Spring calculator
A spring with a constant of 80 N/m stretched by 0.05 m pulls back with a force of −4 N, the minus sign pointing toward rest. Enter the stiffness and the signed displacement to get the restoring force in newtons. Free in your browser.
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Run — free
Worked example
- Spring constant
- 80
- Displacement
- 0.05
- Force
- -4 N
- Restoring force
- -4
- Magnitude
- 4
An ideal spring restores toward equilibrium with a force proportional to how far the free end has moved from the unstretched length. This spring calculator encodes that statement as F equals minus k times x: you send a non-negative spring constant in newtons per metre and a signed displacement from equilibrium in metres, and the solver returns the restoring force in newtons, including the textbook minus sign so a positive stretch produces a negative force along the chosen axis. Compression — a negative displacement — yields a positive restoring force that tries to expand the coil. Zero stiffness is allowed and yields zero force. Missing fields, empty strings, NaN, Infinity, and non-numeric text also fail and are not billed.
What the restoring force of an ideal spring actually is
An ideal spring is a linear elastic element whose restoring force depends only on how far the free end sits from the unstretched, unloaded length. That unloaded length is the equilibrium position: the coil is neither stretched nor compressed, so the net elastic force is zero. Displace the end by a signed distance x along a chosen axis — positive for extension, negative for compression — and the spring answers with a force that always points back toward equilibrium.
Hooke's law writes that restoring force as F equals minus k times x. The spring constant k is stiffness in newtons per metre: a larger k means a stiffer coil and a larger force for the same displacement. The minus sign is not decoration.
If x is positive, F is negative, so the force pulls the mass back toward zero. If x is negative, F is positive, so the force pushes the mass back toward zero.
Where a spring restoring-force calculator earns its keep
Classrooms and tutoring platforms use a spring calculator so learners can check the signed restoring force without dropping the minus sign by hand, especially on compression problems where x is already negative. Exam generators need a deterministic oracle that rejects a negative spring constant instead of leaking a bogus force into a gradebook. Lab notebooks that record a measured stiffness and a measured extension can turn those two numbers into a force in newtons before plotting a load cell trace.
Failed validation does not consume balance. Keep requests small, pin the rounded force in tests, and you get reproducible newtons for homework, LMS plugins, and edge workers without standing up a mechanics engine of your own. If you instead need to solve for k or x given a force, or you want the unsigned classroom form F equals k x, use a dedicated Hooke's law solver rather than this restoring-force landing.
What you can do with it
Lab stiffness to load
Turn a measured spring constant and a measured extension or compression into a signed force in newtons before comparing it with a load-cell reading.
FAQ
What happens if the spring constant is negative?
An ideal spring stiffness cannot be negative. Zero stiffness is allowed and yields zero force. Invalid input is not billed.
What units does the calculator use?
SI: spring constant in newtons per metre, displacement in metres, force in newtons (unit N).
How do I get just the size of the spring force?
Look at the magnitude shown with the result: it is the spring constant times the displacement without its sign. In the example, the force is −4 N and its magnitude is 4 N, the figure most homework asks for.
What happens when the spring is compressed instead of stretched?
Enter the displacement as a negative number. The restoring force then comes out positive, because the coil pushes back outward toward its unstretched length.
Does the spring calculator include mass, damping or gravity?
No. It models an ideal linear spring only, with no mass, damping, gravity or nonlinear coil. It also does not convert pounds per inch or millimetres, so convert to newtons per metre and metres first.
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/spring \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"spring_constant":80,"displacement":0.05}'const res = await fetch("https://api.kit.forhosting.com/phys/spring", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"spring_constant": 80,
"displacement": 0.05
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/spring",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"spring_constant": 80,
"displacement": 0.05
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/spring", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"spring_constant":80,"displacement":0.05}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"spring_constant":80,"displacement":0.05}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/spring", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"spring_constant": 80,
"displacement": 0.05
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.spring",
"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
A negative spring constant is rejected with invalid_input because stiffness cannot be negative for an ideal Hookean spring.
What the restoring force of an ideal spring actually is
The magnitude is simply k times the absolute value of x, which is why classroom problems that only ask for how many newtons often drop the sign, but any free-body diagram, oscillator equation, or signed API must keep it. This calculator returns the signed restoring force in newtons when k is in newtons per metre and x is in metres. It does not model damping, mass, gravity, or a nonlinear coil; those belong to other tools. It also does not convert pounds per inch or millimetres: convert to SI first so the newton result is honest.
Input contract, response shape, and error behaviour
Magnitudes above one trillion are rejected so a mistyped exponent cannot blow a downstream plot. The product rule that a negative spring constant is invalid is enforced in the solver itself: k less than zero fails with a message that an ideal spring stiffness cannot be negative. Zero stiffness is allowed and yields a restoring force of zero. Zero displacement is equilibrium and also yields zero force. POST a JSON body with two required finite numbers: spring_constant, the stiffness k in newtons per metre, and displacement, the signed distance x from equilibrium in metres. Each field may arrive as a JSON number or as a numeric string. Aliases k and stiffness map onto spring_constant; aliases x, extension, and delta_x map onto displacement. Missing values, empty strings, NaN, Infinity, objects, arrays, and non-numeric text fail with invalid_input naming the field, and those failures are not billed. On success the body echoes spring_constant and displacement, returns force as the signed restoring force in newtons, repeats that value as restoring_force for display, reports magnitude as the absolute value, restates the identity in formula as F equals minus k x, sets unit to N, and sets method to ideal_spring so clients can tell this landing from a magnitude-only F-equals-kx solver. Example: spring_constant eighty and displacement zero point zero five yields force minus four newtons, because minus eighty times zero point zero five is minus four. Example: spring_constant four hundred and displacement minus zero point zero two five yields force plus ten newtons.
Where a spring restoring-force calculator earns its keep
Simple harmonic motion sketches start from F equals minus k x to write m x-double-dot plus k x equals zero; calling a tiny parse API avoids pulling a full dynamics package for a two-number product.
Integration use cases
Classroom and homework checks
Let students submit k and a signed displacement and verify the restoring force F = -kx in newtons, including compression (negative x) and the zero-force equilibrium case.
Oscillator and free-body sketches
Seed F = -kx on a mass-spring diagram or simple-harmonic-motion setup without flipping the restoring sign by hand.
Technical questions
How does the spring calculator compute restoring force?
Send a non-negative spring constant k in N/m (field spring_constant, aliases k, stiffness) and a signed displacement x from equilibrium in metres (field displacement, aliases x, extension, delta_x). The API returns F = -k x in newtons, plus the magnitude and the formula string.
Why is there a minus sign in F = -kx?
The force is restoring: it always points toward equilibrium. A positive extension (x > 0) produces a negative force; a negative displacement (compression) produces a positive force. Magnitude is k |x|; the sign is required on a free-body diagram.
What does the spring calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.