Escape & Orbital Velocity Calculator

Understanding the escape and orbital velocity calculator — concept and principle

Escape velocity is the minimum launch speed an unpowered object needs to leave a planet's gravity for good, while orbital velocity is the speed needed to stay in a circular orbit at a given altitude. This calculator gives both, along with the orbital period and the surface gravity, from a planet's mass and radius. The defaults use the Earth and a 400 km orbit, close to the altitude of the International Space Station.

7.67 km/s keeps you circling at 400 km; 11.19 km/s from the ground lets you leave for good.

How it is calculated

With GM = G × M (G = 6.6743 × 10⁻¹¹ N·m²/kg²), radius R and orbit radius r = R + h (converted to metres):

Escape velocity at the surface: v_esc = √(2GM ÷ R)
Circular orbit speed: v = √(GM ÷ r)
Orbital period: T = 2π √(r³ ÷ GM), shown in minutes
Surface gravity: g = GM ÷ R²

Speeds are shown in km/s.

The principle

Escape velocity comes from energy: kinetic energy ½mv² must equal the work needed to climb out of the gravity well, GMm ÷ R. Solving gives v = √(2GM/R); the object's own mass cancels.

Orbital speed comes from force: for a circular orbit, gravity supplies exactly the centripetal force, GMm ÷ r² = mv² ÷ r, so v = √(GM/r). The period is the circumference 2πr divided by that speed. At the same radius, escape speed is always √2 ≈ 1.414 times the circular speed.

Worked example

Inputs: M = 5.972 × 10²⁴ kg, R = 6,371 km, h = 400 km.
GM = 6.6743 × 10⁻¹¹ × 5.972 × 10²⁴ = 3.98589 × 10¹⁴ m³/s².
v_esc = √(2 × 3.98589 × 10¹⁴ ÷ 6,371,000) ≈ 11,186 m/s = 11.18597789 km/s.
r = 6,771,000 m, so v = √(3.98589 × 10¹⁴ ÷ 6,771,000) ≈ 7.672490413 km/s.
T = 2π √(6,771,000³ ÷ 3.98589 × 10¹⁴) ≈ 5,545 s ≈ 92.41555528 min.
g = 3.98589 × 10¹⁴ ÷ 6,371,000² ≈ 9.819973426 m/s².

Each point is the calculator re-run with only “Radius (km)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Radius (km)	Escape velocity at surface (km/s)
1,593	22.37195578
3,186	15.81936164
4,778	12.91645469
6,371	11.18597789
7,964	10.00504278
9,556	9.133312703
12,742	7.909680822

How to read the result

Higher orbits are slower and take longer: at the surface radius the circular speed would be about 7.91 km/s, at 400 km it is 7.67 km/s, and at geostationary distance about 3.07 km/s. The surface gravity here (9.82 m/s²) is a little above the standard 9.80665 m/s² because the calculation ignores Earth's rotation and flattening. Escape velocity is a speed limit for a coasting object only; a rocket that keeps thrusting can leave slowly.

Common mistakes

Using altitude instead of distance from the centre in the orbit formula.
Mixing km and m.
Thinking escape velocity must point straight up; any direction works if nothing blocks the path, ignoring air drag.

Keep in mind: These are ideal two-body values without atmosphere, rotation or other bodies. Real launches need extra velocity to overcome drag and gravity losses, and mission planning uses far more detailed models.

Frequently asked questions

Why do rockets launch eastward?

Earth's rotation adds up to about 0.46 km/s at the equator, reducing the speed the rocket must supply.

What is the escape velocity from the Moon?

About 2.38 km/s, much lower than Earth's because the Moon has far less mass.

Is escape velocity the same at the ISS altitude?

No. At r = 6,771 km it is √2 × 7.67 ≈ 10.85 km/s, lower than at the surface.

Sources: Halliday, Resnick and Walker, Fundamentals of Physics, chapter on gravitation · H. D. Curtis, Orbital Mechanics for Engineering Students, Elsevier

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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