Hooke's Law Calculator
Variable Key
F= force (N)k= spring constant (N/m)x= displacement from equilibrium (m)PE= elastic potential energy (J)
Force
Restoring force exerted by the spring.
Spring constant
Stiffness of the spring — force needed per unit stretch.
Displacement
How far the spring is stretched or compressed.
Elastic potential energy
Energy stored in a compressed or stretched spring.
F= force (N)
k= spring constant (N/m)
x= displacement from equilibrium (m)
PE= elastic potential energy (J)
Hooke's Law states that a spring's restoring force is proportional to displacement: F = kx. The spring constant k (stiffness) determines how much force is needed per unit of stretch or compression.
- 1Measure the displacement x from the equilibrium (rest) position
- 2Multiply by the spring constant k: F = kx
- 3Elastic potential energy stored: PE = ½kx²
- 4Valid only within the elastic limit — beyond it, the spring permanently deforms
k=200 N/m, x=0.05 m=F=10 N, PE=0.25 J200×0.05=10 N
F=50 N, k=500 N/m=x=0.1 m50÷500=0.1 m
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Fun Fact
Robert Hooke discovered this relationship in 1678. He first published it as an anagram ("ceiiinosssttuu") to protect his priority — decoded it means "ut tensio, sic vis" (as the extension, so the force).
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