Spring Constant Calculator
Solve For
Spring Constant200.000 N/m
Force100.000 N
Displacement0.500 m
Elastic Potential Energy25.000 J
The Spring Constant Calculator works with Hooke law, F = k·x, which relates the force on an ideal spring to how far it stretches or compresses. Choose whether to solve for the spring constant, the applied force, or the displacement, then enter the two known values. The tool returns all three quantities plus the elastic potential energy stored in the spring, ½·k·x², in joules.
Formula
F = k·x ; PE = ½·k·x²
- F
- Restoring force (N)
- k
- Spring constant / stiffness (N/m)
- x
- Displacement from the natural length (m)
- PE
- Elastic potential energy stored (J)
How it works
- Pick what to solve for — spring constant k, force F, or displacement x — using the mode selector at the top.
- Enter the two remaining known values; the calculator applies k = F/x, F = k·x, or x = F/k depending on the chosen mode.
- It also reports the elastic potential energy ½·k·x², the work stored in the deformed spring and released when it returns to its natural length.
Worked example
A spring is stretched 0.5 m by a 100 N force; find its stiffness.
- Spring constant = F ÷ x = 100 ÷ 0.5 = 200 N/m.
- Elastic potential energy = ½ × 200 × 0.5² = ½ × 200 × 0.25 = 25 J.
- The spring stores 25 J that is released when it relaxes.
A spring constant of 200 N/m, storing 25 J of elastic energy.
Frequently asked questions
- What does the spring constant tell you?
- It measures stiffness: the force in newtons needed to stretch or compress the spring by one metre. A higher value means a stiffer spring that resists deformation more strongly.
- Why is there a minus sign in Hooke law in textbooks?
- The restoring force opposes the displacement, so physics texts write F = -k·x. This calculator reports magnitudes, so the sign is dropped while the relationship between force and stretch is unchanged.
- When does Hooke law stop being accurate?
- Only within the elastic limit. Stretch a spring too far and it deforms permanently or breaks, after which force is no longer proportional to displacement and this formula no longer applies.
- How is the stored elastic energy calculated?
- The energy is the area under the force-displacement line, which equals ½·k·x². It represents the work done to deform the spring and is fully recovered when the spring returns to its natural length.