Orbital Distance Calculator
Kepler’s third law links three quantities: how far an object orbits, how long one orbit takes, and how massive the central body is. Know any two and you can find the third. This calculator solves for distance, orbital period, or central mass, with built-in unit conversion and one-click presets for the Sun, Earth, Moon, Mars, and Jupiter.
Kilometers
Astronomical units
Miles
Quick Answer
A body with a 365.25-day orbit around the Sun sits 149,610,785 km from it, or 1.000086 AU. The 0.01% gap to exactly 1 AU comes from the rounded preset masses, not the math. The tool is pre-filled with this exact case: 365.25 days and the Sun preset, so one click reproduces it.
Key takeaways
- One equation, three questions: r³ = G × M × T² ÷ (4π²). Each tab solves it for a different unknown.
- Distance is measured from the central body’s center, not its surface. A 90-minute satellite is 6,652 km from Earth’s center, which is only 281 km of altitude.
- Preset masses are rounded published values, so Earth lands at 1.000086 AU instead of exactly 1. Pick Custom mass for exact work.
- The formula assumes a circular orbit. For an elliptical orbit the answer is the semi-major axis, the standard average-distance measure.
6.67430 × 10⁻¹¹
Gravitational constant G, m³ kg⁻¹ s⁻² (NIST CODATA value)
149,597,870.7 km
One astronomical unit, exact by definition since 2012
1.000086 AU
What the tool gives for Earth’s 365.25-day orbit with the rounded Sun preset
How to use the orbital distance calculator
Pick the tab that matches your unknown, check the pre-filled example, then swap in your own numbers. Results stay hidden until you click Calculate.
- Find distance: enter an orbital period and pick the central body (or type a custom mass in kg). You get the distance in meters, kilometers, AU, and miles. Pre-filled: 365.25 days around the Sun.
- Find period: enter a distance with its unit and pick the central body. You get the period in seconds, days, hours, and years. Pre-filled: 1 AU around the Sun, which returns 365.203 days.
- Find mass: enter a distance and a period. You get the central mass in kg plus Earth and Sun masses. Pre-filled: the Moon’s 384,400 km and 27.32 days, which returns 1.0097 Earth masses.
- Units are free: periods accept seconds through years, distances accept meters through miles, so a question like “how far out is a 90-minute satellite?” needs no hand conversion. The readout already spans meters, km, AU, and miles; for anything further afield the miles to km calculator and the meter to feet calculator cover the rest.
- Copy or share from the results box: the copied text restates the full result with all three distance units, so a shared number never arrives without its context.
The formula: Newton’s form of Kepler’s third law
The square of the orbital period is proportional to the cube of the orbital distance: T² × (G × M) = 4π² × r³. Every tab in this calculator is that one relation, rearranged.
Period = √(4π² × r³ ÷ G × M)
Central mass = 4π² × r³ ÷ (G × T²)
G is the Newtonian constant of gravitation, 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², the CODATA value published by NIST. M is the central mass, T the period in seconds, r the distance in meters from the central body’s center. Kepler published the proportional form in 1619 from Tycho Brahe’s observations; Newton later showed it follows from universal gravitation, as Britannica’s account of Kepler’s laws and the HyperPhysics derivation both explain. Two honest limits: the orbiting body’s own mass is ignored (fine everywhere except binary stars, where you should use the sum of both masses), and r is the semi-major axis, so for eccentric orbits it is the average distance, not the closest or farthest point. Once you have the radius, the energy side of the same orbit is a short step away with the kinetic energy formula calculator: a 90-minute satellite at 6,652 km from Earth’s center moves at about 7.74 km/s.
Worked example: Earth around the Sun, verified against the tool
The pre-filled Find distance run uses period 365.25 days and the Sun preset (1.989 × 10³⁰ kg). Every number below is the calculator’s own output.
- Orbital distance = 149,610,784,913 m, shown as 149,610,785 km, 1.000086 AU, 92,963,832 mi
- The defined AU is 149,597,870.7 km, so the tool lands 0.01% high. That gap is the rounded preset mass, not an error in the law: type the unrounded solar mass as a custom mass and the gap shrinks.
- Light crosses that gap in about 8 minutes 20 seconds, which is why the AU doubles as a travel-time unit in the light speed distance calculator.
Three more checks, each a separate run of the tool:
- The Moon around Earth: 27.32 days with Earth’s mass gives 383,164.17 km, within half a percent of the Moon’s 384,400 km mean distance.
- Low Earth orbit: 90 minutes with Earth’s mass gives 6,652.49 km from Earth’s center, about 281 km of altitude, matching real LEO altitudes and the ISS’s 90 to 93 minute period.
- Reverse checks: 1 AU around the Sun in Find period returns 365.203 days; 384,400 km and 27.32 days in Find mass returns 6.0300 × 10²⁴ kg, or 1.0097 Earth masses.
The table below runs every planet through Find distance with its real orbital period (periods and accepted distances from NASA’s planetary fact sheet). Each row is a separate tool run with the Sun preset.
| Planet | Orbital period (days) | Tool result (AU) | Accepted (AU) |
|---|---|---|---|
| Mercury | 87.97 | 0.3871 | 0.39 |
| Venus | 224.70 | 0.7234 | 0.72 |
| Earth | 365.25 | 1.0001 | 1.00 |
| Mars | 686.98 | 1.5238 | 1.52 |
| Jupiter | 4,332.59 | 5.2017 | 5.20 |
| Saturn | 10,759.22 | 9.5389 | 9.58 |
| Uranus | 30,688.5 | 19.1850 | 19.22 |
| Neptune | 60,182 | 30.0577 | 30.05 |
Planetary distances from the tool (logarithmic scale, AU)
What competing calculators miss
The ranking Kepler tools each do one slice of the job well and stop there:
- BraveCalculator: clean formula teaching with a geostationary worked example, but inputs are raw SI only: seconds and kilograms with exponents. A 90-minute satellite question becomes a manual conversion exercise first.
- Calculator Ultra (Kepler’s Third Law): solves all three variables with solid historical background, but no central-body presets and no unit selection beyond the basics.
- CalculatorLabs (Orbital Radius from Period): frames the answer as the semi-major axis, which is the honest quantity, but again seconds and kilograms only.
- OmniCalculator (Kepler’s Third Law): the best interactive teaching of the set, with a worked Mars example, but fixed in a solar-system frame of years and AU, with no custom masses.
- GEGCalculators: headlines the relation as r ≈ (T²)⅓, which is only true in AU and years around the Sun, and never says so. Dimensionally it is wrong as a general formula.
- SatNow: dead simple P² = D³ in AU and years, which is fine for planets around the Sun and useless for anything else: no mass term at all.
- The gap this page fills: all three variables like Calculator Ultra, unit selection on every input like nobody else, one-click presets for the five bodies people actually ask about, and outputs in four distance units at once, with the rounding honestly labeled instead of hidden.
Frequently asked questions
r = cube root of (G × M × T² ÷ 4π²), where G is the gravitational constant (6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²), M the central mass in kilograms, and T the orbital period in seconds. The answer r is the distance in meters from the central body’s center.
One astronomical unit is exactly 149,597,870.7 km by definition, roughly Earth’s average distance from the Sun. Light takes about 8 minutes 20 seconds to cross it.
Yes, approximately: r then represents the semi-major axis, the standard average distance over one orbit. For a circle the semi-major axis is just the radius; for a stretched ellipse the body swings closer and farther than this average.
Because it is negligible next to the central body in almost every case: Earth is 333,000 times lighter than the Sun. For two comparable masses, such as binary stars, use the sum of both masses as M.
About 90 to 93 minutes at roughly 400 km altitude. Try 90 minutes with Earth’s mass in the Find distance tab: the tool returns 6,652 km from Earth’s center, which is 281 km of altitude once you subtract Earth’s radius.
Convert the period to seconds, square it, multiply by G and the central mass in kilograms, divide by 4π², and take the cube root. The result is in meters. The calculator does this instantly and converts the units for you.
Distance in meters, kilometers, AU, and miles; period in seconds, days, hours, and years; mass in kilograms plus Earth and Sun masses. Inputs accept the same unit families, so no hand conversion is needed on either side.
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References
- National Institute of Standards and Technology. Newtonian constant of gravitation. CODATA recommended value. Accessed October 23, 2026.
- Encyclopaedia Britannica. Gravitational constant. Accessed October 23, 2026.
- NASA, National Space Science Data Center. Planetary Fact Sheet. Accessed October 23, 2026.
- NASA Science, Solar System Exploration. Planets overview. Accessed October 23, 2026.
- NASA StarChild. What is Kepler’s third law? Accessed October 23, 2026.
- NASA Jet Propulsion Laboratory, Center for Near Earth Object Studies. Astronomical unit (AU) glossary entry. Accessed October 23, 2026.
- EarthSky. What is the astronomical unit? Accessed October 23, 2026.
- Georgia State University, HyperPhysics. Kepler’s Third Law. Accessed October 23, 2026.
- Encyclopaedia Britannica. Kepler’s laws of planetary motion. Accessed October 23, 2026.
- OpenStax, Astronomy 2e. The Laws of Planetary Motion. Accessed October 23, 2026.