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Physics

Hooke's Law Calculator

F = kx. Free online Hooke's Law Calculator. Calculate hooke's law online — fast, accurate, mobile-friendly, no signup needed.

F = −k·x.
Force (N)
20

Derivation

  1. ├── 01Givenk = 200, x = 0.1
  2. ├── 02Formulae.k × e.x
  3. ├── 03Substitutee.200 × e.0.1
  4. └── 04Compute Force (N)20
Did you know?

Robert Hooke published F = −k·x in 1676 as the Latin anagram "ceiiinossssttuv" — decoded three years later as "Ut tensio, sic vis" ("as the extension, so the force").

§01What is

Understanding the Hooke's Law Calculator

The Hooke's Law Calculator computes Force (N) from 2 inputs: spring constant (n/m), displacement (m). F = kx.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Hooke's Law Calculator sits in that toolkit — it F = kx. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

e.k × e.x

Where

k
Spring constant (N/m)
x
Displacement (m)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Spring constant (N/m) = 200, Displacement (m) = 0.1.

  1. 01Start by noting the input — Spring constant (N/m): 200.
  2. 02Start by noting the input — Displacement (m): 0.1.
  3. 03Substitute these values into the formula: e.k × e.x
  4. 04Compute Force (N): the calculator returns 20.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Hooke's Law Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Spring constant (N/m) halved

k = 100 (from 200)

Keep every other input at its default and halve the spring constant (n/m). See how force (n) responds.

  1. 01New Spring constant (N/m): 100
  2. 02Baseline Force (N): 20
  3. 03New Force (N): 10
  4. 04Force (N) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Spring constant (N/m) doubled

k = 400 (from 200)

Keep every other input at its default and double the spring constant (n/m). See how force (n) responds.

  1. 01New Spring constant (N/m): 400
  2. 02Baseline Force (N): 20
  3. 03New Force (N): 40
  4. 04Force (N) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Displacement (m) halved

x = 0.05 (from 0.1)

Keep every other input at its default and halve the displacement (m). See how force (n) responds.

  1. 01New Displacement (m): 0.05
  2. 02Baseline Force (N): 20
  3. 03New Force (N): 10
  4. 04Force (N) decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Displacement (m) doubled

x = 0.2 (from 0.1)

Keep every other input at its default and double the displacement (m). See how force (n) responds.

  1. 01New Displacement (m): 0.2
  2. 02Baseline Force (N): 20
  3. 03New Force (N): 40
  4. 04Force (N) increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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