Hookes Law Calculator
The spring's contract: F = k·x — the restoring force at any stretch, the work stored growing as the square, and the elastic limit where the contract quietly dies.
Hookes Law Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Linear region only — the elastic limit is taught, not measured
- Ideal springs: no mass, damping or buckling
In short: A spring of stiffness k = 250 N/m stretched 0.12 m fights back with F = kx = 30.000000 N, pointing home — double the stretch and the bill doubles linearly to 60. But the WORK stored squares: ½kx² = 1.800000 J at 0.12 m becomes 7.200000 J at 0.24 m, four times for twice the pull-per-metre. Two such springs in parallel hold 2k = 500 N/m (stiffer); in series they sag to k/2 = 125.000000 N/m (softer). All of it holds only inside the elastic limit — the unlabelled line every spring carries and no formula can find for you. Compression is the same law signed the other way: −30.000000 N, pushing back out.
Formula
F = −k·x (restoring) · W = ½k·x² · parallel: k₁+k₂ · series: 1/k = 1/k₁+1/k₂
Hooke's law is LINEAR by experiment, not by right: within the elastic limit, force tracks stretch with the constant k. The minus sign says the force points home — this page prices magnitude and names the direction. The stored work is the area under the force-stretch line: a triangle, hence the half and the square.
Worked Example
- Enter the spring's stiffness (measure it on the spring-constant page if unknown).
- Enter the stretch from rest — sign honest: negative is compression.
- Read the restoring force and the work stored at double the stretch to see the square.
- Respect the limit card: no page can tell you where your spring's linearity ends.
Defaults: 30.000000 N at 0.12 m; 1.800000 J stored, 7.200000 J at double. Parallel 2k = 500 N/m, series k/2 = 125.000000 N/m. At x = −0.12 the spring pushes back out with 30.000000 N.
Strengths & Limits Of This Model
Where this engine is strong
- Squared work shown beside linear force
- Series/parallel combos priced from the single k
Where it stops
- No progressive or non-linear springs
- No oscillation dynamics — snapshot, not movie
Practical Use Cases
Engineering
spring selection against a force budget
Workshop
what a compressed spring is holding — before the circlip flies
Teaching
linear force, squared energy — both in one spring
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Hookes Law Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does the force carry a minus sign?
Because the spring pushes back toward rest: stretch it right, it pulls left. The minus is the restoring direction — the feedback that makes springs oscillate instead of runaway. This page prints the magnitude and names the direction; the sign matters when forces share a diagram.
Why does work grow as the square when force is linear?
Because work is force accumulated over distance, and the force GROWS as you stretch: the area under a rising line is a triangle, ½kx². Each extra millimetre costs more than the last — the same square tax as speed, wearing a spring.
Parallel or series — which is stiffer?
Parallel doubles k (both springs stretch together, both push); series halves it (the same force passes through both, each adding its sag). Two identical springs: 500 vs 125.000000 N/m here. The combo card prices your pair from the single k you typed.
What is the elastic limit?
The stretch beyond which the spring takes a permanent set and F = kx stops describing it. The law is a contract INSIDE the limit; outside, the metal flows. No calculator can locate it for an unmarked spring — the catalogue, or a deliberate, sacrificial test, must.
Compression — same law?
Yes, signed the other way: compress 0.12 m and the spring pushes back out with the same 30.000000 N. Coil springs can buckle rather than comply, which is a stability story the linear law does not cover — the page prices the law, not the buckling.
Where does the oscillation come in?
Released off-center, the spring trades stored work back and forth with motion, giving f = (1/2π)√(k/m) — priced on the spring-constant page beside its dynamic k route. Same law, run as a movie instead of a snapshot.
Is every spring linear?
Only within its limit and design: progressive suspension springs stiffen ON PURPOSE as they compress, and rubber bands go soft then stiff. Hooke's law is the straight-line ideal; the page is honest that it is pricing the straight part.
How do I measure k for this page?
That is the spring-constant page's own question: hang a known weight, divide by the stretch, or time the bounce and use the dynamic route. This page assumes k and asks about forces; that page assumes forces and asks about k — inverse questions sharing one border.