Hooke's Law Spring Force Calculator
Calculate spring restoring force F = −kx and elastic potential energy PE = ½kx². Enter spring constant k (N/m) and displacement x (m).
How to use this tool
- Enter spring constant k and displacement x in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your restoring force f and the full breakdown beneath it.
Hooke's Law states the restoring force of a spring is proportional to displacement: F = −kx, where k is the spring constant (N/m) and x is displacement from equilibrium. Elastic potential energy stored is PE = ½kx².
Formula
Restoring force: F = −k x
Elastic potential energy: PE = ½ k x2
How it works
Hooke's Law states that the force a spring exerts is proportional to its displacement from equilibrium and always directed back toward equilibrium (hence the negative sign). The spring constant k (N/m) quantifies stiffness. Elastic potential energy stored in the spring equals ½kx², which is always non-negative regardless of the direction of displacement. This model assumes a linear (ideal) spring with no damping or mass effects.
Worked example
Worked example
- Inputs: k = 100 N/m, x = 0.1 m (spring stretched 0.1 m from equilibrium).
- Restoring force: F = −100 × 0.1 = −10.0 N (directed back toward equilibrium).
- Elastic PE: PE = 0.5 × 100 × 0.1² = 0.5 × 100 × 0.01 = 0.5 J.
Restoring force F = −10.0 N; magnitude = 10.0 N; elastic PE = 0.5 J.
Key terms
- Spring constant (k)
- A measure of a spring's stiffness in N/m; a higher k means more force is needed to stretch or compress the spring by a given amount.
- Displacement (x)
- How far the spring end is moved from its natural (equilibrium) length, positive for extension and negative for compression by convention.
- Restoring force
- The force the spring exerts on the attached mass, always pointing back toward the equilibrium position to oppose the displacement.
- Elastic potential energy
- Energy stored in a deformed spring, recoverable when the spring returns to its natural length. Given by PE = ½kx².
- Equilibrium
- The position at which the spring exerts no force, corresponding to its natural (unstretched, uncompressed) length.
Frequently asked questions
- What are typical spring constants?
- Car suspension: 10,000–50,000 N/m; pen spring: ~2 N/m; lab spring: 10–100 N/m; human Achilles tendon: ~1000 N/m.
- What does the negative sign mean?
- The restoring force always opposes the displacement, pulling back toward equilibrium. Stretch it right (+x) and the force acts left (−F).