Escape Velocity Calculator

What is the Escape Velocity Calculator?

The Escape Velocity Calculator is a free online tool for computing the minimum speed needed for a projectile to coast away to infinity against the gravity of a central body. Using the formula vₑ = √(2GM/R), it solves for escape velocity, central body mass, or launch radius given the other two inputs. The calculator uses G = 6.6743 × 10⁻¹¹ N·m²/kg² and supports multiple units for mass, distance, and velocity with built-in planetary presets.

Escape velocity is independent of the launching object's mass — a feather and a rocket both need the same vₑ to escape. This tool is essential for astrophysics students, rocket scientists, space mission planners, and anyone curious about the fundamental physics of gravitational escape.

How to Use the Escape Velocity Calculator

The calculator offers three solve modes:

Solve for Escape Velocity: Enter the central body's mass and radius (or launch distance from center) to compute the escape speed. Use the planetary presets to quickly load values for the Sun, Moon, and planets.
Solve for Mass: Enter the escape velocity and launch radius to determine the central body's mass — useful for characterizing unknown celestial objects.
Solve for Radius: Enter the escape velocity and central body mass to find the launch distance from the center — helpful for calculating orbital altitudes.

Understanding the Escape Velocity Formula

The escape velocity formula derives from setting kinetic energy equal to gravitational potential energy:

½mvₑ² = GMm/R → vₑ = √(2GM/R)

Where G = 6.6743 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant, M is the central body's mass in kilograms, and R is the distance from the body's center to the launch point in meters. The launching object's mass m cancels out, making escape velocity independent of the projectile's weight.

Applications of Escape Velocity Calculator

Spacecraft design: Setting delta-v budgets for interplanetary launches
Astrophysics: Predicting atmospheric retention on planets
Black hole physics: The Schwarzschild radius is where vₑ = c
Mission planning: Calculating lunar and Martian ascent requirements
Education: Teaching gravitational physics and energy conservation

Frequently Asked Questions

How do you calculate escape velocity?

Apply vₑ = √(2 × G × M / R), where G = 6.6743 × 10⁻¹¹ N·m²/kg², M is the central body's mass in kilograms, and R is its radius (or launch distance from center) in meters.

What is Earth's escape velocity?

About 11,186 m/s or 11.19 km/s — roughly 25,020 mph. That is the minimum speed needed at Earth's surface to coast to infinity ignoring air drag.

Does escape velocity depend on the object's mass?

No. The formula vₑ = √(2GM/R) shows escape velocity depends only on the central body's mass M and the launch radius R — not on the projectile's own mass. A feather and a rocket both need the same vₑ to escape.

Is escape velocity the same as orbital velocity?

No. Orbital velocity at radius r is v = √(GM/r), which equals vₑ/√2 — about 71% of escape velocity. At Earth's surface, orbital velocity is about 7.9 km/s while escape velocity is 11.2 km/s.

What is the escape velocity from the Moon and Mars?

The Moon's escape velocity is 2.38 km/s, and Mars' is 5.03 km/s. Jupiter's is 59.5 km/s, and the Sun's is about 617.5 km/s — the steepest gravitational well in our solar system.

What happens at exactly escape velocity?

At exactly vₑ, the object decelerates asymptotically and reaches infinity with zero residual speed. It never quite stops if energy is conserved. Achieving escape velocity does not mean escaping immediately.

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