Skip to content
Free calculators and practical guides for smarter home projects.
DIY Cost Tools

DIY Cost Tools

Orbital Velocity Calculator

Calculate ideal circular-orbit speed and period from a body’s gravitational parameter and the orbital radius measured from its center.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the stated units and domain limits.

Circular orbital velocity (km/s)7.668558175
Orbital period (s)5553.624271

How to use this calculator

  1. Enter every quantity in the unit printed beside its field.
  2. Select Calculate or press Enter.
  3. Read the labeled results and compare them with the assumptions below.

Formula and method

For a circular orbit, v = √(μ/r) and T = 2πr/v.

The calculation runs locally in your browser. If any entry is invalid or a mathematical condition is undefined, the prior result is hidden so it cannot be mistaken for a new answer.

Worked example

Using Gravitational parameter μ (km³/s²) = 398600.4418, Circular orbit radius (km) = 6778.137, the formula returns Circular orbital velocity (km/s) = 7.668558175, Orbital period (s) = 5553.624271. The displayed default result is generated from these same inputs.

Limitations and safety

Applies only to a two-body circular orbit. It excludes drag, oblateness, maneuvers, other bodies and uncertainty. It is educational, not operational flight-dynamics guidance. Results use floating-point arithmetic and are displayed to about 10 significant digits; measurement uncertainty usually supports fewer. Verify units before relying on a result.

Frequently asked questions

Is orbit radius the same as altitude?

No. Add the central body’s reference radius to altitude before entering the orbital radius.

Why might a measured result differ?

The formula isolates the stated model. Real systems can add uncertainty, losses, changing properties, geometry or forces that are not among the inputs.

How should I handle units?

Convert every value to the unit shown beside its field before calculating. A numerically valid value in the wrong unit will still produce a wrong result.

Review notes and reference

Reviewed October 3, 2026. The default example and an independent edge or scaling case were checked against expected values. The live script was also checked for blank, text, comma-formatted, non-finite and out-of-range entries. Method reference. Constants use the values stated in the formula. This page’s explanation and example are original.

Related calculators

Science calculators · Gravitational Force Calculator · Projectile Motion Calculator · Free Fall Calculator · All calculators