Skip to content
ENExplore Calculators

Planet Orbital Period (Kepler) Calculator

Work out planet orbital period (kepler) instantly with clear inputs, formula shown and shareable results.

About Planet Orbital Period (Kepler) Calculator

Kepler's third law in solar units is beautifully simple: the period in years is the square root of the semi-major axis in AU cubed, divided by the central mass in solar masses. Mars at 1.524 AU gives 1.881 years, or 687 days, with a mean orbital speed of 24.1 km/s. Period squared equals axis cubed exactly for a one solar mass primary.

Formulas

Kepler's third law

T^2 = a^3 / M, with T in years, a in AU and M in solar masses

Circular orbital velocity

v = sqrt(GM / a)

Worked example

With the default values below, Planet Orbital Period (Kepler) Calculator returns Orbital Period of 1.8814. Change any input above and every figure here is recalculated in your browser.

Inputs used

Semi-major axisminimum 0 AU
1.524 AU
Central body massminimum 0 solar masses
1 solar masses

Results

Orbital Period
1.8814 years
Same Period In Days
687.2
Mean Orbital Velocity
24.130 km/s
Period Squared
3.5396

Step by step

  1. 1Values used
  2. 2Kepler's third law
  3. 3Circular orbital velocity
  4. 4Orbital Period= 1.8814 years
  5. 5Same Period In Days= 687.2
  6. 6Mean Orbital Velocity= 24.130 km/s
  7. 7Period Squared= 3.5396

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does the law take such a simple form in AU and years?

Because Earth's orbit is defined as 1 AU and 1 year around 1 solar mass, so all the constants become one.

Does the orbiting body's mass matter?

Only slightly. Strictly the sum of both masses appears, but for planets around stars the planet's contribution is negligible.

Related Calculators

Planet Orbital Period (Kepler) Calculator | Calcrivo