Spring Constant Calculator
Spring constant from force and extension — with the energy stored, and the extension any other load produces.
Hooke's law says force is proportional to extension: F = kx.
How the spring constant calculator works
Hooke's law says force is proportional to extension: F = kx. The constant k is the stiffness in newtons per meter, and it is a property of the spring, not of the load.
The energy stored is ½kx², which is quadratic — doubling the extension stores four times the energy. That is why a spring at twice its working extension is far more dangerous than it looks, and why the law stops holding once the metal yields.
Formula: F = kx; E = ½kx²
Worked examples
| Inputs | Spring constant (N/m) | Note |
|---|---|---|
| 24 N over 6 cm | 400 | 400 N/m |
| A stiffer spring | 1,200 | 1,200 N/m |
| A heavier load | 400 | extension scales linearly, energy quadratically |
FAQFrequently asked questions
What is Hooke's law?
Force is proportional to extension: F = kx. It holds until the material reaches its elastic limit, after which the spring deforms permanently.
What are the units of a spring constant?
Newtons per meter. A 400 N/m spring needs 400 N to stretch it one meter, or 4 N per centimeter.
Why is stored energy quadratic?
Because the force grows as you stretch, so the work done is the area under a rizing line — a triangle, which gives the half.
Does the law hold for compression?
Yes, with the same constant, until the coils touch. Beyond that the spring becomes effectively rigid.
What happens past the elastic limit?
The spring yields and does not return to its original length. The constant is no longer defined, which is why the law is stated with that caveat.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.