Elastic Potential Energy Calculator

Calculation mode

Spring inputs

Spring constant *

Spring constant unit

Elastic energy *

Extension or compression *

Initial displacement *

Final displacement *

Displacement unit

Spring constants list *

Use commas, spaces, or semicolons.

Spring arrangement

Deformation direction

Rod or wire inputs

Axial force

Elongation alternative

Elongation unit

Original length *

Length unit

Cross-sectional area *

Area unit

Material preset

Young’s modulus *

Modulus unit

Stress–strain inputs

Stress

Stress unit

Strain

Material volume *

Volume unit

Young’s modulus alternative

Copy this value into the shared modulus field below when needed.

Output units and precision

Energy unit

Force unit

Display precision

Formula used

Spring energy: U = ½kx²

Hooke’s law: F = kx

Energy change: ΔU = ½k(x₂² − x₁²)

Rod energy: U = F²L / 2AE

Energy density: u = ½σε

Elastic potential energy is stored during reversible deformation. The basic spring model follows Hooke’s law. Real materials may stop behaving linearly.

The calculator converts all values into SI units. It then applies the selected formula. Results return in your chosen units.

Use displacement measured from the equilibrium position. Enter magnitudes as positive values. Select stretch or compression separately.

How to use

Select the calculation mode.
Enter the known physical values.
Choose units for every quantity.
Select the required output units.
Press Calculate to view results and steps.
Copy, export, or print the calculation.

This tool assumes linear elasticity, negligible damping, and no permanent deformation. Check elastic limits before using engineering results.

Example data

Scenario	Spring constant	Displacement	Energy
Laboratory spring	250 N/m	0.20 m	5 J
Compression spring	8 N/mm	25 mm	2.5 J
Vehicle suspension	30 kN/m	0.08 m	96 J
Exercise spring	60 lbf/ft	8 in	Approximately 10.85 J

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Frequently asked questions

What is elastic potential energy?

It is energy stored by reversible deformation. Springs commonly store this form of energy. The energy returns when deformation decreases.

Why is displacement squared?

Spring force rises linearly with displacement. Work equals the force-displacement graph area. That triangular area produces the squared term.

Can compression use the same formula?

Yes, the energy formula uses displacement magnitude. Compression and extension both store positive energy. Direction matters mainly for force signs.

What units should spring constant use?

The standard SI unit is newtons per metre. Other stiffness units are converted automatically. Keep units consistent during manual calculations.

How do series springs behave?

Series springs share the same force. Their individual extensions add together. Equivalent stiffness is smaller than each stiffness.

How do parallel springs behave?

Parallel springs share the same displacement. Their carried forces add together. Equivalent stiffness equals the stiffness sum.

Does the calculator include material strain energy?

Yes, rod and stress-strain modes are included. They assume linear, uniform material behaviour. Validate geometry and modulus before design use.

What happens beyond the elastic limit?

The object may deform permanently or fail. Hooke’s law then becomes inaccurate. Use tested material limits for safety.

Can I export my calculation?

Yes, results can download as CSV. Printing can create a PDF file. Copying captures the complete result table.