Poisson's ratio calculator
A lateral strain of −0.003 with an axial strain of 0.01 gives a Poisson’s ratio of 0.3, typical of many metals. The leading minus sign of the formula, the one most often forgotten, is applied for you. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Lateral
- -0.003
- Axial
- 0.01
- Poisson ratio
- 0.3
- Precision
- 10
This Poisson's ratio calculator finds the classic lateral-contraction measure used throughout solid mechanics and materials science when you already know the transverse (lateral) engineering strain and the axial (longitudinal) engineering strain of a specimen under uniaxial load. Most isotropic solids under tension contract sideways while they elongate along the load axis, so a negative lateral strain and a positive axial strain yield a positive Poisson's ratio near zero point three for many metals and near zero point two five for many ceramics and concretes. Axial strain must be non-zero because division by a zero axial strain is undefined. The engine is fully deterministic arithmetic: no network calls, no sampling, and no date-dependent shortcuts.
What Poisson’s ratio tells you about a material
In continuum mechanics and materials testing, Poisson's ratio measures how much a bar or coupon contracts or expands sideways relative to the stretch or compression along the load axis. With lateral strain epsilon lateral and axial strain epsilon axial, the small-strain uniaxial definition is nu equals negative epsilon lateral divided by epsilon axial.
The quantity is dimensionless: both strains must already be engineering ratios in consistent form, whether computed from delta L over L zero on two gauges or taken from a data sheet, and the result has no unit of its own. Under pure axial tension a typical metal shortens transversely, so lateral strain is negative, axial strain is positive, and nu is positive; rubber-like materials can approach zero point five in the incompressible limit, while some foams and auxetic metamaterials show zero or negative nu.
Zero lateral strain is valid and yields zero Poisson's ratio when the axial strain is finite and non-zero.
Where Poisson's ratio fits in study, testing, and software
Students meet nu equals negative epsilon lateral over epsilon axial when a textbook introduces isotropic elasticity, when a lab asks for Poisson's ratio from axial and diametral gauges on a tensile coupon, or when a contest problem gives two strain components and asks for the material ratio without finite-element software. Teachers can pre-generate answer keys for modest strain pairs without trusting opaque calculator apps that silently drop the leading minus sign or mix true strain with engineering strain.
Developers call the same contract from scripts to seed deterministic test vectors for materials-property UIs, to normalize user-entered lateral and axial strains before an elasticity plot, or to satisfy programming-challenge statements that demand a single dimensionless nu rather than a hand-waved sketch. Product and first-order mechanical checks use Poisson's ratio when only measured strains are known before full modulus matrices or anisotropic models are introduced.
What you can do with it
Homework and lab checks
Compute Poisson's ratio ν = −ε_lat/ε_ax from measured lateral and axial engineering strains before grading worksheets or lab reports.
Design and tutoring software
Normalize user-entered lateral and axial strains into a dimensionless Poisson ratio for elasticity demos and interactive lessons.
FAQ
What does the Poisson's ratio calculator cost?
It is free in your browser on this page.
How is Poisson's ratio defined here?
Poisson's ratio is ν = −ε_lateral / ε_axial, where ε_lateral is transverse engineering strain and ε_axial is axial (longitudinal) engineering strain. The result is dimensionless.
What happens if the axial strain is zero?
Poisson's ratio is undefined when the axial (longitudinal) strain is zero because it would require division by zero.
Does this tool compute Young's modulus or shear modulus?
No. It only returns Poisson's ratio from lateral and axial strain. Use dedicated modulus tools if you need E, G, or K from stress and strain.
Can lateral strain be positive?
Yes. Positive lateral strain under positive axial strain yields a negative Poisson's ratio (auxetic-like response). Zero lateral strain yields ν = 0 when axial strain is non-zero.
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/sci/poisson-ratio \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"lateral_strain":-0.003,"axial_strain":0.01}'const res = await fetch("https://api.kit.forhosting.com/sci/poisson-ratio", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"lateral_strain": -0.003,
"axial_strain": 0.01
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/sci/poisson-ratio",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"lateral_strain": -0.003,
"axial_strain": 0.01
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/sci/poisson-ratio", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"lateral_strain":-0.003,"axial_strain":0.01}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"lateral_strain":-0.003,"axial_strain":0.01}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/sci/poisson-ratio", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"lateral_strain": -0.003,
"axial_strain": 0.01
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "sci.poisson_ratio",
"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_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 definition is the closed form nu equals negative epsilon lateral over epsilon axial: the negative ratio of lateral strain to axial strain.
What Poisson's ratio means and what the response contains
This calculator returns the normalized inputs lateral_strain and axial_strain, the computed poisson_ratio, the precision used, a method tag poisson_ratio, a short formula reminder, and a unit hint that the ratio is dimensionless. There is no stress conversion, no modulus chain, and no Monte Carlo sampling: the engine either evaluates negative lateral over axial inside the supported numeric range or rejects the input with invalid_input. Rejected cases include a missing lateral_strain or axial_strain, non-finite values, magnitudes above the documented ceilings, and any axial strain that is zero or numerically zero, because Poisson's ratio is undefined when the axial strain vanishes.
How lateral and axial strain are read and how the ratio stays reproducible
Lateral strain may be positive, zero, or negative: under axial tension a conventional solid has negative lateral strain, while auxetic or constrained setups can reverse the sign. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces and non-numeric tokens are rejected. The preferred field for the transverse strain is lateral_strain, but aliases transverse_strain, epsilon_lateral, e_lat, lateral, eps_t, and eps_lat are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. The preferred field for the load-axis strain is axial_strain, with aliases longitudinal_strain, epsilon_axial, e_axial, axial, eps_a, and eps_ax. Axial strain must be finite and non-zero: a zero value fails with invalid_input and a message that names the field and explains that nu equals negative epsilon lateral over epsilon axial is undefined when the axial strain is zero, so a bad cell does not become a silent infinity or NaN. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the numeric outputs, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the Poisson-ratio formula yourself.
Where Poisson's ratio fits in study, testing, and software
Education tools use the endpoint when a learner types lateral and axial strain and the UI must show the resulting Poisson ratio. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with strain, stress, or modulus helpers when you need related mechanics, and with other science endpoints when you are building a small lab of free, deterministic calculators.
Integration use cases
Deterministic test fixtures
Generate reproducible Poisson-ratio values for unit tests, materials UIs, and CI assertions on ν = −ε_lateral/ε_axial.