Earth Orbit Calculator - Speed and Period from Altitude

The earth orbit calculator estimates the orbital speed and orbital period of a satellite circling Earth at a chosen altitude, using Newton's form of Kepler's third law and the standard gravitational parameter of Earth.

• • ISS orbit check: Type 400 km to read the orbital speed and 92.4-minute period of the International Space Station in one panel.
• • GPS constellation timing: Type 20,200 km to verify the 12-hour half-day period used by the GPS satellite constellation.
• • Geostationary belt planning: Type 35,786 km to confirm the altitude that gives a 23 h 56 min sidereal-day period for geostationary satellites.
• • Physics and astronomy homework: Plug in textbook altitudes to check the inverse-square relationship between orbital speed and orbital radius.

The earth orbit calculator treats the orbit as circular. That assumption matches the ISS, the GPS constellation, and most operational satellites because their eccentricity is below 0.05.

The two outputs answer different questions. Orbital speed tells you how fast the satellite is moving, which sizes a tracking antenna or a rendezvous burn. Orbital period tells you how long it takes to come back over the same point, which drives revisit time and constellation spacing.

Both numbers come from the same two inputs - altitude and Earth itself. The calculation pins the central body to Earth, so you do not need to enter the gravitational constant or Earth's mass.

When you already know the orbital radius and only need the period, the Orbital Period Calculator skips the speed panel and goes straight to T = 2 pi sqrt(a^3 / mu) for any central body.

The calculator takes your altitude, adds Earth's mean radius to get the orbital radius, divides the standard gravitational parameter by that radius to get orbital speed squared, and applies the same root three times to orbital radius to get orbital period.

• h: Altitude of the satellite above Earth's mean sea level, entered in kilometers and converted to meters inside the formula.
• R_E: Mean radius of Earth, 6,371,000 m (6,371 km), from the NASA Earth fact sheet.
• r = R_E + h: Orbital radius, the distance from Earth's center to the satellite, the only length that matters for circular orbital motion.
• G: Newtonian gravitational constant, 6.6743e-11 m^3 / (kg s^2), from NIST CODATA 2018.
• M_E: Mass of Earth, 5.9722e24 kg, from the NASA Earth fact sheet.
• mu = G * M_E: Standard gravitational parameter of Earth, 3.986004418e14 m^3/s^2, the shortcut NASA uses for Earth orbit math.

Orbital speed is v = sqrt(mu / r). Doubling the orbital radius cuts the speed by sqrt(2), which is why a GPS satellite at 20,200 km moves at about half the speed of the ISS at 400 km.

Orbital period is T = 2 pi sqrt(r^3 / mu). The cube inside the square root is what makes period grow so fast with altitude: a doubling of orbital radius adds a factor of sqrt(8) ≈ 2.83 to the period.

The two-body Kepler formula is the starting point every engineer uses first, even at geostationary altitude where solar and lunar perturbations matter.

According to Wikipedia Circular Orbit, for a circular orbit the orbital speed is v = sqrt(GM/r) and the orbital period is T = 2 pi sqrt(r^3/GM)

The speed and period formulas above come straight from Newton's law of gravitation and the second law of motion, and the Forces Newton's Laws Calculator is the right tool when you need to see the force, mass, and acceleration values that balance the orbit at the same altitude.

Four ideas show up in every derivation of orbital speed and period. Knowing them turns the calculator from a black box into a tool you can reason about.

Two of those ideas sit behind the input layout. Picking altitude instead of orbital radius keeps the calculator usable for someone planning a satellite.

If you compare Earth-orbit numbers with lunar or planetary orbits, the only quantity that changes is mu. The rest of the formula is the same shape, which is why a single orbital-period-calculator can handle Earth, the Moon, and Mars.

The same gravitational potential that drives the orbit also slows clocks at lower altitudes, and the Gravitational Time Dilation Calculator shows how that effect scales between an ISS orbit and a GPS orbit.

Type the altitude of the satellite you care about, watch the result panel update, and read both outputs in the units that match your workflow.

1. 1 Pick the satellite altitude: Type the altitude in kilometers. Use 400 for the ISS, 20,200 for GPS, 35,786 for geostationary, or 384,400 for the Moon.
2. 2 Read orbital speed: Look at the primary orbital speed value in km/s, then at the m/s and mph lines below it for ground-station or reporting contexts.
3. 3 Read orbital period: Check the period in minutes for low Earth orbit work, in hours for medium and high altitude orbits, and in days for the Moon and beyond.
4. 4 Spot-check with a known satellite: Confirm the calculator with the ISS (92.4 min), GPS (about 12 h), or geostationary (23 h 56 min) before trusting an unfamiliar altitude.
5. 5 Use Reset for a clean re-run: Hit Reset to return to the 400 km default and clear any error state before entering the next altitude.

An aerospace engineering student is asked to find the orbital period at the GPS constellation altitude. Entering 20,200 km returns about 11 h 58 min, which rounds to the published 12-hour sidereal period and confirms the calculation.

After you read the orbital speed for your satellite, the Drift Velocity Calculator is the next step when you want to size a station-keeping or rendezvous burn relative to the same spacecraft.

A focused earth orbit calculator removes the unit-conversion noise from textbook and mission-planning work, so the numbers come out in the right unit on the first try.

• • Speed and period in one panel: enter one altitude and read orbital speed in km/s, m/s, and mph plus period in minutes, hours, and days at the same time.
• • Kepler's third law built in: the formula is wired in with NIST G and NASA Earth mass, so you do not need to look up constants or convert them by hand.
• • Works across the whole altitude range: from a theoretical circular orbit at sea level to the Moon at 384,400 km, the same two formulas apply.
• • Direct unit conversions: km/s to m/s and mph, and minutes to hours and days, are computed inside the result panel so you do not need a second calculator.
• • Spot-check with familiar satellites: the 400 km default makes the ISS a built-in sanity check, and switching to 20,200 or 35,786 km covers GPS and geostationary references.

Pick a single altitude source for every comparison. The calculator always reads h above mean sea level and uses R_E = 6,371 km, so two runs with the same altitude give the same answer.

Use the period in hours when you compare medium-altitude satellites. GPS at about 12 hours is half a sidereal day, so the constellation geometry repeats every other orbit.

For ground-station or horizon calculations that sit beside an orbital-speed result, the Earth Curvature Calculator gives the line-of-sight geometry across the same Earth radius used in this calculator.

Four quantities set the two outputs the calculator returns. Three of them are baked in; the altitude is the one the user controls.

• • Atmospheric drag below about 200 km makes any 'circular orbit' assumption break down quickly. The calculator returns the two-body answer, but the satellite will not stay there for long.
• • Beyond roughly 100,000 km, solar and lunar gravity are strong enough that a pure two-body Kepler treatment overstates how stable the orbit is. For lunar-distance orbits, use a dedicated lunar-orbit tool.
• • Earth's actual gravity is not perfectly spherical. The J2 zonal harmonic adds an altitude-dependent correction that the calculator ignores, which can shift low-altitude periods by tens of seconds.

Treat the calculator as a clean two-body reference. It gives the answer a textbook problem expects and the answer an aerospace engineer uses as the first cut before adding perturbations.

According to NASA Earth Fact Sheet, the standard gravitational parameter mu = G M_E = 3.986004418e14 m^3/s^2 and the mean Earth radius R_E = 6,371 km are the NASA-published values that anchor Earth-orbit calculations.

According to NIST CODATA, the Newtonian gravitational constant is G = 6.67430 × 10^-11 m^3 / (kg s^2), the value used to derive Earth's standard gravitational parameter mu.