Orbital & Escape Velocity

Orbital period, circular velocity, and escape velocity

v = √(GM/r) · v_esc = √(2GM/r) · T = 2π√(r³/GM)

Circular orbital velocity

7.672 km/s

7,672.5 m/s

Escape velocity

10.851 km/s

10,850.5 m/s

Orbital period

5,545 s

1.54 h

Gravitational parameter (μ = GM)

3.9859E14 m³/s²

Escape velocity is √2 ≈ 1.414× the circular orbital velocity at the same radius; orbital speed and period both depend only on the central mass and the radius, not on the orbiting object's mass.

About this calculator

The Orbital & Escape Velocity Calculator computes the circular orbital velocity √(μ/r), the escape velocity √(2μ/r), and the orbital period T = 2π·√(r³/μ) around any central body, where μ = G·M is the standard gravitational parameter. Presets cover the Sun, Earth, Moon, Mars, and Jupiter, with the mass entered in units of 10²⁴ kg and the radius in km from the body's centre. Both inputs must be positive.

How to use the Orbital & Escape Velocity calculator

Enter the quantities you know, using the units shown on each field.
Read the computed results — they update instantly as you type.
Use the visual explanation to see how the quantities relate.
Copy the page URL to share the exact calculation.

Common examples

Earth at r = 6771 km (ISS altitude) → v ≈ 7672 m/s, period ≈ 5545 s ≈ 1.54 h
Earth at r = 42164 km → period ≈ 23.93 h: the geostationary orbit
Low lunar orbit (r = 1837 km) → v ≈ 1634 m/s, escape velocity ≈ 2310 m/s
Sun at 1 AU (1.496×10⁸ km) → v ≈ 29784 m/s and a period of ≈ 8766 h — one year, Earth's orbit

Frequently asked questions

How does the Orbital & Escape Velocity calculator work?

Enter the known quantities and the calculator applies the governing physical law or scientific formula to find the unknowns, stating the equation it used and the units of every result. Computations run at high precision.

When would I use the Orbital & Escape Velocity calculator?

It suits physics and chemistry homework, lab work, engineering estimates, and any time you want to explore how changing one quantity affects the others in a well-defined scientific relationship.

How accurate are the results?

The formula itself is evaluated at 30 significant digits of precision. Keep in mind that idealized models — such as neglecting friction, air resistance or measurement error — bound the real-world accuracy more than the arithmetic does.

Can I share a specific calculation with someone else?

Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.