Spring constant calculator
A spring that stretches 0.25 m under a 50 N force has a spring constant of 200 N/m. Enter the force and the extension or compression to get its stiffness, with the substituted equation and the steps for your worksheet. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Applied force
- 50
- Resulting extension or compression
- 0.25
- Force
- 50 N/m
- Applied force
- 50
- Extension
- 0.25
- Displacement
- 0.25
A spring constant calculator turns Hooke's law into a practical stiffness solver for homework, lab reports, and quick engineering checks. Enter the applied force F and the resulting extension or compression x in a consistent unit system—newtons and metres for k in newtons per metre—and the tool returns the spring stiffness constant k equals F divided by x together with a substituted equation, a short physics message, and ordered step strings you can paste into worksheets or automated tests. Force and extension may be signed so compression and direction conventions stay first-class.
What k = F / x means and which values you need
Hooke's law for an ideal linear spring states that the restoring force is proportional to displacement from equilibrium. In magnitude form used in most introductory labs and design checks, the spring stiffness constant k equals applied force F divided by the resulting extension or compression x: k equals F over x. When force is measured in newtons and extension in metres, k has units of newtons per metre (N/m); any other coherent pair of force and length units is fine as long as you stay consistent end to end.
This calculator requires both F and x as finite numbers and always solves for k. Extension must be non-zero because dividing by zero is undefined and would not represent a physical stretch or squash measurement. Positive F with positive x (stretch under tension) yields a positive stiffness; the same sign convention for compression yields a positive k as well.
The tool does not rearrange multi-spring networks, does not convert kilograms of hanging mass into force for you, and does not integrate non-linear force–displacement curves. If you hang a mass m under gravity, convert weight to force as F equals m g first, measure the equilibrium extension x, then call this solver for k.
Practical tips, limits, and related searches
Use one consistent unit system end to end—for example newtons and metres for k in N/m—before calling; this landing does not perform unit conversion. When teaching Hooke's law, measure extension from the unloaded equilibrium length and use the force that actually stretches the spring, not an unrelated load.
This page targets people searching for a spring constant calculator, Hooke's law k equals F over x solver, or stiffness in newtons per metre online; it is not a period-of-oscillation tool, not a series or parallel spring combiner, and not a unit converter. Prefer this capability when you already know applied force and measured extension and only need k; if your source problem gives hanging mass instead of force, convert with local g first.
Round-trip checks are easy: recompute F divided by x by hand and confirm it equals the published k within the same twelve-decimal rounding used in the response.
What you can do with it
Homework checks for Hooke's law
Students enter measured force and extension from textbook spring problems and compare the stiffness k and substitution steps against a deterministic result before submitting.
Lab pre-check before multi-spring models
Pipelines validate single-spring stiffness from force and extension first, then branch to series or parallel combinations only when the single-spring k matches lab notes.
FAQ
What formula does the spring constant calculator use?
It uses k = F / x, where F is applied force, x is extension (or compression), and k is the spring stiffness constant.
What happens if extension is zero?
Spring constant k = F / x is undefined when extension is zero because that would be division by zero.
What units should I use?
Use any consistent force and length pair. With force in newtons and extension in metres, k is in newtons per metre (N/m). The calculator does not convert units.
Can extension be negative?
Yes. Negative x can represent compression under a signed coordinate convention. Zero is still rejected; non-zero compression is allowed.
Is the spring constant calculator free?
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/mech/spring-constant \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"F":50,"x":0.25}'const res = await fetch("https://api.kit.forhosting.com/mech/spring-constant", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"F": 50,
"x": 0.25
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/spring-constant",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"F": 50,
"x": 0.25
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/spring-constant", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"F":50,"x":0.25}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"F":50,"x":0.25}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/spring-constant", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"F": 50,
"x": 0.25
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.spring_constant",
"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 | 1000000000000 |
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
If extension is zero, validation fails with a clear invalid_input error so division by zero never silently invents a number. Pricing is a flat $0.002 per successful API request; failed validation is never charged.
How to call the API and what comes back
Absolute values must stay within the published limit of one trillion; extension must have absolute value strictly greater than one times ten to the minus fifteen so k equals F over x is well defined. Send a JSON body with the required finite fields F (aliases force, applied_force, and f) and x (aliases extension, displacement, delta_x, and dx). Failed validation—missing fields, non-finite numbers, values outside absolute limits, zero extension, or a non-finite quotient—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price. Prefer JSON numbers when you control the client; string numbers are accepted only when they match a strict finite numeric pattern for homework-form paste paths.
Practical tips, limits, and related searches
Keep F and x inside the published absolute range so the quotient remains finite in IEEE double precision on the Worker and in the browser. Pair classroom examples deliberately: F equals fifty and x equals zero point two five yields k equals two hundred; F equals ten and x equals zero point zero five yields k equals two hundred; F equals twenty-four and x equals zero point one two yields k equals two hundred; and x equals zero with any force demonstrates the hard invalid_input path. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set extension to zero.
Integration use cases
Unit tests for simulation helpers
Generate known-good k equals F over x cases plus deliberate zero-extension rejections for coding kata expected values in games or physics engines.