Hooke's Law
Calculate spring force, spring constant, or displacement with F = kx. Free online calculator with formulas and step-by-step solutions.
Key formula
F = kx; U = ½kx²
How do you use Hooke's law and elastic PE?
Hooke's law is F = kx. If you know two of F, k, and x, solve for the third: k = F / x or x = F / k. Elastic potential energy stored in the spring is U = ½ k x² (joules). Stretch and compression with the same |x| store the same energy.
About this tool
Hooke's law says the restoring force of an ideal spring is proportional to stretch or compression: F = kx. The work stored while stretching is elastic potential energy U = ½kx². This page keeps F, k, and x rearrangements visible and links spring force to spring energy.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: force from k = 200 N/m and x = 0.15 m
F = kx = (200)(0.15) = 30 N. The spring pulls back with 30 N when stretched 15 cm from equilibrium.
Example 2: elastic PE for the same stretch
Same k = 200 N/m, x = 0.15 m. U = ½(200)(0.15)² = 2.25 J. Force was 30 N; energy is 2.25 J — do not mix the two.
Example 3: find k from F = 40 N and x = 0.080 m
k = F / x = 40 / 0.080 = 500 N/m. Leaving x as 8 cm without converting to 0.080 m would make k wrong by a factor of 100.
Frequently asked questions
What is the Hooke's law formula?
F = kx, where F is the spring force magnitude, k is the spring constant in N/m, and x is the change in length from the unstretched (equilibrium) position in meters.
What is the elastic potential energy formula?
U = ½ k x². It is the work stored in an ideal spring stretched or compressed by x from equilibrium. Units are joules when k is in N/m and x is in meters.
Is the force direction important?
Yes. The restoring force is opposite the displacement. Many homework answers report the magnitude F = kx and state the direction in words. Energy U = ½kx² is a scalar.
What are the units of the spring constant k?
Newtons per meter (N/m). A k of 100 N/m means 100 N of force for each meter of stretch.
When does Hooke's law stop working?
Beyond the elastic limit the spring permanently deforms and F is no longer proportional to x, so U ≠ ½kx² either. Use the linear formulas only when the problem says the spring is ideal or within its elastic range.