Mechanics
Escape Velocity
Minimum velocity to escape gravitational field.
Variables
vem/s
Escape velocity
Minimum escape speed
GN·m²/kg²
Gravitational constant
6.674×10⁻¹¹
In SI units: m³/(kg·s²)
Allowed values: greater than 0
Mkg
Mass
Mass of body
Allowed values: 0 or more
rm
Radius
Starting distance
Allowed values: greater than 0
Derivation
Set total energy = 0: ½mv² - GMm/r = 0.
Your notes
0/5000
Constants in this formula
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 (Mass)
- r = 3 m (Radius)
Result: ve = 9.433486 × 10⁻⁶ m/s
Other mechanics formulas with the same quantities
- Gravitational Field (Gravitation) shares Gravitational constant, Mass
- Surface Gravity (Gravitation) shares Gravitational constant, Mass
- Universal Gravitation (Gravitation) shares Gravitational constant
- Orbital Period (Gravitation) shares Gravitational constant
- Geosynchronous Orbit Radius (Gravitation) shares Gravitational constant
Where this formula is listed
- Mechanics formulas, under Gravitation.
- In the mechanics list it comes after Orbital Period and before Surface Gravity.
- 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 Escape Velocity formula?
Escape Velocity is written v_e = √(2GM/r). Minimum velocity to escape gravitational field. It belongs to Mechanics, under Gravitation.
What are the units in v_e = √(2GM/r)?
In SI units, v_e is escape velocity, measured in m/s; G is gravitational constant, measured in m³/(kg·s²); M is mass, measured in kg; r is radius, measured in m.
How is the Escape Velocity formula derived?
Set total energy = 0: ½mv² - GMm/r = 0. The result is v_e = √(2GM/r).