Hooke's Law Calculator (Spring Force)
By Santaji GadepatilinUpdated October 27, 2026
The force needed to stretch or compress a spring is proportional to how far you move it — Hooke's law. It describes springs, scales and the elastic behaviour of materials.
How to use the Hooke’s law calculator
Enter the spring constant and the extension or compression. The calculator gives the force and the elastic energy stored. Fill any two fields to solve for the others — for example, force and extension to find k.
Hooke’s law formulas
F = k × x · E = ½ × k × x²
- k = spring constant (stiffness), N/m
- x = change in length from the natural length, m
Example
A spring with k = 500 N/m stretched by 4 cm (0.04 m):
- Force = 500 × 0.04 = 20 N
- Energy = ½ × 500 × 0.04² = 0.4 J
Springs in series and parallel
| Arrangement | Combined stiffness |
|---|---|
| Parallel (side by side) | k = k₁ + k₂ |
| Series (end to end) | 1/k = 1/k₁ + 1/k₂ |
Two identical springs in parallel are twice as stiff; in series they are half as stiff.
Typical spring constants
| Spring | Approximate k |
|---|---|
| Ballpoint pen spring | 100–500 N/m |
| Kitchen scale spring | 1,000–5,000 N/m |
| Car suspension spring | 20,000–60,000 N/m |
| Railway buffer | over 1,000,000 N/m |
Mass on a spring
A mass m on a spring oscillates with period T = 2π√(m ÷ k). A 0.5 kg mass on a 500 N/m spring bounces with a period of 0.199 s.
Beyond springs
Hooke’s law also describes small stretches of solid materials, where stress = Young’s modulus × strain. Steel has a Young’s modulus of about 200 GPa.
Frequently asked questions
What is Hooke's law?
The force needed to stretch or compress a spring is proportional to the distance — F = kx — as long as the spring stays within its elastic limit.
How do I find the spring constant?
Hang a known weight from the spring and measure the extension. k = F ÷ x. A 10 N weight stretching a spring by 2 cm gives k = 500 N/m.
What happens beyond the elastic limit?
The spring deforms permanently and no longer returns to its original length, so Hooke's law stops applying.
How much energy does a spring store?
E = ½kx². A 500 N/m spring compressed 4 cm stores 0.4 J.