Mechanics
Spring Potential Energy
Elastic potential energy stored in a spring.
Variables
PEJ
Potential energy
Energy in spring
In SI units: kg·m²/s²
kN/m
Spring constant
Spring stiffness
In SI units: kg/s²
Allowed values: greater than 0
xm
Displacement
Stretch/compression
Derivation
Work to stretch spring: W = ∫kx dx = ½kx².
Your notes
0/5000
Check value
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- k = 2 N/m (Spring constant)
- x = 3 m (Displacement)
Result: PE = 9 J
Other mechanics formulas with the same quantities
- Gravitational Potential Energy (Work & Energy) shares Potential energy
Where this formula is listed
- Mechanics formulas, under Work & Energy, alongside Work, Kinetic Energy, Power, Work-Energy Theorem and Conservation of Mechanical Energy.
- In the mechanics list it comes after Gravitational Potential Energy and before Power.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Spring Potential Energy formula?
Spring Potential Energy is written PE = (1/2)kx². Elastic potential energy stored in a spring. It belongs to Mechanics, under Work & Energy.
What are the units in PE = (1/2)kx²?
In SI units, PE is potential energy, measured in kg·m²/s²; k is spring constant, measured in kg/s²; x is displacement, measured in m.
How is the Spring Potential Energy formula derived?
Work to stretch spring: W = ∫kx dx = ½kx². The result is PE = (1/2)kx².