Elastic Potential Energy Calculator
Calculate elastic potential energy stored in a spring using ½kx². Find energy from force and displacement, rubber band draw weight, release velocity, and series/parallel spring energy.
Elastic PE (Joules)
—
Elastic PE (kJ) —
Spring Force F = kx (N) —
Extended More scenarios, charts & detailed breakdown ▾
Elastic PE = ½kx² (J)
—
Spring Force kx (N) —
Equivalent Height (m) —
Professional Full parameters & maximum detail ▾
%
Energy & Motion
Elastic PE (J) —
Release Velocity (m/s) —
Transferred KE (J, with efficiency) —
Spring Combinations
Series Spring k_eff (N/m) —
Parallel Spring k_eff (N/m) —
Series Spring Energy (J) —
Parallel Spring Energy (J) —
How to Use This Calculator
- Enter spring constant k and displacement x for the stored elastic energy.
- Optionally add mass to calculate equivalent height (mgh = ½kx²).
- Use From Force and x if you know the applied force instead of k.
- Use Rubber Band/Bow for archery or elastic band energy from draw weight and draw length.
- Switch to Professional for release velocity, energy transfer efficiency, and series/parallel spring comparisons.
Formula
Elastic PE = ½kx²
Elastic PE = ½Fx (since F = kx)
Release velocity v = √(kx²/m) = x√(k/m)
Series: 1/k_eff = 1/k₁ + 1/k₂ | Parallel: k_eff = k₁ + k₂
Example
Example: k = 200 N/m, x = 0.1 m. PE = ½ × 200 × 0.01 = 1 J. With m = 0.5 kg, release velocity = √(200 × 0.01 / 0.5) = 2 m/s.
Frequently Asked Questions
- Elastic potential energy is the energy stored in a deformed elastic object (spring, rubber band, bow) due to compression or extension. Formula: PE = ½kx², where k = spring constant (N/m) and x = displacement from equilibrium (m).
- Gravitational PE = mgh (depends on height). Elastic PE = ½kx² (depends on spring displacement). Both are forms of potential energy, but stored by different mechanisms — gravity vs elastic deformation.
- When all elastic PE converts to kinetic energy (ideal, no losses): ½kx² = ½mv². Solving: v = √(kx²/m) = x√(k/m). This is the maximum velocity achievable from the spring.
- Series: 1/k_eff = 1/k₁ + 1/k₂ (softer). Parallel: k_eff = k₁ + k₂ (stiffer). Series springs store less energy at the same displacement; parallel springs store more.
- For a bow or rubber band, stored energy ≈ ½ × Draw Force × Draw Length. This uses the same ½Fx formula (since F = kx, PE = ½kx² = ½Fx). The result gives the maximum energy available to launch a projectile.