MasterTool

Orbital Velocity Calculator

Calculate orbital velocity instantly in your browser — the published formula, worked locally with no data sent anywhere.

NASA planetary masses and radii last updated · reference source

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Dated static reference; no live data is fetched. Verify current source values and assumptions before relying on results.

What this tool does

Calculate orbital velocity instantly in your browser — the published formula, worked locally with no data sent anywhere. Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.

How to use the Orbital Velocity Calculator

  1. Enter or select body.
  2. Enter or select orbit altitude above the surface (km).
  3. Read the calculated result; change any measurement to compare alternatives.

Formula

circular-orbit velocity v = √(GM/r) (Kepler: period T = 2πr/v, so T² ∝ r³); r is measured from the body's centre — surface radius plus altitude, using NASA factsheet masses and radii.
planet
Body
altKm
Orbit altitude above the surface (km)

Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.

Worked example

For orbital velocity calculator, the following measurements illustrate the exact method: Body: earth; Orbit altitude above the surface (km): 0.

Inputs

  • BodyEarth
  • Orbit altitude above the surface (km)0

Result

  • Orbital velocity (km/s)7.91
  • Orbital velocity (m/s)7,909.5
  • Orbital period (minutes)84.35
  • Orbital period (hours)1.41
  • Escape velocity at this radius (km/s)11.19

Results explained

Orbital velocity (km/s)
Orbital velocity (km/s) from the formula above. Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.
Orbital velocity (m/s)
Orbital velocity (m/s) from the formula above. Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.
Orbital period (minutes)
Orbital period (minutes) from the formula above. Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.
Orbital period (hours)
Orbital period (hours) from the formula above. Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.
Escape velocity at this radius (km/s)
Escape velocity at this radius (km/s) from the formula above. Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.

Frequently asked questions

circular-orbit velocity v = √(GM/r) (Kepler: period T = 2πr/v, so T² ∝ r³); r is measured from the body's centre — surface radius plus altitude, using NASA factsheet masses and radii.

Circular orbit around a spherical body, ignoring atmosphere and other bodies' gravity. At Earth's surface radius this gives the theoretical 7.9 km/s 'first cosmic velocity'; real low orbits (~400 km) need about 7.67 km/s.

Every field is labelled with its unit — enter values in exactly the labelled unit and read the result in the labelled output unit. Fields with a unit symbol also support the site-wide imperial/metric switch, which converts before the formula runs.

It uses double-precision arithmetic and the published constants and formulas named on this page. The last displayed digit may be rounded, and real conditions can differ from the idealized model described in the assumptions.

Yes. Every calculation runs entirely in your browser; nothing you enter is uploaded, stored or shared.