A Spring Force Calculator
Stretch a spring and it pushes back in proportion to how far you stretched it. That single sentence is Hooke's law, and it is the reason springs appear in suspension, in scales, in mattresses and in the shock absorbers that keep a door from slamming. The force is easy to compute; the subtlety is knowing how far the linear rule actually holds.
Spring force
30
- Stored energy
- 1.8
- Angular frequency
- 12.9099
- Oscillation period
- 0.4867
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
F = -k x
- k
- Spring constant in newtons per metre
- x
- Displacement from the natural length in metres
- m
- Mass hung on the spring in kilograms
How to check the result by hand
- 1
Measure the displacement from the natural length
Record how far the spring is stretched or compressed away from the length it settles at with nothing attached. Take this in the same unit you want the answer in; metres is the convenient choice because the spring constant is quoted per metre.
- 2
Read or measure the spring constant
Take k from the manufacturer's datasheet, or find it by hanging a known mass and dividing the weight by the extension. Newtons per metre is the standard unit; a car coilover is in the tens of thousands, a pen spring in the single digits.
- 3
Multiply to get the force
Restoring force equals k times displacement. A 250 newton per metre spring pulled 0.12 metres gives 30 newtons. If the spring is compressed rather than stretched, the magnitude is identical and only the direction flips.
- 4
Compute the stored energy
Energy equals one half times k times the displacement squared. For the numbers above that is 0.5 x 250 x 0.12 x 0.12, or 1.8 joules, which is the work you did stretching it.
- 5
Find the oscillation period if a mass is attached
Period equals two pi times the square root of mass over k. With 1.5 kilograms on the 250 newton per metre spring the period is about 0.487 seconds, so the mass completes roughly two cycles per second.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Spring Force page.