Hooke's Law Calculator: F = kx

The force in a spring from its stiffness and how far it is stretched or compressed.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • F = k\,x
  • k = \frac{F}{x}
  • x = \frac{F}{k}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the spring force: spring force = spring constant x extension or compression
  2. Put the values in (every value in its SI unit): spring force = 200 x 0.05
  3. The answer: spring force: 10 N
  4. The same answer in other units: 0.01 kN; 1.01972 kgf; 2.24809 lbf

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Spring constant; Spring force (leave it as it is if this is what you are finding) 10 N; Extension or compression (leave it as it is if this is what you are finding) 0.05 m.

  1. The formula, arranged to find the spring constant: spring constant = (spring force) / (extension or compression)
  2. Put the values in (every value in its SI unit): spring constant = (10) / (0.05)
  3. The answer: spring constant: 200 N/m
  4. The same answer in other units: 0.2 N/mm; 1.14203 lbf/in

Common questions

What is Hooke's law?

The force in a spring is proportional to its extension: F = kx. A 200 N/m spring stretched 0.05 m pulls with 10 N.

How do I find the spring constant?

Divide the force by the extension.

What is the unit of the spring constant?

Newtons per metre.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (Hooke's law).

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