value, while large extensions diverge further because true strain integrates dL over L along the loading path. Compression above the minus-one bound yields a negative true strain whose magnitude exceeds the engineering figure.
What true strain is and how it relates to engineering strain
True strain, also called logarithmic strain, natural strain, or uniaxial Hencky strain, is the integral of incremental length change over current length from the original gauge length L0 to the current length L. That integral evaluates to the natural logarithm of L over L0. Engineering strain is defined as the change in length divided by the original length, which rearranges to L over L0 equals one plus the engineering strain.
Substituting that identity gives the conversion this calculator implements: true strain equals the natural logarithm of one plus engineering strain. The two measures agree to first order for tiny deformations, so a one-percent extension is essentially one percent in both languages. They split as soon as geometry changes enough that the instantaneous gauge length is no longer the original length.
At ten percent engineering strain the true strain is already about 9.53 percent; at one hundred percent engineering strain, a doubling of length, the true strain is the natural logarithm of two, about 0.693, not one. In compression the gap opens the other way: an engineering strain of minus 0.20, a twenty percent shortening, is a true strain of the natural logarithm of 0.80, about minus 0.223.
Materials scientists plot true stress against true strain because the current area and the current length are the physically relevant references once necking or large plastic flow begins. This calculator performs only the kinematic conversion from a supplied engineering strain to true strain. It does not convert stress, does not integrate a multi-axial strain tensor, and does not look up a material flow curve.
What to enter, its lower limit and the result
The value is the engineering, Cauchy, or nominal strain as a dimensionless ratio, not a percent: ten percent elongation is 0.1, not 10. The number may be positive for extension, zero for no deformation, or negative for compression, but it must be strictly greater than minus one. At minus one the stretch ratio L over L0 would be zero, corresponding to a specimen crushed to vanishing length, and the logarithm of zero is not a finite real number.
Below minus one the stretch ratio is negative and the real logarithm is undefined. Magnitudes above the documented ceiling are rejected so a pasted overflow cannot become Infinity inside the logarithm. Classic textbook checks include 0.1 mapping to the logarithm of 1.1, 1 mapping to the logarithm of 2, and 0 mapping to 0.
Convert percents to ratios before calling: divide a percent elongation by one hundred.
Where true strain conversion is used in labs, forming, and software
Uniaxial tensile tests in metals labs routinely record engineering stress and engineering strain from load and original gauge length, then convert to true strain with this logarithm before comparing flow curves, necking strains, or constitutive fits. Metal-forming problems in rolling, drawing, extrusion, and forging quote reductions as true strain because sequential passes add in logarithmic strain space: two equal reductions of the logarithm of 1.2 compose as twice that logarithm, which is not true of engineering strain.
Secondary-school and college courses introduce the conversion as soon as students leave the small-strain Hooke's-law chapter, and contest problems often give an engineering elongation and ask for true strain without a computer-algebra system. Software tests for materials user interfaces need a deterministic oracle that rejects engineering strain of minus one or below instead of silently emitting Infinity or a complex logarithm.
If you later need engineering strain from a length change and a gauge length, true stress from load and current area, or a full strain-tensor polar decomposition, treat those as separate search intents and landings rather than overloading this true strain calculator page.
What you can do with it
Tensile-test reduction to true strain
Convert recorded engineering strain on a coupon to dimensionless true strain before comparing flow curves, necking, or constitutive-model fits.
Metal-forming and large-deformation homework
Evaluate ε_t = ln(1+ε) for rolling, drawing, and forging reductions so sequential logarithmic passes add correctly.
FAQ
How is true strain computed from engineering strain?
True strain is ε_t = ln(1 + ε), where ε is the engineering (nominal) strain as a dimensionless ratio.
Why must engineering strain be greater than minus one?
At ε = −1 the current length would be zero, and below that the stretch ratio is negative.
Is true strain the same as percent elongation?
No. Send the engineering strain as a ratio (0.1 for 10% elongation), not a percent. True strain is the logarithm of one plus that ratio, not 100 times engineering strain.
Can engineering strain be negative?
Yes, when it remains strictly greater than −1. Negative values model compression or shortening and return a negative true strain whose magnitude is larger than |ε|.
What does the true strain calculator cost?
The browser tool is free and runs locally.
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/phys/true-strain \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"engineering_strain":0.1}'const res = await fetch("https://api.kit.forhosting.com/phys/true-strain", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"engineering_strain": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/true-strain",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"engineering_strain": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/true-strain", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"engineering_strain":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"engineering_strain":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/true-strain", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"engineering_strain": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.true_strain",
"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.
Limits
max_abs_engineering_strain | 1000000000000000 |
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
The same deterministic function powers the free browser tool and the API, so homework keys, lab notebooks, and automated pipelines never disagree on the same inputs.
Input contract, the minus-one bound, and the response shape
Send a single required finite number under the field engineering_strain. Aliases strain, e_eng, epsilon_eng, engineering, and e_engineering are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Those cases fail with invalid_input, the message names the field, and the call is not billed. Missing fields, empty strings, NaN, and Infinity also fail with invalid_input. On success the response echoes the cleaned engineering strain, returns true_strain as the dimensionless logarithm, returns stretch_ratio as one plus engineering strain which is L over L0, and includes a formula string and a method tag true_strain. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where true strain conversion is used in labs, forming, and software
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Deterministic fixtures for materials software
Generate reproducible true-strain oracles for unit tests and auto-graders, including the minus-one rejection.