Elastic Potential Energy

U = \tfrac{1}{2} k x^{2}

U =

k =

x =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

Compressing or stretching a spring stores energy equal to the average force (½kx) times the distance — hence the ½kx². The square matters: double the stretch and you bank four times the energy. A 400 N/m spring compressed 0.05 m stores 0.5 J. Solving for x takes the principal positive root, the displacement magnitude.

Elastic Potential Energy

U = \tfrac{1}{2} k x^{2}

Where

$U$ = Elastic potential energy
$k$ = Spring constant
$x$ = Displacement from rest

Missing one of these? Work it out first, then come back

Elastic potential energy — Gravitational Potential Energy (U = mgh), Gravitational Potential Energy (Orbital)
Spring constant — Hooke's Law, Period of a Spring-Mass Oscillator
Displacement from rest — Hooke's Law, Displacement (Uniform Acceleration)

Part of these formula sets

Simple harmonic motion

7 formulasDisplacement, maximum velocity and maximum acceleration in an oscillation, with the two periods and the restoring force that generate them.

Work, energy and power

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