Spring (Hooke’s Law) Calculator
Solve Hooke’s law F = kx for the force, the spring constant or the stretch, with the energy the spring stores. Also finds the bounce period of a mass on a spring and combines springs in series or parallel.
How to Use
- Pick a mode: Force, Spring constant or Extension for F = kx; Oscillation for a mass bouncing on a spring; Combine for springs in series and parallel.
- Enter the known values and pick a unit for each: N/m, N/mm or lbf/in for the spring constant, N or lbf for force, mm, cm, m or inches for the stretch.
- In Oscillation mode choose whether to find the period, the mass or the spring constant from the other two.
- Read the answer in the highlighted field and the readouts, with the stored energy and the mass the spring would hold up.
- Press a preset to load an example, and check Show Work for each step and conversion.
Worked Example
Force from a stretch. A spring with k = 200 N/m is stretched 5 cm. Convert first: 5 cm = 0.05 m. F = kx = 200 × 0.05 = 10 N, and the energy stored is ½kx² = ½ × 200 × 0.05² = 0.25 J.
A mass bouncing on a spring. 0.5 kg on a 20 N/m spring: T = 2π√(m ÷ k) = 2π × √(0.5 ÷ 20) = 0.9935 s, a frequency of 1.007 Hz. Hanging at rest it sits mg ÷ k = 0.5 × 9.80665 ÷ 20 = 24.52 cm below the spring’s unloaded length.
The common mistake: mixing centimetres with N/m. Multiplying 200 N/m by 5 straight from “5 cm” gives 1,000 N, a hundred times too much; the stretch must be in metres to match the N/m, so F = 200 × 0.05 = 10 N. The same slip in E = ½kx² is ten thousand times out, because x is squared.
Show Work
Formulas
Hooke’s Anagram
Robert Hooke first published his law in 1676 as an anagram, “ceiiinosssttuv”, a common way to claim a discovery without giving it away. In 1678, in De Potentia Restitutiva, he revealed the answer: ut tensio, sic vis, “as the extension, so the force”. He used it to explain springs in watches and the stretch of wires, and it became the starting point of the theory of elasticity.
The law is a straight-line approximation. Every real spring has an elastic limit; stretch it further and it takes a permanent set or breaks. In the early 1800s Thomas Young extended the idea from springs to materials, giving each one a stiffness of its own, now called Young’s modulus.
About This Tool
This calculator covers the three things people most often need from a spring: Hooke’s law solved for any one of force, spring constant and stretch, the bounce period of a mass on a spring solved for any one of period, mass and spring constant, and two or three springs combined end to end or side by side. Every field takes its own unit, including N/mm and lbf/in spring rates, and the working shows each conversion. The diagram draws the spring relaxed and stretched, bounces the mass at the computed period, or lays out the series and parallel arrangements.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Pendulum Calculator, Force Calculator, and Physics Playground.
Frequently Asked Questions
What is Hooke’s law?
The force a spring pushes or pulls back with is proportional to how far it is stretched or squashed: F = kx, where k is the spring constant. A 200 N/m spring stretched 5 cm (0.05 m) pulls back with 200 × 0.05 = 10 N. It holds until the spring is stretched past its elastic limit.
How do I find the spring constant of a spring?
Hang a known mass from it and measure the stretch, then k = mg ÷ x. If 0.5 kg stretches a spring 2.5 cm, k = 0.5 × 9.80665 ÷ 0.025 = 196.1 N/m. Measure from where it hangs with no load, not from the hook.
How much energy does a stretched spring store?
E = ½kx². A 200 N/m spring stretched 5 cm stores ½ × 200 × 0.05² = 0.25 J. Because x is squared, stretching it twice as far, to 10 cm, stores four times as much: 1 J.
How do springs combine in series and in parallel?
Side by side (parallel), the stiffnesses add: 100 N/m and 300 N/m make 400 N/m. End to end (series), the reciprocals add: 1 ÷ (1/100 + 1/300) = 75 N/m, softer than either spring alone. Under a 30 N load the series pair stretches 40 cm and the parallel pair 7.5 cm.
What sets the bounce period of a mass on a spring?
Only the mass and the spring constant: T = 2π√(m ÷ k). A 0.5 kg mass on a 20 N/m spring bounces with T = 0.9935 s, on Earth or on the Moon. Four times the mass (2 kg) doubles the period, to 1.987 s.
How do I use the Spring (Hooke’s Law) Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Car suspension
A coil spring that squashes 10 cm under 4,000 N has a rate of 40,000 N/m, which is 40 N/mm or 228.4 lbf/in.
Spring balances
A 196.1 N/m spring stretches 5 mm for every 100 g hung on it, so a 10 cm scale reads up to 2 kg.
Vibration mounts
A 50 kg machine on mounts totalling 200,000 N/m has a natural frequency of 10.07 Hz; keep the running speed well away from it.
Physics labs
A 0.5 kg mass on a 20 N/m spring bounces at 1.007 Hz and hangs 24.52 cm below the spring’s unloaded length.
Choosing a spring
To bounce a 2 kg load once a second, the spring constant must be 4π² × 2 ÷ 1² = 78.96 N/m.
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