π Spring Force Calculator
Calculate spring force F = -kx using Hooke's Law.
How to Use This Calculator
This calculator finds the spring force from Hooke's law. Enter the spring constant and the displacement from the spring's natural length.
Enter the spring constant k in newtons per meter. Stiff car springs are tens of thousands; a pen spring might be 100.
Enter the displacement x in meters from the natural length. Use 0.05 for a 5 cm stretch.
Click Calculate. The restoring force appears in newtons, directed back toward the natural length.
Stay within the elastic range: the formula only holds while the spring returns to its original shape.
Hooke's Law
Hooke's law is the simplest force law in physics: the restoring force is directly proportional to the displacement. Pull twice as far and the spring pulls back twice as hard. The negative sign is the physics: the force always opposes the stretch, dragging the end back toward equilibrium. Without that minus sign you would have anti-springs that fling things away.
Robert Hooke published it in 1678 as an anagram, revealing it only later. It holds for springs, rubber bands at small stretch, and even the microscopic bonds in solids, which is why the same mathematics describes sound waves in materials.
Worked Example
Where This Comes Up
Hooke's law sizes car suspensions, mattress springs, pogo sticks, and the tiny silicon springs inside phone accelerometers. Experimental physicists measure unknown spring constants by hanging known masses and reading the stretch, then use k everywhere else. It is also the first step into oscillations: combine F = -kx with F = ma and you get simple harmonic motion, the mathematics behind pendulums, guitar strings, and AC circuits.
The usual error is unit mixing: k in N/cm with x in meters silently corrupts the answer by a factor of 100. Convert everything to N/m and meters first. And respect the elastic limit. A spring stretched past it does not obey Hooke's law anymore, and your calculation becomes fiction.
Frequently Asked Questions
What does the negative sign in F = -kx mean?
It marks the force as restoring: it always points opposite to the displacement, back toward the spring's natural length. The magnitude is simply k times x.
What are the units of the spring constant?
Newtons per meter (N/m). A stiffer spring has a larger k: it takes more force to stretch it the same distance.
When does Hooke's law stop working?
Beyond the elastic limit. Stretch a spring too far and it deforms permanently, then the force is no longer proportional to displacement. Every real spring has this limit.
How much energy is stored in a stretched spring?
1/2kx^2. Note the square: doubling the stretch quadruples the stored energy, which is why a fully drawn bow is so much more powerful than a half-drawn one.
Does it work for compression too?
Yes. Squeezing a spring by x takes the same force as stretching it by x, as long as you stay within the elastic range. The coils must not bind solid, though.