Does escape velocity depend on launch mass?
No — the mass cancels in the derivation. A pebble and a rocket need the same escape speed.
Escape Velocity Calculator
v = √(2GM/r)
Calculate escape velocity from a planet or star. v = √(2GM/r) — the speed needed to escape gravity.
Calculate
Enter values above to calculate
How it calculates
1
G = 6.674×10⁻¹¹ N·m²/kg²
2
v = √(2GM/r)
3
Result in m/s (divide by 1000 for km/s)
Formula
v = √(2GM/r)
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| v | Escape velocity | m/s |
| G | Gravitational constant = 6.674×10⁻¹¹ | N·m²/kg² |
| M | Mass of body | kg |
| r | Distance from centre | m |
How to Use This Calculator
This escape velocity calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula v = √(2GM/r) is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
Escape velocity from Earth (M = 5.972×10²⁴ kg, r = 6.371×10⁶ m).
Step 1: v = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ / 6.371×10⁶)
Step 2: v = √(1.253×10⁸)
Answer: v ≈ 11,186 m/s ≈ 11.2 km/s
Common Mistakes
- Escape velocity is independent of the escaping object's mass
- It decreases with altitude: v ∝ 1/√r
- Escape velocity = √2 × circular orbital velocity at the same radius
Related
Frequently Asked Questions
What is Earth's escape velocity?
About 11.2 km/s from the surface, ignoring air resistance.