Spring Force Calculator (Hooke's Law)

Hooke’s Law states that the force needed to extend or compress a spring is proportional to the distance it is stretched or compressed from its natural (rest) length. This law was published by Robert Hooke in 1678 in England.

The formula:

F = k × x

Where:

• F = restoring force exerted by the spring (in Newtons)
• k = spring constant (in N/m), a measure of the spring’s stiffness
• x = displacement from the rest position (in meters)

The negative sign is sometimes included (F = −kx) to indicate the force acts in the opposite direction of displacement, but for magnitude calculations we use the positive form.

Elastic Potential Energy:

A stretched or compressed spring stores energy: PE = ½ × k × x²

This stored energy is what makes springs useful in everything from mechanical watches to car suspension systems.

Oscillation Frequency:

A mass on a spring will oscillate with a natural frequency: f = (1 / 2π) × √(k / m). This is the basis of many timing mechanisms and vibration systems.

Solving for different unknowns:

• Spring constant: k = F / x
• Displacement: x = F / k

Practical examples:

• A car suspension spring might have k = 25,000 N/m (very stiff).
• A Slinky toy has k ≈ 1 N/m (very soft).
• A typical pen click spring has k ≈ 200–400 N/m.
• Bathroom scales use springs to measure your weight by measuring compression.

Metric and Imperial: Force is typically measured in Newtons (N) in metric and pounds-force (lbf) in imperial. Displacement is in meters (m) or inches (in). Spring constants are in N/m or lbf/in. This calculator uses metric units (N and m) for all calculations.

Important limitation: Hooke’s Law only applies within the elastic limit of the material. If you stretch a spring too far, it deforms permanently and the linear relationship breaks down.