Spring constant calculator
This spring constant calculator gives the stiffness of a spring. Example: 50 N stretch a spring by 0.1 m, so k = 500 N/m.
Example: What is given: Force and extension (Hooke’s law) · Force F 50 N · Extension x 0.1 m → Result: k = 500 N/m (spring constant). Source: Halliday/Resnick/Walker, Fundamentals of Physics (F = −k·x, E = ½·k·x², T = 2π·√(m/k)). Updated: .
How it is calculated
The spring constant k (also spring rate or stiffness) states how much force it takes to stretch or compress a spring by one metre. The larger k is, the stiffer the spring. The unit is N/m.
Formulas
Hooke’s law gives F = k·x, so k = F / x. If you know the energy stored in the spring, E = ½·k·x², then k = 2·E / x². For a spring pendulum with mass m and period T, T = 2π·√(m / k), rearranged to k = 4π²·m / T².
Worked example
A force of 50 N stretches a spring by 0.1 m: k = 50 / 0.1 = 500 N/m, which is 0.5 N/mm or 2.85507 lbf/in. The spring stores E = ½ · 500 · 0.1² = 2.5 J. From E = 2.5 J and x = 0.1 m you get the same k = 500 N/m. A spring pendulum with 0.5 kg and T = 0.2 s gives k = 4π² · 0.5 / 0.2² = 493.48 N/m at a frequency of 5 Hz.
- The extension must be in metres; divide centimetres by 100.
- Two identical springs in series have half the spring constant, in parallel twice as much.
- Hooke’s law only holds in the elastic range; beyond the elastic limit the spring deforms permanently.
Frequently asked questions
What does a high spring constant mean?
A high spring constant means a stiff spring: even a small extension needs a lot of force. At k = 500 N/m, each millimetre of extension takes 0.5 N, so about 5 N per centimetre of travel.
How do I find the spring constant from the oscillation period?
Use k = 4π²·m / T². For m = 0.5 kg and T = 0.2 s you get k = 493.48 N/m.
How do I convert N/m to N/mm?
Divide by 1000: 500 N/m is 0.5 N/mm. For lbf/in, divide by 175.127.
Sources and legal basis
- Halliday/Resnick/Walker, Fundamentals of Physics (F = −k·x, E = ½·k·x², T = 2π·√(m/k))
- Wikipedia – Federkonstante
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