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Physics

Kepler 3rd Law

T² = a³ (in AU and years). Free online Kepler 3rd Law. Calculate kepler 3rd law online — fast, accurate, mobile-friendly, no signup needed.

Orbital period (years)
1

Derivation

  1. ├── 01Givena = 1
  2. ├── 02Formula√((t)^(3))
  3. └── 03Compute Orbital period (years)1
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§01What is

Understanding the Kepler 3rd Law

The Kepler 3rd Law computes Orbital period (years) from 1 input: semi-major axis (au). T² = a³ (in AU and years).

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 Kepler 3rd Law sits in that toolkit — it T² = a³ (in AU and years). 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

√((t)^(3))

Where

a
Semi-major axis (AU)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Semi-major axis (AU) = 1.

  1. 01Start by noting the input — Semi-major axis (AU): 1.
  2. 02Substitute these values into the formula: √((t)^(3))
  3. 03Compute Orbital period (years): the calculator returns 1.
  4. 04Cross-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 Kepler 3rd 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

Semi-major axis (AU) halved

a = 0.5 (from 1)

Keep every other input at its default and halve the semi-major axis (au). See how orbital period (years) responds.

  1. 01New Semi-major axis (AU): 0.5
  2. 02Baseline Orbital period (years): 1
  3. 03New Orbital period (years): 0.353553
  4. 04Orbital period (years) decreases by 64.6% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Semi-major axis (AU) doubled

a = 2 (from 1)

Keep every other input at its default and double the semi-major axis (au). See how orbital period (years) responds.

  1. 01New Semi-major axis (AU): 2
  2. 02Baseline Orbital period (years): 1
  3. 03New Orbital period (years): 2.82843
  4. 04Orbital period (years) increases by 182.8% → 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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