spring potential energy formulas and interpretation
An ideal spring stores elastic energy when compressed or extended.
The calculator preserves direct solutions and supported spring-constant and distance units.
How to use the spring potential energy calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Elastic potential energy equals one-half the spring constant times displacement squared.
PEs = ½kx²- PEs — Spring energy
- Stored elastic energy (J)
- k — Spring constant
- Spring stiffness (N/m)
- x — Displacement
- Compression or extension (m)
Compressed spring example
A 200 N/m spring is compressed by 0.1 m.
- Spring constant
- 200 N/m
- Displacement
- 0.1 m
- PEs = ½ × 200 × 0.1²
- PEs = 1 J
Result: The spring stores 1 joule.
Equal compression and extension magnitudes store equal energy.
Understanding your results
Interpreting the result
Energy grows with displacement squared while the spring remains in its elastic range.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.