Hooke's Law Calculator (F = kx)
Solve Hooke's law F = kx for spring force, spring constant, or displacement. Enter any two values and get the third with step-by-step working shown.
Hooke's law
Hooke's law describes the restoring force of an ideal spring: the force needed to stretch or compress it is proportional to the displacement from its natural length.
- F — spring force, in newtons (N)
- k — spring constant, in newtons per metre (N/m) — always positive; a measure of stiffness
- x — displacement from the spring's natural (unstretched) length, in metres (m)
Enter any two values and leave the third blank; the calculator solves for it and shows the substitution step.
Worked example
A spring with a spring constant of 200 N/m is stretched 0.1 m. What force does it exert?
- Formula: F = kx
- Substitute: F = 200 × 0.1
- Result: F = 20 N
Solving in reverse
The same formula rearranges to find the spring constant or displacement when force is known:
- Spring constant: k = F / x — enter F and x, leave k blank.
- Displacement: x = F / k — enter F and k, leave x blank.
For example, a 20 N force stretching a spring 0.1 m means k = 20 / 0.1 = 200 N/m. And a 20 N force on a 200 N/m spring gives x = 20 / 200 = 0.1 m.
Common mix-ups
- Forgetting the spring constant is per unit length. k already includes the "per metre" — don't multiply by length again.
- Mixing displacement with total length. x is how far the spring has moved from its natural length, not the spring's total stretched length.
- Assuming Hooke's law works for any deformation. It only holds within a spring's elastic limit — stretch it too far and the force is no longer proportional to displacement.
Where this shows up
Hooke's law underlies the energy stored in a stretched or compressed spring, U = ½kx², which is derived directly from this same F = kx relationship. Like the general force calculator (F = ma), Hooke's law relates a force to a displacement rather than a mass, and the force it produces can do work on whatever the spring is attached to.
Frequently asked questions
- What is Hooke's law?
- Hooke's law says the force a spring exerts is proportional to how far it is stretched or compressed: F = kx, where F is the spring force in newtons (N), k is the spring constant in newtons per metre (N/m), and x is the displacement from the spring's natural length, in metres (m).
- How do I find the spring constant from force and displacement?
- Rearrange the formula to k = F / x. Enter the force and displacement, leave the spring constant field blank, and the calculator solves it for you automatically.
- What does the spring constant k tell you?
- A larger k means a stiffer spring — it takes more force to stretch or compress it by the same amount. A small k means a soft, easily-stretched spring.
- Why is there sometimes a minus sign in Hooke's law?
- The full form is F = -kx, where the minus sign shows the spring's force is a restoring force pointing back toward its natural length, opposite the direction of displacement. This calculator solves for the magnitude, F = kx, without the sign.
- Why must the spring constant be positive?
- The spring constant is a physical stiffness — it cannot be zero (that would mean no spring at all) or negative, which has no physical meaning for a real spring.
- Why can't I leave two fields blank?
- The calculator solves for exactly one unknown from the other two known values. With two blanks there are infinitely many (k, x) pairs that give the same F, so leave only the single variable you want solved blank.
- What units does this calculator use?
- SI units — newtons (N) for force, newtons per metre (N/m) for the spring constant, and metres (m) for displacement. Convert other units (pounds, inches) to SI before entering them.