Orbital Velocity

v = \sqrt{\frac{GM}{r}}

Velocity for circular orbit at radius r.

Variables

Orbital velocity

Circular orbit speed

m/s

Gravitational constant

6.674×10⁻¹¹

In SI units: m³/(kg·s²)

Allowed values: greater than 0

N·m²/kg²

Central mass

Mass being orbited

Allowed values: greater than 0

Orbital radius

Distance from center

Allowed values: greater than 0

Derivation

Set gravitational force = centripetal force: GMm/r² = mv²/r.

Your notes

0/5000

Constants in this formula

Gravitational Constant

6.674 30 × 10⁻¹¹ ± 0.000 15 × 10⁻¹¹. Measured (CODATA 2018).

N·m²/kg²

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

G = 6.674 30 × 10⁻¹¹ N·m²/kg² (Gravitational constant)
M = 2 kg (Central mass)
r = 3 m (Orbital radius)

Result: v = 6.670482 × 10⁻⁶ m/s

Other mechanics formulas with the same quantities

Geosynchronous Orbit Radius (Gravitation) shares Orbital radius, Gravitational constant
Gravitational Field (Gravitation) shares Gravitational constant
Gravitational Potential Energy (General) (Gravitation) shares Gravitational constant
Escape Velocity (Gravitation) shares Gravitational constant
Surface Gravity (Gravitation) shares Gravitational constant

Where this formula is listed

Mechanics formulas, under Gravitation.
In the mechanics list it comes after Gravitational Potential Energy (General) and before Orbital Period.
Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Orbital Velocity formula?

Orbital Velocity is written v = √(GM/r). Velocity for circular orbit at radius r. It belongs to Mechanics, under Gravitation.

What are the units in v = √(GM/r)?

In SI units, v is orbital velocity, measured in m/s; G is gravitational constant, measured in m³/(kg·s²); M is central mass, measured in kg; r is orbital radius, measured in m.

How is the Orbital Velocity formula derived?

Set gravitational force = centripetal force: GMm/r² = mv²/r. The result is v = √(GM/r).