For a spring that obeys Hooke's law, the force exerted is found with the equation force = spring constant × extension, or F = k × e. The spring constant, k, tells you how stiff the spring is. It is the force needed to produce each metre of extension, so it is measured in newtons per metre, N/m. Rearranging the equation gives k = F ÷ e.
The extension must be in metres before you use the equation, so divide a length in centimetres by 100. For example, 5 cm is 0.05 m. Worked example: a force of 4 N stretches a spring by 8 cm. The extension is 0.08 m, so k = 4 ÷ 0.08 = 50 N/m.
A stiffer spring has a larger spring constant. A spring with k = 40 N/m is stiffer than one with k = 20 N/m, because it needs twice the force for the same extension. On a force-extension graph with force on the vertical axis, the spring constant is the gradient of the straight line, so a steeper line means a stiffer spring.