escape velocity formulas and interpretation
Escape velocity is the minimum ideal speed needed to reach infinite distance with no remaining speed.
It depends on the attracting body’s mass and starting distance from its centre.
How to use the escape velocity calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Escape speed follows from conservation of mechanical energy in an inverse-square gravitational field.
ve = √(2GM/r)- ve — Escape velocity
- Minimum ideal escape speed (m/s)
- G — Gravitational constant
- Universal gravity constant (m³/kg·s²)
- M — Body mass
- Mass being escaped (kg)
- r — Starting radius
- Distance from body centre (m)
Earth example
Use Earth mass 5.972 × 10²⁴ kg and radius 6.371 × 10⁶ m.
- Mass
- 5.972 × 10²⁴ kg
- Radius
- 6.371 × 10⁶ m
- ve = √(2GM/r)
- ve ≈ 11.19 km/s
Result: Ideal escape velocity is about 11.2 km/s.
Atmosphere and planetary rotation are excluded.
Understanding your results
Interpreting the result
More mass raises escape speed; a larger starting radius lowers it.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.