THE NUMORIX GUIDE
How to use the Escape Velocity Calculator
Last reviewed September 14, 2026
What this calculator does
In mass mode, ideal escape speed is v_e = sqrt(2GM/r).
Formula and method
In mass mode, ideal escape speed is v_e = sqrt(2GM/r). In gravity mode, substituting surface gravity gives v_e = sqrt(2gr). The engine uses r = body radius + altitude, so the radius is measured from the body's center.
Variables and inputs
Choose body mass M in kg or local gravity g in m/s^2, then enter body radius in m and altitude in m. Mass or gravity and radius must be positive, altitude must be nonnegative, and the outputs are m/s, km/s, and mph.
Worked example
For Earth-like mass M = 5.972e24 kg, radius r = 6,371,000 m, and altitude 0: v_e = sqrt(2(6.6743e-11)(5.972e24)/6,371,000) = 11,185.98 m/s, or about 11.186 km/s.
How to interpret the result
Escape velocity is the ideal speed at which an object can reach arbitrarily large distance with zero remaining speed in a two-body Newtonian model. It is a speed threshold, not a direction or a complete launch plan.
Common mistakes to avoid
Use distance from the center, not altitude alone, in the denominator. Do not confuse escape velocity with the launch vehicle's required delta-v, and do not mix kilometers with the SI meters expected by the formula.
Assumptions and limitations
The engine models an ideal Newtonian two-body system and explicitly does not calculate launch delta-v. It ignores atmosphere, drag, gravity losses, planetary rotation, steering, nonuniform bodies, and other gravitational bodies, although it does account for the entered altitude by adding it to radius.
Practical use and checks
The Escape Velocity Calculator estimates the ideal speed needed to reach arbitrarily large distance with zero remaining speed in a two-body Newtonian model. Enter an Earth-like mass of 5.972e24 kg, radius 6,371,000 m, and altitude 0 in mass mode as a check; the result should be about 11,186 m/s, or 11.186 km/s. In gravity mode, the same surface estimate follows from square root of 2*g*r when local gravity is supplied. Use distance from the body's center in the radius term; altitude is added to the body radius rather than used alone. Escape velocity is a threshold speed, not a launch vehicle's delta-v budget, trajectory, or direction. The model ignores atmosphere, drag, gravity losses, planetary rotation, steering, body irregularity, and other gravitational bodies. At greater altitude the ideal escape speed falls, but reaching that altitude consumes energy and real launch planning can gain or lose speed through rotation and flight path. Nonpositive mass, radius, or gravity is invalid, and the engine does not model a changing gravitational field beyond the simple radius formula. Treat the output as a baseline for comparing bodies or explaining orbital mechanics, not as a complete mission requirement or a safety margin.