Classical Mechanics
Hooke's Law Calculator
Calculate spring force, spring constant or extension using F = kx. Also computes spring potential energy PE = ½kx². Live spring animation updates with your result.
Solve for
F = k × x
PE = ½kx²
Spring examples
Spring visualisation
Enter positive values to calculate.
Hooke's Law equations
Hooke's Law
F = kx
Spring constant
k = F/x
Extension
x = F/k
Spring PE
PE = ½kx²
PE from force
PE = F²/(2k)
Force from PE
F = √(2kPE)
Hooke's Law
Hooke's Law states that the force exerted by a spring is proportional to its extension from its natural length: F = kx. The spring constant k (also called the stiffness) has units of N/m — a stiffer spring has a higher k. The negative sign in the formal expression (F = −kx) indicates the restoring force acts opposite to the extension direction.
The elastic potential energy stored in a spring is PE = ½kx². This energy is released when the spring returns to its natural length. Hooke's Law holds until the elastic limit — beyond that, the spring deforms permanently.