Hookes Law Calculator

1. Enter any two of force, spring constant and displacement.
2. Leave the one you want to find blank.
3. Read the result.
4. See which value was solved for and the formula used.

Here is what each result means:

Hooke's law says the force a spring exerts is proportional to how far it is stretched or compressed. Pull a spring twice as far and it pulls back twice as hard. The constant of proportionality is the spring constant, written k, which measures how stiff the spring is: a large k means a stiff spring that resists stretching, and a small k means a soft, easily stretched one.

In symbols the law is force equals k times x, where x is the displacement from the spring's natural resting length. The force always acts to return the spring to that resting length, which is why it is called a restoring force. In SI units the force is in newtons, the spring constant in newtons per meter and the displacement in meters.

Hooke's law is an idealisation that holds only while the spring stays within its elastic limit. Stretch a spring too far and it deforms permanently, and the neat straight-line relationship breaks down. Within that limit, though, the law is remarkably accurate and underlies everything from weighing scales to vehicle suspension and the tiny springs inside a clock.

It rearranges one relation to solve for whichever value you leave blank.

1. For force, multiply the spring constant by the displacement.
2. For the spring constant, divide the force by the displacement.
3. For displacement, divide the force by the spring constant.

Springs store energy as they stretch; see the force calculator and potential energy calculator.

A spring with a stiffness of 200 newtons per meter is stretched 0.1 meters.

Calculation: F = k x = 200 x 0.1 = 20 newtons. To find the stiffness of a spring that needs 50 newtons to stretch 0.25 meters, divide: 50 over 0.25 is 200 newtons per meter.

One relation, rearranged for whatever you need to find.

All three come from F equals k x, so any two of the values give the third. Because the relationship is a straight line through the origin, the spring constant is simply the slope: the steeper the line, the stiffer the spring.

The spring constant tells you at a glance how a spring behaves.

For the same force, a stiff spring stretches only a little while a soft one stretches a lot. This is why heavy vehicles use stiff springs and delicate instruments use soft ones, matching the spring constant to the load it must carry.

The Spring Constant

A stiffer spring produces more force for the same stretch, in direct proportion to k.

The Displacement

Stretching or compressing the spring further increases the force. Twice the stretch gives twice the force.

The Elastic Limit

Beyond the elastic limit the spring no longer obeys Hooke's law and may not return to its original length.

Physics Homework

Solve for spring force, stiffness or displacement in an elasticity problem.

Engineering and Design

Choose or check a spring for a suspension, latch or mechanism.

Experiments

Find a spring constant from measured force and extension data.

1. Measuring from the Wrong Point

Displacement is measured from the spring's natural length, not from the ground or a random mark.

2. Going Past the Elastic Limit

Hooke's law only holds while the spring springs back. Overstretched springs break the rule.

3. Mixing Units

Use newtons per meter for k and meters for displacement to get a force in newtons.

4. Confusing Stiffness with Force

The spring constant is a fixed property of the spring; the force depends on how far it is stretched.

5. Zero Displacement or Stiffness

Solving for the spring constant or displacement cannot divide by zero.

The relation is exact; only the displayed decimals are rounded.

Hooke's law says the force a spring exerts is proportional to how far it is stretched or compressed: force equals the spring constant times the displacement. A 200 newton per meter spring stretched 0.1 meters pulls with 20 newtons.

Multiply the spring constant by the displacement. A spring of stiffness 200 newtons per meter stretched 0.1 meters gives 200 times 0.1, which is 20 newtons.

The spring constant, k, measures a spring's stiffness in newtons per meter. A large value means a stiff spring that is hard to stretch, and a small value means a soft, easily stretched spring.

Divide the force by the displacement. Leave the spring constant field blank and enter force and displacement, and the calculator solves for it.

Displacement is how far the spring is stretched or compressed from its natural resting length, measured in meters. The force always acts to return the spring to that length.

It holds only while the spring stays within its elastic limit. Stretch a spring too far and it deforms permanently, and the force is no longer proportional to the displacement.

Force is in newtons, the spring constant in newtons per meter and displacement in meters. Keep the units consistent for a correct result.

Yes. The same law describes compressing a spring as well as stretching it. The force acts in the opposite direction but has the same size for the same displacement.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Hooke's law (Wikipedia).
• Springs and Hooke's law (Maths Is Fun).
• Elasticity (Wikipedia).