Escape Velocity Calculator
Calculate escape velocity from Earth, the Moon, Mars, Jupiter or a custom body.
Step-by-step working
- r = radius + altitude = 6.3710e+6 m
- vₑ = √(2GM/r) = √(2 × 6.6743e-11 × 5.9722e+24 / 6.3710e+6) = 11186.1652 m/s
Mathematical Formula
Overview & Explanation
Escape velocity is the speed needed to leave a body’s gravity without further propulsion.
How It Works
- Add altitude to radius.
- Apply the formula.
Practical Applications
- Spaceflight basics.
- Astronomy homework.
Example 1: Earth surface
≈ 11.19 km/s.
Inputs
Body: Earth · Altitude above surface (km): 0
Step 1
r = radius + altitude = 6.3710e+6 m
Step 2
vₑ = √(2GM/r) = √(2 × 6.6743e-11 × 5.9722e+24 / 6.3710e+6) = 11186.1652 m/s
Escape velocity
Result
Example 2: Moon surface
≈ 2.38 km/s.
Inputs
Body: Moon · Altitude above surface (km): 0
Step 1
r = radius + altitude = 1.7374e+6 m
Step 2
vₑ = √(2GM/r) = √(2 × 6.6743e-11 × 7.3420e+22 / 1.7374e+6) = 2375.063 m/s
Escape velocity
Result
How it's calculated & sources
vₑ = √(2GM / r), r = radius + altitude, G = 6.6743 × 10⁻¹¹.
Frequently Asked Questions
Does direction matter?
Why is it √2 × orbital speed?
Is air resistance included?
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