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Spring Potential Energy Calculator

Use this free calculator to find the elastic potential energy stored in a compressed or stretched spring using Hooke's Law formula PE = ½kx².

Enter a positive spring constant and a displacement to see results.

Formula

PE = ½ × k × x² — where k is the spring constant (N/m) and x is the displacement from the natural length (m).

The formula is derived from Hooke's Law: F = kx. Integrating the force over displacement gives the stored elastic potential energy.

Quick answer

Spring potential energy (elastic potential energy) is the energy stored in a spring when it is compressed or stretched from its natural length. It is calculated using the formula PE = ½kx², where k is the spring constant in N/m and x is the displacement in meters. For example, a spring with k = 200 N/m compressed by 0.05 m stores 0.25 joules of potential energy. The stiffer the spring or the greater the displacement, the more energy is stored.

Formula & method

PE = ½ × k × x²
  • PE — Elastic potential energy (joules, J)
  • k — Spring constant / stiffness coefficient (N/m)
  • x — Displacement from equilibrium / natural length (meters, m)

Elastic potential energy stored in a spring (Hooke's Law)

Examples

Example 1: Soft spring compressed 5 cm
Input
k = 200 N/m, x = 0.05 m
Result
PE = 0.25 J
Why
PE = 0.5 × 200 × (0.05)² = 0.5 × 200 × 0.0025 = 0.25 J. A relatively soft spring compressed just 5 cm stores only 0.25 joules.
Example 2: Stiffer spring compressed 10 cm
Input
k = 500 N/m, x = 0.10 m
Result
PE = 2.5 J
Why
PE = 0.5 × 500 × (0.10)² = 0.5 × 500 × 0.01 = 2.5 J. Doubling k and doubling x yields 10 times more energy than the first example.
Example 3: Stiff automotive spring compressed 20 cm
Input
k = 1000 N/m, x = 0.20 m
Result
PE = 20 J
Why
PE = 0.5 × 1000 × (0.20)² = 0.5 × 1000 × 0.04 = 20 J. A car suspension spring with k = 1000 N/m displaced 20 cm stores 20 joules.
Example 4: Light spring stretched 30 cm
Input
k = 50 N/m, x = 0.30 m
Result
PE = 2.25 J
Why
PE = 0.5 × 50 × (0.30)² = 0.5 × 50 × 0.09 = 2.25 J. Even a gentle spring stores meaningful energy when stretched a significant distance.

Frequently asked questions

What is spring potential energy?

Spring potential energy (also called elastic potential energy) is the energy stored in a spring when it is deformed — either compressed or stretched — from its natural equilibrium length. This energy is released when the spring returns to its rest position, converting to kinetic energy.

What is the spring constant (k)?

The spring constant k (also called the stiffness coefficient) measures how stiff a spring is. A higher k means the spring is harder to compress or stretch. It is measured in newtons per meter (N/m). It is determined experimentally by measuring how much force is needed to displace the spring a given distance (k = F / x).

Does it matter if the spring is compressed or stretched?

No — because displacement x is squared in the formula PE = ½kx², the sign of x does not matter. A spring compressed by 0.1 m stores the same energy as one stretched by 0.1 m, assuming the spring constant is the same in both directions.

What units should I use?

For a result in joules (J), use the spring constant in N/m and the displacement in meters. If you have centimeters, convert to meters by dividing by 100 before calculating.

How is spring potential energy related to kinetic energy?

By conservation of energy, all of the stored spring potential energy converts to kinetic energy when the spring returns to its natural length (ignoring friction and air resistance). At the equilibrium point KE = PE_initial, so mv² / 2 = kx² / 2.

What is Hooke's Law?

Hooke's Law states that the restoring force of a spring is proportional to its displacement: F = -kx. The negative sign indicates the force opposes the displacement. The potential energy formula PE = ½kx² is derived by integrating this force over the displacement.

Sources & references

External references open in a new tab. We are independent and not affiliated with these organizations.

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