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Spring constant calculator (Hooke's law)

Hooke's law three ways: solve for the spring constant k = F/x, the restoring force F = k·x, or the displacement x = F/k. It handles single springs and N identical springs in series (k/N) or parallel (N·k), and adds the stored elastic energy ½kx².

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Need Result, Effective k (N/m), Elastic energy (J)? The Spring constant calculator (Hooke's law) derives it from Solve for, Configuration, Number of springs N, Force F (N), Displacement x (m), Spring constant k (N/m) in one step. For instance, with Solve for = Spring constant k, Configuration = Single spring, Number of springs N = 2, Force F (N) = 50, Displacement x (m) = 0.1 and Spring constant k (N/m) = 500 it returns Result = 500, Effective k (N/m) = 500 and Elastic energy (J) = 2.5.

How to use it

  1. Enter your values: Solve for, Configuration, Number of springs N, Force F (N), Displacement x (m), Spring constant k (N/m).
  2. Read the result instantly: Result, Effective k (N/m), Elastic energy (J).

Frequently asked questions

What does the Spring constant calculator (Hooke's law) actually compute?

It takes Solve for, Configuration, Number of springs N, Force F (N), Displacement x (m) and Spring constant k (N/m) and derives Result, Effective k (N/m) and Elastic energy (J) from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

6 values: Solve for, Configuration, Number of springs N, Force F (N), Displacement x (m) and Spring constant k (N/m). Nothing else is required — no account, no file upload.

Can you show a worked example?

With Solve for = Spring constant k, Configuration = Single spring, Number of springs N = 2, Force F (N) = 50, Displacement x (m) = 0.1 and Spring constant k (N/m) = 500, the calculator returns Result = 500, Effective k (N/m) = 500 and Elastic energy (J) = 2.5. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Solve for = Force F, Configuration = N in series (k/N), Number of springs N = 4, Force F (N) = 100, Displacement x (m) = 0.2 and Spring constant k (N/m) = 1,000 instead, Result goes from 500 to 50 — which is why it is worth testing a few scenarios rather than trusting a single figure.

Which “Solve for” option should I choose?

You can pick between « Spring constant k », « Force F » and « Displacement x ». Each one changes what the calculator works out, so switch and compare — the default is « Spring constant k ».

What does it give for smaller values?

Scaled down to Solve for = Spring constant k, Configuration = Single spring, Number of springs N = 1, Force F (N) = 25, Displacement x (m) = 0.05 and Spring constant k (N/m) = 250, Elastic energy (J) comes out at 0.625. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Checking a homework answer, sizing something before building it, and getting an order of magnitude before committing to a design — a torque on a bolt, the force a spring returns, the frequency a circuit resonates at, how long light takes to arrive.

What is the most common mistake?

Feeding in a value in the wrong unit. Physics formulas assume SI throughout, so grams instead of kilograms or centimetres instead of metres shifts the answer by powers of ten without any warning.

What is the difference between the Spring constant calculator (Hooke's law) and the Hooke's law calculator?

This one returns Result and Effective k (N/m); the Hooke's law calculator returns Spring force (N). That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Spring potential energy calculator is the closest one after this: Compute the elastic potential energy stored in a spring (E = ½kx²).

Further reading

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ExplainerHooke's Law Explained: F = kx, Real Spring Constants, and Where It Stops HoldingHooke's law says force is proportional to stretch — but only below the elastic limit. Here is F = kx with worked numbers, what a 200 N/m spring actually feels like, and how springs combine.ExplainerHow Buoyancy Works: Archimedes' Principle, and Why Ice Floats With 10.5 % Above WaterThe upward force equals the weight of the fluid pushed aside. That one sentence decides whether something floats, and if it floats, exactly how much of it stays under.ExplainerHow the Doppler Effect Works: The Formula, the Sign Convention, and Why Moving the Source Is Not the Same as Moving the ListenerFor sound, f' = f(v + v_o)/(v − v_s) — and getting the signs backwards is the classic error. Here is the convention spelled out, a 440 Hz source computed at four speeds, and why light needs a different equation entirely.ExplainerWhat Is the Reynolds Number? The Formula, the Units That Cancel, and Why 2 300 Is Only for PipesRe = ρvL/μ compares inertia with viscosity, and the units really do cancel. See the number worked out for honey, a household pipe, an artery, a swimmer and a wing — and why the 2 300 threshold belongs to pipe flow alone.GuideThe Four Kinematics Equations: Which One to Use, and What Each One Leaves OutFive variables, four equations, and each equation is missing exactly one of them. Choose by looking at the variable the question never mentions.ExplainerProjectile Motion Explained: Range, Height, Flight Time — and Why 45° Is Not Always BestThree formulas cover the whole of projectile motion on level ground. The catch is level ground: the moment launch and landing heights differ, the 45° result stops being true.