Hooke's Law Calculator
Spring force, extension and spring constant from F = kx.
What is Hooke's Law?
Hooke's law says the force a spring exerts is proportional to how far it is stretched: F = kx. The constant k measures how stiff the spring is, and the relationship holds only up to the spring's elastic limit — beyond that the material deforms permanently and the straight line becomes a curve.
How it works
F = kx, rearranged for whichever field is blank. The force is the restoring force, opposite in direction to the extension, which is why a spring pulling down on a hanging mass is described with the same equation as one being compressed. Spring constants are commonly quoted in N/m, N/cm or N/mm — and those differ by a factor of a hundred, so the unit selector is not decorative.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
What is a spring constant?
How much force is needed per unit of extension, in newtons per metre. A spring with k = 200 N/m needs 200 N to stretch it one metre, or 20 N to stretch it 10 cm.
What is the elastic limit?
The point beyond which the spring does not return to its original length when the force is removed. Hooke's law describes the straight region before it.
Is F positive or negative?
The full statement is F = −kx, where the minus sign says the force opposes the displacement. This calculator reports the magnitude, which is what a problem usually asks for.