Elastic Potential Energy Calculator
Calculate elastic potential energy using EPE = ½k·x². Enter spring constant and displacement to get energy, force, and velocity results with charts.
About This Calculator
Elastic Potential Energy Explained
Elastic potential energy is the energy stored in a deformed elastic object, such as a spring, rubber band, or any material that obeys Hooke's Law. When you stretch or compress a spring, work is done against the restoring force, and that work is stored as elastic potential energy.
The fundamental formula is EPE = 1/2 x k x x^2, where k is the spring constant (stiffness) in N/m and x is the displacement from the equilibrium position in metres. Because displacement is squared, the energy grows quadratically -- doubling the stretch stores four times the energy.
This calculator also computes the spring restoring force (F = k·x) from Hooke's Law. When a mass is attached to the spring and released, the stored elastic PE converts to kinetic energy, giving a maximum velocity at equilibrium of v_max = x · sqrt(k / m) by conservation of energy.
Real-World Applications
Mechanical Engineering: Spring design in suspension systems, valves, and mechanical watches relies on accurate elastic PE calculations to ensure proper energy storage and release.
Sports Equipment: Tennis racket strings, archery bowstrings, diving boards, and pole vault poles all store and release elastic potential energy during use.
Medical Devices: Stents, surgical retractors, and prosthetic components use elastic deformation principles to deliver controlled forces within the body.
Regional Units
This calculator uses SI units universally (N/m, m, kg, J, N, m/s). No currency or region-specific unit conversions are needed for physics calculations.
Frequently Asked Questions
What is elastic potential energy?
Elastic potential energy is the energy stored in a deformable body such as a spring when it is stretched or compressed. It is given by EPE = 1/2k·x^2, where k is the spring constant in N/m and x is the displacement from equilibrium in metres.
How do I calculate elastic potential energy?
Use the formula EPE = 1/2 x k x x^2. Multiply half the spring constant by the square of the displacement. For example, a 100 N/m spring stretched 0.5 m stores 1/2 x 100 x 0.5^2 = 12.5 J of energy.
What is the spring constant (k) and how is it measured?
The spring constant k measures a spring's stiffness in newtons per metre (N/m). It is the force required to stretch or compress the spring by one metre. Stiffer springs have higher k values. Measure it by applying a known force F and measuring displacement x, then k = F/x.
How are Hooke's Law and elastic potential energy related?
Hooke's Law (F = k·x) gives the restoring force exerted by a spring. Elastic potential energy (EPE = 1/2k·x^2) is the integral of that force over displacement. The two are directly related -- force is the slope, energy is the area under the force-displacement curve.
Can I calculate the maximum velocity of a mass on a spring?
Yes. If you provide the mass (kg), the calculator computes the maximum velocity at the equilibrium position using v_max = x·sqrt(k/m). This comes from conservation of energy: all elastic PE converts to kinetic energy as the mass passes through equilibrium.
What units does this calculator use?
This calculator uses SI units: spring constant in N/m, displacement in metres, energy in joules (J), force in newtons (N), and velocity in m/s. The optional mass input is in kilograms (kg).
Does elastic potential energy apply to things other than springs?
Yes. Elastic potential energy applies to any deformable body including rubber bands, trampolines, bowstrings, diving boards, and biological tissues such as tendons and arteries. The same formula EPE = 1/2k·x^2 holds as long as the deformation follows Hooke's Law.
What happens if I enter negative displacement?
Since displacement is squared in the formula EPE = ½k·x², the energy result is always positive regardless of whether displacement is entered as positive (stretch) or negative (compression). The sign indicates direction but does not affect the energy value.