What is Hooke's law and what does F = k·x mean?

Hooke's law says the force a spring exerts is proportional to how far it is stretched or compressed: F = k·x. Here F is the spring force in newtons, k is the spring constant (stiffness) in newtons per metre, and x is the displacement from the spring's natural length in metres. Example: a spring with k = 100 N/m stretched x = 0.05 m pushes back with F = 100 × 0.05 = 5 N. Double the stretch and the force doubles, which is what makes a spring a predictable, linear element.

What are the units of the spring constant k?

The spring constant k is measured in newtons per metre (N/m): it is how many newtons of force the spring produces per metre of stretch. A stiff car suspension spring might be 30000 N/m, a soft ballpoint-pen spring around 100 N/m. To find k from a measurement, divide the force by the displacement: k = F / x. Example: hang a 2 N weight and the spring stretches 0.04 m, so k = 2 / 0.04 = 50 N/m. This tool computes k for you when you enter F and x.

How do I calculate the elastic potential energy of a spring?

A stretched or compressed spring stores elastic potential energy PE = ½·k·x², measured in joules. The square means energy grows much faster than force: stretch the spring twice as far and it stores four times the energy. Example: with k = 100 N/m and x = 0.1 m, PE = 0.5 × 100 × 0.1² = 0.5 J. That is the work the spring will release when it returns to its natural length, which is why a longer pull on a slingshot launches a projectile much faster, not just a bit faster.

What is the elastic limit and why does Hooke's law stop working?

Hooke's law is linear only up to the material's elastic limit, the point past which it no longer springs all the way back. Stretch a steel spring gently and it returns to shape, so F = k·x holds. Pull it too far and it yields: it stays permanently longer and the force no longer tracks the displacement. Example: a paperclip bends elastically for a tiny nudge but stays bent once you pass its yield point. Treat the numbers from this calculator as valid only while the spring is operating within its elastic range.

How do I solve for the displacement x or the spring constant k?

Rearrange F = k·x. To find displacement, divide force by the spring constant: x = F / k. Example: a 5 N force on a 100 N/m spring gives x = 5 / 100 = 0.05 m, or 5 cm. To find the spring constant, divide force by displacement: k = F / x, so 5 N over 0.05 m gives k = 100 N/m. This tool does the rearranging automatically: enter the two values you know and the third field fills in, with the energy ½kx² shown alongside.

Why is the real spring force often written with a minus sign, F = −k·x?

Physics textbooks write F = −k·x for the restoring force, the force the spring exerts on whatever is attached to it. The minus sign means the force points opposite to the displacement: pull the spring right and it pulls back left. This calculator reports the magnitude of that force, the size without the direction, because that is what you usually want for sizing a spring or computing energy. Example: stretch a 200 N/m spring by 0.1 m and it pulls back with 20 N toward its rest position. The energy ½kx² is always positive regardless of direction.

Find the spring constant from a physics lab measurement

You hang known masses on a spring and record how far it stretches. Convert the weight to newtons (mass × 9.81) and read off the stretch, then enter F and x to get k = F / x. Do it for several masses and the k values should agree, which is your check that the spring is behaving within its elastic limit. Example: a 0.5 kg mass (4.9 N) stretches the spring 0.049 m, so k ≈ 100 N/m. Share the URL with your lab partner and the numbers reopen exactly as you entered them.

Size a return spring for a mechanism

A latch needs to snap back with at least 8 N when it travels 12 mm. Enter F = 8 N and x = 12 mm (the tool converts to 0.012 m) and read the required spring constant, about 667 N/m. Now you can shop a catalogue spring whose rate meets or beats that figure, and the elastic-energy readout tells you how much the spring will store and release on each cycle so you can judge wear and snap speed.

Compute the energy stored in a compressed spring

A toy launcher compresses a 300 N/m spring by 4 cm. Enter k and x, switch displacement to centimetres, and the tool returns the force at full compression plus PE = ½kx² = 0.24 J. That stored energy is what converts into the projectile's kinetic energy at release, so you can estimate launch speed by pairing this with a kinetic-energy calculation. Longer compression stores disproportionately more energy because of the x² term.

Teach Hooke's law and the elastic limit in class

Walk students through F = k·x by solving the same spring three ways: give F and k to find x, then F and x to find k, then k and x to find F. The energy term ½kx² shows up alongside every solve, so the link between force, displacement and stored energy becomes concrete. Pair it with a reminder that all of this only holds below the elastic limit, where a real spring stops springing back.

Check a suspension or trampoline spring rate

A trampoline spring is quoted to stretch 0.2 m under a 240 N pull. Enter F and x to confirm its rate, k = 1200 N/m, then read the potential energy it stores at that stretch, 24 J, which is the energy returned to the jumper on the way up. Comparing spring rates this way helps you decide whether a replacement spring will feel softer or stiffer than the original.

Hooke's Law Calculator (F = k·x Spring Solver)

F = k·x spring calculator: solve any one of force, spring constant or displacement from the other two, plus elastic potential energy ½kx² — browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Enter any two of force, spring constant and displacement. The third is solved instantly, with the elastic potential energy ½kx² alongside.

Examples

Solve for

Spring constant k

N/m

Displacement x

Result

Force F (N)

Spring constant k (N/m)

100

Displacement x (cm)

Elastic potential energy (PE = ½kx²)

0.125 J

Formula used

F = k · x

Hooke’s law F = k·x holds only within the elastic limit, where the spring returns to its natural length. Past the yield point a real spring deforms permanently and these numbers no longer apply.

What this tool does

Free Hooke's law calculator that turns the spring equation F = k·x into a three-way solver. Enter any two of spring force F (newtons), spring constant k (newtons per metre) and displacement x (the stretch or compression), and it returns the third. The same inputs also give the elastic potential energy stored in the spring, PE = ½·k·x², so you can read off how much work the spring will release when it springs back. Displacement accepts metres, centimetres or millimetres and the value is converted to SI before the math runs, which keeps a "spring compressed 3 cm" question in the units you actually measured. Every answer carries one-click copy and a shareable URL that reopens the exact calculation. Hooke's law holds only within the elastic limit of the material, so the tool is for springs and elastic bodies that return to their original shape, not for plastic deformation past the yield point. Everything runs in your browser with no upload and no account.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Hooke's Law Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Find the spring constant from a physics lab measurement
You hang known masses on a spring and record how far it stretches. Convert the weight to newtons (mass × 9.81) and read off the stretch, then enter F and x to get k = F / x. Do it for several masses and the k values should agree, which is your check that the spring is behaving within its elastic limit. Example: a 0.5 kg mass (4.9 N) stretches the spring 0.049 m, so k ≈ 100 N/m. Share the URL with your lab partner and the numbers reopen exactly as you entered them.
Size a return spring for a mechanism
A latch needs to snap back with at least 8 N when it travels 12 mm. Enter F = 8 N and x = 12 mm (the tool converts to 0.012 m) and read the required spring constant, about 667 N/m. Now you can shop a catalogue spring whose rate meets or beats that figure, and the elastic-energy readout tells you how much the spring will store and release on each cycle so you can judge wear and snap speed.
Compute the energy stored in a compressed spring
A toy launcher compresses a 300 N/m spring by 4 cm. Enter k and x, switch displacement to centimetres, and the tool returns the force at full compression plus PE = ½kx² = 0.24 J. That stored energy is what converts into the projectile's kinetic energy at release, so you can estimate launch speed by pairing this with a kinetic-energy calculation. Longer compression stores disproportionately more energy because of the x² term.
Teach Hooke's law and the elastic limit in class
Walk students through F = k·x by solving the same spring three ways: give F and k to find x, then F and x to find k, then k and x to find F. The energy term ½kx² shows up alongside every solve, so the link between force, displacement and stored energy becomes concrete. Pair it with a reminder that all of this only holds below the elastic limit, where a real spring stops springing back.
Check a suspension or trampoline spring rate
A trampoline spring is quoted to stretch 0.2 m under a 240 N pull. Enter F and x to confirm its rate, k = 1200 N/m, then read the potential energy it stores at that stretch, 24 J, which is the energy returned to the jumper on the way up. Comparing spring rates this way helps you decide whether a replacement spring will feel softer or stiffer than the original.

Common pitfalls

Forgetting to convert displacement to metres. The spring constant is in newtons per metre, so a stretch typed as "3 cm" must become 0.03 m before it goes into F = k·x. Entering 3 instead of 0.03 inflates the force a hundredfold. This tool's centimetre and millimetre options convert for you, but if you compute by hand, get everything into SI first.
Confusing weight in grams or kilograms with force in newtons. The force in F = k·x is a force, not a mass. A 200 g mass does not push with 200 of anything useful here; its weight is 0.2 kg × 9.81 = 1.96 N. Convert mass to newtons before entering it as F, or your spring constant will be off by a factor of about ten.
Trusting the formula past the elastic limit. F = k·x is linear only while the spring springs all the way back. Stretch it past its yield point and the real force is lower than k·x predicts and the spring is permanently deformed. If your displacement is large relative to the spring's free length, the calculator's number is an idealisation, not a measurement.

Privacy

Every calculation here, the F = k·x solve, the unit conversion and the elastic-energy term, is plain JavaScript that runs in your browser tab. The force, spring constant and displacement values never reach a server, and there is no logging of what you compute. The one caveat: the shareable URL encodes your inputs and chosen mode in the query string, so a "share link" pasted into chat records those numbers in the recipient server's access log. Spring figures are rarely sensitive, but if you would rather not expose them, use the copy button and paste the text instead.

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Hooke's Law Calculator (F = k·x Spring Solver)

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Hooke's Law Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Find the spring constant from a physics lab measurement

Size a return spring for a mechanism

Compute the energy stored in a compressed spring

Teach Hooke's law and the elastic limit in class

Check a suspension or trampoline spring rate

Common pitfalls

Privacy

FAQ

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