What this calculator does
A spring constant tells you how stiff a spring is: how much force it takes to stretch or compress it by a given distance. Hooke's Law states that force and displacement are directly proportional, F = kx, so if you already know the force applied and how far the spring moved, rearranging that equation to k = F / x gives the spring constant directly.
This is the reverse of the usual textbook question. Most spring calculators start from a known k and ask for the force or the stored energy. Here the spring constant is the unknown: measure how far a known force stretches or compresses the spring, and this works backwards to the stiffness itself, in newtons per metre.
The formula
Divide the applied force by the resulting displacement from the spring's rest length. The result, k, is measured in newtons per metre (N/m) and stays constant for a given spring as long as it is not stretched or compressed past its elastic limit, where Hooke's Law stops holding.
| Term | Meaning |
|---|---|
| k | Spring constant: how much force is needed per unit of displacement, in N/m. |
| F | Force applied to stretch or compress the spring, in newtons. |
| x | Displacement from the spring's natural, unstretched length, in metres. |
The inputs explained
| Field | What to enter |
|---|---|
| Force applied (N) | The force applied to the spring, in newtons. |
| Displacement from rest length (m) | How far the spring moved from its rest length under that force, in metres. |
When to use it
Identifying an unknown or unlabelled spring
Springs salvaged from old equipment or bought without a datasheet rarely come with a stated k. Hang a known weight on it, measure the stretch, and this calculator gives the spring constant so it can be matched to a replacement or used in a design.
Checking a manufacturer's spec
If a spring is rated at a certain k but behaves differently under load, measuring force and displacement directly and comparing the result catches a mismatched or worn part before it causes a design problem.
Physics coursework and lab reports
A common lab exercise hangs a series of masses on a spring and measures the extension at each weight. Working out k from a single measurement, or checking it against several, is the standard write-up calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does spring constant change with displacement, for a fixed force?
The same 12 N force applied to springs that stretch by different amounts.
| Displacement | Spring constant | Elastic potential energy stored |
|---|---|---|
| 0.02 m | 600.000 N/m | 0.1200 J |
| 0.04 m | 300.000 N/m | 0.2400 J |
| 0.06 m | 200.000 N/m | 0.3600 J |
| 0.08 m | 150.000 N/m | 0.4800 J |
| 0.1 m | 120.000 N/m | 0.6000 J |
| 0.2 m | 60.000 N/m | 1.200 J |
How does spring constant change with applied force, for a fixed displacement?
A range of forces, each stretching the spring by the same 0.05 m.
| Force applied | Spring constant | Elastic potential energy stored |
|---|---|---|
| 5 N | 100.000 N/m | 0.1250 J |
| 10 N | 200.000 N/m | 0.2500 J |
| 15 N | 300.000 N/m | 0.3750 J |
| 20 N | 400.000 N/m | 0.5000 J |
| 30 N | 600.000 N/m | 0.7500 J |
| 50 N | 1,000.000 N/m | 1.250 J |
Questions
What units is spring constant measured in?
Newtons per metre (N/m) in SI units, meaning the force in newtons needed to stretch or compress the spring by one metre. Smaller or stiffer springs are sometimes quoted in N/mm or lb/in, which need converting to N/m before comparing.
Does the spring constant change with how far I stretch it?
Not within a spring's elastic range, where Hooke's Law holds and k stays constant regardless of the displacement used to measure it. Past the elastic limit the spring deforms permanently and the F = kx relationship no longer applies.
How is this different from just calculating force from a known k?
This calculator solves the same equation, F = kx, but for a different unknown. If k is already known, use it to find force or stored energy at any displacement. If k is unknown but force and displacement were measured, this rearranges the formula to find k itself.
Why does the calculator also show stored energy?
Elastic potential energy, ½kx², is the work done stretching or compressing the spring, and it is a useful check: it should always come out positive and roughly proportional to how far the spring moved, given the same force.
To go the other direction, calculating force or stored energy from a known spring constant, see the Hooke's Law and spring energy calculator.