Spring potential energy calculator
A spring of 200 N/m stretched 0.1 m stores 1 J of elastic energy. Enter the stiffness and the stretch or compression to get the stored energy; this is spring energy, not gravitational. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Spring constant
- 200
- X
- 0.1
- Pe
- 1 J
- Precision
- 10
This spring potential energy calculator finds the elastic energy stored in an ideal Hooke's-law spring when you know its spring constant and how far it is stretched or compressed from the unstretched length. The definition is the closed form PE equals one-half k times x squared, which is the standard introductory model used in mechanics homework, energy conservation problems, and first-order engineering checks on linear springs. When the spring constant is given in newtons per metre and the extension in metres, the result is reported in joules; any consistent force-per-length and length pair works the same way. Zero stiffness or zero displacement is valid and yields zero elastic potential energy; a negative extension means compression and produces the same PE as the equal positive stretch because of the square; a negative spring constant is rejected because it has no physical meaning for a stable restoring spring in this model. The engine is fully deterministic arithmetic: no network calls, no sampling, and no date-dependent shortcuts.
What spring energy means and what you get
In classical mechanics, an ideal linear spring that obeys Hooke's law stores elastic potential energy when its free end is displaced from the unstretched length. With spring constant k and displacement x measured from that equilibrium length, the stored energy is PE equals one-half k times x squared. Displacement may be an extension (positive x) or a compression (negative x); because energy depends on x squared, the sign of the displacement does not change the stored energy magnitude for a given |x|.
Elastic potential energy is not the same as the instantaneous spring force or the work already done along a particular path when friction or other forces are present: under the ideal model it is a state variable of the current stretch. Zero k or zero x is valid and yields zero PE when the other factor is finite.
Where spring potential energy fits in study, design, and software
Students meet PE equals one-half k x squared when a textbook introduces Hooke's law energy, when a conservation problem asks how much kinetic energy appears after a spring releases a known stretch, or when a contest problem gives k and x and asks for elastic PE without calculus. Teachers can pre-generate answer keys for modest stiffness and extension values without trusting opaque calculator apps that silently switch units or confuse force with energy.
Developers call the same contract from scripts to seed deterministic test vectors for game physics demos, to normalize user-entered spring parameters before an energy diagram, or to satisfy programming-challenge statements that demand joules rather than a hand-waved sketch. Product and first-order mechanical checks use PE equals one-half k x squared when only linear stiffness and a design stroke are known before nonlinear springs or multi-axis dynamics are modeled.
What you can do with it
Homework and lab checks
Compute PE = ½kx² from spring constant and extension before grading worksheets or comparing energy balances.
Tutoring and teaching software
Normalize user-entered spring constant and displacement into PE for interactive lessons and step helpers.
FAQ
What does the spring potential energy calculator cost?
It is free in your browser on this page.
What formula is used for spring potential energy?
Elastic (spring) potential energy is PE = ½ · k · x², where k is the spring constant and x is the extension or compression from the unstretched length. With SI inputs (N/m and m) the unit is joules (J).
What happens if the spring constant is negative?
A negative spring constant is not accepted because PE = ½kx² has no standard meaning for a negative k in this calculator.
Can the extension x be negative?
Yes. A negative x means compression from the unstretched length. Because energy depends on x², PE is the same for +x and −x of equal magnitude. Zero x yields zero PE for any finite k.
Is this the same as gravitational potential energy?
No. Gravitational PE near constant g is m·g·h. This tool computes elastic energy stored in a linear spring (½kx²). Use the gravitational calculator when you need mass, height, and g.
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-potential-energy \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k":200,"x":0.1}'const res = await fetch("https://api.kit.forhosting.com/mech/spring-potential-energy", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k": 200,
"x": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/spring-potential-energy",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k": 200,
"x": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/spring-potential-energy", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k":200,"x":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k":200,"x":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/spring-potential-energy", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"k": 200,
"x": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.spring_potential_energy",
"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_k | 1000000000000000 |
max_abs_x | 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
What spring potential energy means and what the response contains
The spring constant is the stiffness: force per unit extension in the linear regime. This calculator returns the normalized inputs k and x, the computed pe, the precision used, a method tag spring_potential_energy, a short formula reminder, and a unit hint J for SI inputs. There is no numerical integration of a nonlinear force law, no multi-spring network reduction, and no Monte Carlo sampling: the engine either evaluates one-half k x squared inside the supported numeric range or rejects the input with invalid_input. Rejected cases include a missing k or x, non-finite values, magnitudes above the documented ceilings, and any spring constant that is negative, because a negative k is not accepted in this calculator.
How spring constant and extension are read and how PE stays reproducible
Zero stiffness is allowed and returns zero PE. Extension may be positive, zero, or negative; negative values mean compression from the unstretched length and produce the same PE as the equal positive magnitude because of the square, which is intentional for bidirectional spring problems. 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 spring constant is k, but aliases spring_constant, stiffness, and K are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. The spring constant must be finite and non-negative: a negative value fails with invalid_input and a message that names the field and explains that PE equals one-half k x squared is undefined for a negative spring constant in this calculator, so a bad cell does not become a silent nonsense result. The preferred field for displacement is x, with aliases extension, displacement, delta_x, and X. 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 spring energy formula yourself.
Where spring potential energy fits in study, design, and software
Education tools use the endpoint when a learner types spring constant and extension and the UI must show joules. 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 gravitational potential energy or spring-force helpers when you need related mechanics, and with other math endpoints when you are building a small lab of free, deterministic physics calculators.
Integration use cases
Deterministic test fixtures
Generate reproducible elastic potential-energy values for unit tests, game-physics demos, and CI assertions on PE = ½kx².