Orbital Velocity Calculator

Calculate circular orbital velocity (v = √(GM/r)) or elliptical velocity using the vis-viva equation. Covers LEO, GEO, and transfer orbit speeds.

kg
m
Orbital Velocity
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Escape Velocity —
Orbital Period —
Extended More scenarios, charts & detailed breakdown ▾
kg
m
Orbital Velocity
—
Escape Velocity —
Period —
Professional Full parameters & maximum detail ▾
kg
m
m

Velocities

Orbital Velocity (vis-viva) —
Escape Velocity at r —

Angular & Energy

Angular Velocity ω —
Specific Orbital Energy —

Period

Orbital Period —

How to Use This Calculator

  1. Enter the central body mass and orbital radius for circular orbital velocity.
  2. Switch to Vis-Viva tab for elliptical orbits (also enter semi-major axis).
  3. Use Earth Orbits tab for quick LEO/GEO/Lunar results.
  4. Professional tier adds angular velocity, specific orbital energy, and period.

Formula

Circular: v = √(GM/r)

Elliptical (vis-viva): v = √(GM(2/r − 1/a))

Escape velocity ratio: v_esc = v_orb × √2

Example

ISS: M_Earth = 5.972×10²⁴ kg, r = 6779 km → v = √(6.674×10⁻¹¹ × 5.972×10²⁴ / 6.779×10⁶) ≈ 7.66 km/s

Frequently Asked Questions

  • Orbital velocity is the speed needed to maintain a stable circular orbit: v = √(GM/r), where G is the gravitational constant, M is the central body mass, and r is the orbital radius from the center.
  • The vis-viva equation gives velocity at any point in an elliptical orbit: v = √(GM(2/r − 1/a)), where r is the current distance and a is the semi-major axis. For circular orbits r = a and it reduces to v = √(GM/r).
  • The ISS orbits at about 408 km altitude with radius ~6779 km from Earth's center. Its orbital velocity is approximately 7.66 km/s (27,576 km/h).
  • GEO is at 35,786 km altitude (radius ~42,164 km from Earth's center). Orbital velocity there is approximately 3.07 km/s.
  • Escape velocity = orbital velocity × √2 at the same radius. To escape from LEO (~7.8 km/s orbital), you need the orbital velocity plus an additional ~3.2 km/s delta-v.

Related Calculators

🚀 Escape Velocity Calculator 🌍 Orbital Period Calculator ⚖️ Surface Gravity Calculator 🌌 Gravitational Force Calculator
Sources & References (5) ▾
  1. Orbital Mechanics — NASA Space Place — NASA
  2. Mission Design — NASA JPL — NASA Jet Propulsion Laboratory
  3. University Physics Vol. 1 — Satellite Orbits and Energy — OpenStax
  4. Vis-viva Equation — HyperPhysics — Georgia State University HyperPhysics
  5. JPL Horizons — Solar System Dynamics — NASA JPL