Hooke's Law Calculator: F = k × x
Solve spring force, spring constant or displacement with F = kx. Use N/m, N/cm or lbf/in and m, cm, mm or in, with the sign explained. Free and private in your browser.
Fill in all but one field: the empty field is the one you solve for.
About the Hooke's Law Calculator
The Hooke's Law Calculator solves F = k × x for a spring. Fill in any two of Force, Spring constant and Displacement and the third appears as you type. The page shows the equation with the solved symbol highlighted and a one-line substitution such as 200 N/m × 0.05 m = 10 N.
Hooke's law says that the force needed to stretch or compress a spring is proportional to how far it is moved from its resting length. The spring constant k measures stiffness: a large k is a stiff spring, a small k is a soft one. The law holds only below the spring's elastic limit. Past that point the spring is permanently deformed and the straight-line relation stops.
How to use the Hooke's law calculator
Steps
- Enter two of the three values and leave the one you want to find empty.
- Choose units. Force offers N, kN and lbf. The spring constant offers N/m, N/cm and lbf/in. Displacement offers m, cm, mm and in.
- Read the answer under the formula, together with the same value in every other unit of that quantity.
The spring constant must be greater than zero. Force and displacement can be negative, and the sign carries meaning, explained below. If you solve for k and the displacement is zero, the calculator says it cannot divide by zero instead of showing a number.
Formula
F is the force applied to the spring, k is the spring constant in newtons per metre and x is the displacement from the resting length. Units are converted to newtons, newtons per metre and metres before the calculation, and the answer is converted back, so mixed units such as N/cm with mm work.
What the sign means
Written as the force the spring exerts, Hooke's law has a minus sign: F = −k x. The spring pushes back against the stretch, so its force points the opposite way to the displacement. This calculator uses the force you apply to the spring, F = k x. A force and a displacement that point the same way are both positive, so stretching 5 cm with 10 N is +10 N and +0.05 m. Pushing in the other direction gives a negative force and a negative displacement. Enter a negative force and the displacement comes out negative, which tells you the spring is compressed.
Worked examples
Example 1: force from stretch
A spring with k = 200 N/m is stretched by 0.05 m. F = 200 × 0.05 = 10 N.
Example 2: find the spring constant
A 10 N load stretches a spring by 2 cm. k = 10 ÷ 0.02 = 500 N/m, which is 5 N/cm.
Example 3: find the stretch
A spring with k = 500 N/m carries 25 N. x = 25 ÷ 500 = 0.05 m, or 5 cm.
Example 4: imperial units
A spring with k = 1 lbf/in compressed by 1 in needs 1 lbf. In SI units, 1 lbf/in is about 175.127 N/m.
Good to know
- Springs side by side (in parallel) add their constants: k = k₁ + k₂. Springs end to end (in series) combine as 1/k = 1/k₁ + 1/k₂.
- The energy stored in a stretched spring is U = ½ k x². Use the Elastic Potential Energy Calculator to find it.
- A scale or a car suspension is designed by choosing k so that the expected load gives the wanted displacement.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
Use the Elastic Potential Energy Calculator for the energy in the spring, the Force Calculator for F = m a and the Length Converter to prepare a displacement in another unit.
Frequently asked questions
What is Hooke's law?
Hooke's law says the force needed to stretch or compress a spring is proportional to its displacement from the resting length: F = k × x. The constant k is the spring constant, a measure of how stiff the spring is.
How do I find the spring constant?
Divide the force by the displacement: k = F ÷ x. A 10 N load that stretches a spring by 2 cm gives 10 ÷ 0.02 = 500 N/m. Enter the force and displacement, leave k empty and read the answer in N/m, N/cm or lbf/in.
Why is there a minus sign in F = −kx?
The minus sign belongs to the force the spring exerts: it points against the displacement, restoring the spring to its resting length. This calculator uses the force applied to the spring, F = kx, so a stretch and the force that causes it are both positive.
What does a negative displacement mean?
It means the spring is moved in the opposite direction to the one you chose as positive, for example compressed instead of stretched. Entering a negative force with a positive k gives a negative displacement.
What units does the spring constant use?
The calculator offers newtons per metre (N/m), newtons per centimetre (N/cm) and pounds-force per inch (lbf/in). One N/cm equals 100 N/m, and one lbf/in is about 175.127 N/m.
When does Hooke's law stop working?
Beyond the elastic limit the spring deforms permanently and force no longer rises in a straight line with displacement. Very small springs and rubber bands also depart from the law. Use the results only within the working range of the spring.
Can I find the stored energy too?
Yes. The energy in the spring is U = ½ k x². The Elastic Potential Energy Calculator solves it for energy, spring constant or displacement, with the same units.
Does it send my numbers anywhere?
No. The force, spring constant and displacement you enter are solved locally in your browser, and nothing is uploaded, stored or shared with any server.