The spring constant, k, tells you how stiff a spring is. It is the force needed to produce 1 m of extension, and it is measured in newtons per metre (N/m). A stiff spring has a large spring constant. For a spring within its limit of proportionality, force = spring constant × extension, or F = k × e, with force in newtons (N) and extension in metres (m). Rearranging gives k = F ÷ e.
Extension must be in metres. To convert centimetres to metres, divide by 100, so 3 cm is 0.03 m. For example, a force of 6 N stretches a spring by 3 cm. The extension is 0.03 m, so the spring constant is 6 ÷ 0.03 = 200 N/m. This spring needs 200 N for every 1 m of extension.
On a force-extension graph with force on the vertical axis, the spring constant is the gradient of the straight line. A steeper line means a stiffer spring.