Spring Calculator

What Is Hooke's Law?

Hooke's law describes how an ideal spring responds to deformation. Within the elastic limit, restoring force is proportional to displacement from equilibrium. Compressed or stretched springs store elastic potential energy.

Spring Formulas

$$F = kx$$ $$PE = \frac{1}{2}kx^2$$

$F$ is force in newtons, $k$ is the spring constant in N/m, $x$ is displacement in meters, and $PE$ is stored elastic energy in joules. Choose which variable to solve for and enter the other two.

Example: $k = 500\,\text{N/m}$ and $x = 0.1\,\text{m}$ gives $F = 50\,\text{N}$ and $PE = 2.5\,\text{J}$.

Spring Constant and Stiffness

A higher spring constant means a stiffer spring: more force is needed for the same compression. Automotive suspension, valve springs, and mechanical watches all rely on these relationships.

Related tools: Spring Rate Calculator and Spring Rate Converter.

Frequently Asked Questions

What does the spring constant k mean?

k is stiffness in N/m. A 500 N/m spring needs 500 N to compress or stretch 1 meter (within its elastic range).

When does Hooke's law stop being accurate?

Beyond the elastic limit the spring permanently deforms and the linear F = kx model no longer applies.

How is potential energy related to displacement?

Energy grows with the square of displacement: doubling compression quadruples stored energy because PE = ½kx².

Can displacement be negative?

Sign indicates direction (compression vs extension). This calculator uses magnitude; direction follows your coordinate choice.

How is this different from the spring rate calculator?

The spring calculator also computes elastic potential energy. The spring rate calculator focuses on the k = F/x relationship only.

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What Is Hooke's Law?

Spring Formulas

Spring Constant and Stiffness

Frequently Asked Questions

Related Tools

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