Hooke's Law: formula
Use a spring constant in N/m and displacement from equilibrium in meters. A manufacturer’s stiffness or a measured force–displacement slope must apply over the modeled range. Record extension relative to equilibrium rather than the spring’s entire length; convert centimeters to meters first.
Hooke's Law: worked example
| Spring constant (N/m) | 200 |
|---|---|
| Stretch or compression (m) | 0.15 |
| Spring force (N) | 30 |
| Stored energy (J) | 2.3 |
The constant-stiffness approximation applies within the material and geometry’s linear response range. Nonlinearity can occur before permanent deformation; an elastic material is not necessarily linear over every extension. The ideal stored-energy result excludes damping, friction and hysteresis.
Hooke's Law: changing Spring constant (N/m)
| Spring constant (N/m) | Spring force (N) | Stored energy (J) |
|---|---|---|
| 160 | 24 | 1.8 |
| 180 | 27 | 2 |
| 200 (example) | 30 | 2.3 |
| 220 | 33 | 2.5 |
| 240 | 36 | 2.7 |
Hooke's Law: compare input ranges
| Input | Tested from | To | Spring force (N): low input | Spring force (N): high input | Swing |
|---|---|---|---|---|---|
| Spring constant (N/m) | 180 | 220 | 27 | 33 | 6 (20%) |
| Stretch or compression (m) | 0.14 | 0.17 | 28 | 34 | 6 (20%) |
Hooke's Law: individual input comparisons
| Input | Value | Spring force (N) | Stored energy (J) |
|---|---|---|---|
| Spring constant (N/m) | 160 | 24 | 1.8 |
| 180 | 27 | 2 | |
| 200 | 30 | 2.3 | |
| 220 | 33 | 2.5 | |
| 240 | 36 | 2.7 | |
| Stretch or compression (m) | 0.12 | 24 | 1.4 |
| 0.14 | 28 | 2 | |
| 0.15 | 30 | 2.3 | |
| 0.17 | 34 | 2.9 | |
| 0.18 | 36 | 3.2 |
Hooke's Law: combined input changes
| Spring constant (N/m) / Stretch or compression (m) | 0.12 | 0.15 | 0.18 |
|---|---|---|---|
| 160 | 19.2 | 24 | 28.8 |
| 180 | 21.6 | 27 | 32.4 |
| 200 | 24 | 30 | 36 |
| 220 | 26.4 | 33 | 39.6 |
| 240 | 28.8 | 36 | 43.2 |
Hooke's Law: which assumptions move the result?
Hooke's Law: values and definitions
| Quantity and definition | Value used |
|---|---|
| Spring constant (N/m) | 200 |
| Stretch or compression (m) | 0.15 |
| Spring force (N) | 30 |
| Stored energy (J) | 2.3 |
Hooke's Law: half and double Spring constant (N/m)
| Spring constant (N/m) | Spring force (N) |
|---|---|
| 100 | 15 |
| 200 | 30 |
| 400 | 60 |
Common error: Entering the spring's total length instead of the change in length. The formula uses only how far it moves from its resting length.
Physics & Mechanics calculators: Ideal Gas Law Calculator, Gravitational Potential Energy Calculator, Work and Power Calculator, Wavelength and Frequency Calculator, Projectile Motion Calculator, Free Fall Calculator.
A spring pushes back with a force in proportion to how far it is stretched, and stores energy in proportion to the square of that stretch. A spring of 200 newtons per meter pulled 0.15 meters pulls back with 30 newtons and holds 2.25 joules. Doubling the stretch doubles the force but quadruples the stored energy, which is why a wide stretch is so much harder to release safely.
Keep the stretch inside the spring's working range. Past it, the spring deforms for good and the straight-line rule no longer applies.
See the force on the force calculator, the energy on the kinetic and potential energy calculators and the oscillation on the pendulum period calculator. The work and power and uniform acceleration pages relate to motion, and the length converter changes units.
What is Hooke's law?
The force a spring exerts is proportional to how far it is stretched or compressed, F equals k times x.
How do I find a spring constant?
Hang a known weight from it, measure how far it stretches and divide the force by that stretch, in newtons per meter.
What is the energy stored in a spring?
Half the spring constant times the square of the stretch, which is 2.25 joules in the example.