Escape Velocity Calculator
Calculate the escape velocity of any planet, moon, or star from its mass and radius — the speed needed to leave its gravity behind forever.
Cómo usar esta calculadora
- 1Pick a body from the list, or choose 'Custom body' to enter your own.
- 2For a custom body, enter its mass in kilograms and its radius in kilometres — scientific notation like 5.972e24 is accepted.
- 3Read the escape velocity, and compare every body in the table.
Cómo funciona
Escape velocity
v_escape = √(2 × G × M ÷ r) G = 6.674 × 10⁻¹¹ N·m²/kg² (gravitational constant) M = mass of the body (kg) r = distance from the body's centre (m) independent of the escaping object's own mass
Escape velocity comes from energy balance: an object escapes when its kinetic energy equals the gravitational potential energy binding it to the body. Setting ½mv² equal to GMm ÷ r, the escaping mass cancels from both sides — which is why a pebble and a spacecraft need exactly the same escape speed. The result depends only on how much mass is pulling and how far you start from its centre.
Ejemplo resuelto
For Earth, mass 5.972 × 10²⁴ kg and radius 6,371 km: v = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ 6.371×10⁶) ≈ 11,186 m/s, or 11.19 km/s — about 25,000 mph. That is the classic figure for escaping Earth from its surface.
Escape Velocity Calculator: la guía completa
What escape velocity really means
Escape velocity is the minimum speed at which an object, given one instantaneous push and then left alone, will coast away from a body forever rather than falling back. Throw a ball upward and it returns; throw it at escape velocity and it never does, because it always has just enough kinetic energy to overcome the remaining gravitational pull as it climbs.
Crucially, it does not depend on the mass of the object escaping. The escaping mass appears on both sides of the energy equation and cancels, so a marble, a person, and a moon all share the same escape velocity from a given body. It depends only on the body you are leaving and how far from its centre you start.
Why rockets don't launch at 25,000 mph
Escape velocity assumes a single push with no further thrust — like a cannonball. Rockets do not work that way. They burn continuously, climbing under sustained power, so they never need to be moving at escape velocity near the ground where the air is thick and drag is fierce. They reach orbital and escape speeds high up, gradually, where there is no atmosphere to fight.
The 11.2 km/s figure still matters, though: it sets the total energy any mission must supply to leave Earth, and it is why launching anything off Earth is so expensive. The Moon's escape velocity is only 2.4 km/s, which is exactly why returning from the Moon needed a far smaller rocket than getting there.
From planets to black holes
The same formula scales across the whole universe. The Sun's escape velocity is 618 km/s. Increase a body's mass or shrink its radius and the escape velocity climbs; push it far enough and you reach the defining property of a black hole — the point where escape velocity equals the speed of light, so not even light can leave.
That threshold is the Schwarzschild radius, and it falls straight out of setting escape velocity to c in this equation. It is a striking demonstration that black holes are not exotic new physics bolted on, but the extreme limit of the ordinary Newtonian relationship you can compute above.
Preguntas frecuentes
What is Earth's escape velocity?
About 11.2 km/s, or roughly 25,000 mph. That is the speed an object would need, with a single push, to leave Earth's gravity permanently from the surface. It ignores air resistance, which is why real launches happen high in the atmosphere.
Does a heavier spacecraft need a higher escape velocity?
No. Escape velocity is independent of the escaping object's mass — a feather and a spaceship need the same speed. A heavier craft needs more energy and therefore more fuel to reach that speed, but the speed itself is identical.
Do rockets travel at escape velocity when they launch?
No. Escape velocity applies to an unpowered object given one push. Rockets thrust continuously and escape gradually, reaching high speeds only in the upper atmosphere and space. Near the ground they move far slower, which keeps air resistance manageable.
How does escape velocity relate to black holes?
A black hole is a body so compact that its escape velocity reaches the speed of light. Setting v equal to c in the escape-velocity formula and solving for radius gives the Schwarzschild radius — the size to which a given mass must be squeezed to trap even light.