Hooke's Law
Also known as F = kx · spring force · spring constant equation
Worked example: 200 N/m stretched 0.1 m → 20 N — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
The spring pushes back →
Grade 11Grade 11 Physics
The spring →
Grade 12Grade 12 Physics
Springs store it →
UniversityEngineering Mechanics
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Hooke's Law explained
Robert Hooke published this law in 1676 as a Latin anagram — ceiiinosssttuv — unscrambled two years later to "ut tensio, sic vis": as the stretch, so the force. An ideal spring pushes or pulls back in proportion to how far you displace it from rest. The spring constant k is the stiffness: a 200 N/m spring stretched 0.1 m pulls back with 20 N, while a car's suspension spring might run tens of thousands of N/m.
This calculator uses the magnitude form; strictly the restoring force points opposite the displacement, which is written F = −kx and is what makes released springs oscillate. The law holds only up to the elastic limit — stretch a spring too far and it deforms permanently. Within that limit it underpins spring scales, force gauges, vehicle suspensions, and even the atomic bonds that make solids springy.
Hooke's Law formula
- = Spring force (N)
- = Spring constant (N/m)
- = Displacement from rest (m)
Missing one of these? Work it out first, then come back
- Spring force — Newton's Second Law, Work (W = Fd cos θ)
- Spring constant — Elastic Potential Energy, Period of a Spring-Mass Oscillator
- Displacement from rest — Elastic Potential Energy, Displacement (Uniform Acceleration)