Solve F = k·x for spring force, spring constant or displacement.
Calculated locally in your browser.
How do you calculate spring force using Hooke's law?
F = k · x, where F is force in newtons, k is the spring constant in N/m and x is displacement in metres. The elastic potential energy stored is ½ · k · x². For example, a spring with k = 200 N/m stretched 0.1 m exerts F = 20 N and stores 1 J, valid within the spring's elastic limit.
Understanding your result
Hooke's law states that the force needed to extend or compress a spring is proportional to the distance, as long as you stay within its elastic limit. A larger spring constant means a stiffer spring. Beyond the elastic limit the relationship breaks down and the spring may deform permanently.
Formula and method
F = k · x, where F is force in newtons, k is the spring constant in N/m and x is displacement in metres. Elastic potential energy is ½ · k · x².
Worked example
A spring with k = 200 N/m stretched 0.1 m exerts F = 200 × 0.1 = 20 N and stores ½ × 200 × 0.1² = 1 J.
How to use this tool
- Enter any two of force, spring constant and displacement.
- Leave the value you want to find blank.
- Read the result and the stored energy.
Common mistakes to avoid
- Using centimetres for displacement instead of metres.
- Leaving more than one box blank.
- Applying the law beyond the spring's elastic limit.
About the Hooke's Law Calculator
The Hooke's Law Calculator solves F = k·x for a spring. Enter any two of force, spring constant and displacement, leave the third blank, and it finds the missing value plus the elastic potential energy stored.
Who should use this tool
Physics and engineering students, teachers and makers working with springs.
Benefits
- Solves for force, spring constant or displacement.
- Also gives the elastic potential energy.
- Shows the formula and worked steps.
- Private — calculated entirely in your browser.
Practical use cases
- Finding the force a stretched spring exerts.
- Working out a spring constant from a measurement.
- Checking physics homework.
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Frequently asked questions
What is the spring constant?
It is a measure of stiffness, in newtons per metre — the force needed to stretch the spring by one metre. A higher value means a stiffer spring.
What is the elastic potential energy?
The energy stored in a stretched or compressed spring, equal to ½ · k · x².
Does Hooke's law always apply?
Only within the elastic limit. Stretch a spring too far and it deforms, so the simple F = k·x relationship no longer holds.