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Orbital Period

T=2πr3GMT = 2\pi \sqrt{\frac{r^{3}}{GM}}
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Worked example: Geostationary: r = 42 164 km around Earth → T = 86 164.8 s. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter
G=6.6743×10−11 m3/(kg⋅s2)G = 6.6743 \times 10^{-11}\ \text{m}^{3}\text{/(kg}{\cdot}\text{s}^{2}\text{)}Newtonian constant of gravitation

Where Orbital Period fits

Your answer feeds
Kepler's Third Law (Ratio Form)
In this toolkit

See also

Escape Velocity: Both use orbital radius and central mass.Gravitational Field Strength: Both use orbital radius and central mass.Gravitational Potential Energy (Orbital): Both use orbital radius and central mass.Orbital Velocity: Both use orbital radius and central mass.Kepler's Third Law (Ratio Form): Both use orbital period.Period-Frequency Relation: Both use orbital period.
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Orbital Period explained

MrT

Kepler noticed in 1619 that the square of a planet's year grows with the cube of its distance from the Sun; Newton later showed why: gravity's inverse-square pull makes T² = 4π²r³/(GM). A worked example: a geostationary satellite must orbit once per sidereal day, T = 86 164 s, so r=(GMT2/4π2)1/3r = (GMT^2/4\pi^2)^{1/3} = (6.674×10−11×5.97×1024×86 1642/39.48)1/3(6.674 \times 10^{-11} \times 5.97 \times 10^{24} \times 86\,164^2 / 39.48)^{1/3} ≈ 4.22 × 10⁷ m, the 35 800 km altitude where every TV broadcast satellite parks.

The rearrangement for M is one of astronomy's sharpest tools: watch anything orbit, time it, measure the orbit's size, and the central mass falls out. The Moon's 27.3-day circuit at 3.84 × 10⁸ m weighs the Earth; Jupiter's moons weigh Jupiter; and the 16-year orbit of the star S2 around Sagittarius A* revealed a central mass of four million Suns packed into a region smaller than our solar system: a black hole.

Orbital Period formula

T=2πr3GMT = 2\pi \sqrt{\frac{r^{3}}{GM}}
Where
  • TT= Orbital period (s)
  • rr= Orbital radius (m)
  • MM= Central mass (kg)
In this toolkit

Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.

Revised 16 October 2026
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formula.expert. (2026, October 16). Orbital Period Formula & Calculator. https://formula.expert/solvers/orbital-period

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