Spring Force Calculator
Calculate spring force, spring constant, or displacement using Hooke's Law: F = kx.
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What is Hooke's Law?
Hooke's Law describes the linear relationship between the force exerted by a spring and its displacement from the equilibrium position. It is one of the most fundamental principles in mechanics and elasticity:
F = kx
Where F is the restoring force in newtons (N), k is the spring constant in N/m (a measure of stiffness), and x is the displacement from equilibrium in meters (m). The force always opposes the displacement � pulling the spring creates a restoring force that pulls back.
Common Spring Constant Reference Values
| Spring Type | k (N/m) |
|---|---|
| Car suspension spring | 35,000 |
| Mattress spring (box spring) | 2,000 |
| Pen click spring | 500 |
| Trampoline spring | 4,000 |
| Slingshot rubber band | 200 |
| Watch mainspring | 0.001 |
| Garage door spring | 10,000 |
| Pogo stick spring | 15,000 |
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Authoritative References
Frequently Asked Questions
What is Hooke's Law?
Hooke's Law states that the force exerted by a spring is proportional to its displacement from equilibrium: F = -kx. The negative sign indicates that the force opposes the displacement (restoring force). The law is named after Robert Hooke and is fundamental to understanding elastic materials and oscillatory motion.
How do I calculate spring force?
Spring force is calculated using F = k × x, where k is the spring constant (stiffness) and x is displacement from equilibrium. For example, a spring with k = 500 N/m compressed by 0.1 m exerts F = 500 × 0.1 = 50 N of restoring force.
What is the spring constant?
The spring constant k measures the stiffness of a spring. A higher k means a stiffer spring that requires more force for the same displacement. Units are N/m (SI). The spring constant depends on the spring material, wire diameter, coil diameter, number of coils, and coil spacing.
What is the limit of Hooke's Law?
Hooke's Law is valid only within the elastic limit of the material. Beyond this limit (yield point), the spring deforms permanently (plastic deformation). The proportional limit is where the linear relationship between force and displacement ends. Springs are designed to operate within their elastic range.
What is the difference between compression and extension springs?
Compression springs shorten when force is applied (pushing), while extension springs lengthen (pulling). Both follow Hooke's Law. Compression springs have coils spaced apart to allow compression; extension springs often have coils touching (closed coils) and hooks at the ends for attachment.
How does spring force relate to spring energy?
The work done to compress or extend a spring is stored as elastic potential energy: PE = ½kx². This energy is released when the spring returns to equilibrium. This relationship comes from integrating Hooke's Law: W = ∫F dx = ∫kx dx = ½kx².