About this calculator
Stretch a spring and it pulls back. Hooke's law says the pull is proportional to the stretch: F = k x, where k is the spring constant that measures how stiff the spring is.
Fill in any two boxes and leave the third empty. Force is in newtons, the spring constant in newtons per metre and the extension in metres. The stored elastic energy is worked out for you as well.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
200 N/m spring stretched 5 cm
- Force (F)
- 10 N
- Spring constant (k)
- 200 N/m
- Extension (x)
- 0.05 m
- Energy stored in the spring
- 0.25 J
Force (F) works out at 10 N.
Show the working
- Hooke's law: force = spring constant × extension, F = k x.
- Force (F) = 200 × 0.05 = 10 N.
- Stored energy = ½ k x² = ½ × 200 × 0.05² = 0.25 J.
10 N stretches a spring by 0.25 m
- Spring constant (k)
- 40 N/m
- Force (F)
- 10 N
- Extension (x)
- 0.25 m
- Energy stored in the spring
- 1.25 J
Spring constant (k) works out at 40 N/m.
Show the working
- Hooke's law: force = spring constant × extension, F = k x.
- Spring constant (k) = Force (F) ÷ (0.25) = 10 ÷ 0.25 = 40 N/m.
- Stored energy = ½ k x² = ½ × 40 × 0.25² = 1.25 J.
How far does 50 N stretch a 400 N/m spring?
- Extension (x)
- 0.125 m
- Force (F)
- 50 N
- Spring constant (k)
- 400 N/m
- Energy stored in the spring
- 3.125 J
Extension (x) works out at 0.125 m.
Show the working
- Hooke's law: force = spring constant × extension, F = k x.
- Extension (x) = Force (F) ÷ (400) = 50 ÷ 400 = 0.125 m.
- Stored energy = ½ k x² = ½ × 400 × 0.125² = 3.125 J.
The formulas
- F = k x: force from spring constant and extension
- E = ½ k x²: energy stored in the stretched spring
- k = F ÷ x: how stiff it is
Use metres for the extension. If your spring stretched 5 cm, enter 0.05.
The limit of proportionality
Hooke's law only holds up to the elastic limit. Stretch a spring too far and it stops returning to its original length, and the force no longer doubles when the extension doubles. The calculator assumes you are inside the linear region.
Springs in series and parallel
Two identical springs side by side (parallel) are twice as stiff. Two springs end to end (series) are half as stiff. So the combined constant is 2k in parallel and k ÷ 2 in series.
Frequently asked questions
What is the spring constant?
The force needed to stretch the spring by one metre. A stiff spring has a large k.
What are the units of k?
Newtons per metre (N/m).
Why is the energy ½kx² and not kx²?
The force grows as you stretch, so the average force over the stretch is half the final force. Energy is average force times distance.
Does it work for compression?
Yes, use the amount the spring is squashed as the extension.
What happens past the elastic limit?
The spring deforms permanently and Hooke's law no longer applies.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.