Escape Velocity Calculator
Enter a celestial body's mass and radius to compute its escape velocity v = √(2GM/r).
Input Data
Results
At a glance:Escape velocity is the speed at which an object's kinetic energy equals the gravitational potential energy needed to reach infinity: ½mv² = GMm/r → v = √(2GM/r). It depends only on the body's mass M and radius r, not on the projectile's mass. Earth's escape velocity is about 11.2 km/s; the Moon's ~2.4 km/s (small mass, small radius) explains its lack of atmosphere; Jupiter's ~60 km/s. Airless bodies with low escape velocity cannot retain gases — hence thin or no atmospheres on small moons and asteroids.
Formula
Escape velocity: v = √(2GM/r)
G = 6.674×10⁻¹¹ N·m²/kg²
$$v = \sqrt{\dfrac{2GM}{r}}$$$$\tfrac{1}{2}mv^2 = \dfrac{GMm}{r}$$How to Use
- Enter the body's mass M (kg).
- Enter its radius r (m).
- The calculator returns escape velocity in m/s and km/s.
Case Studies
Earth's escape velocity
M = 5.97×10²⁴ kg, r = 6.37×10⁶ m.
v = √(2×6.674e-11×5.97e24/6.37e6) ≈ 11200 m/s.
≈11.2 km/s, matching launch requirements.
FAQ
Does escape velocity depend on the object's mass?
No. Both kinetic and potential energy are proportional to the object's mass m, which cancels, so v = √(2GM/r) depends only on the body.
Is escape velocity the same as orbital velocity?
No. Circular orbital speed is v_orb = √(GM/r); escape velocity is √2 times larger: v_esc = √2·v_orb.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.