physics

Orbital Velocity Calculator

Calculate the orbital velocity required for a circular orbit around a massive body using v = √(GM/r). Determine satellite speeds, orbital periods, and understand Keplerian orbital mechanics.

Reviewed by Christopher FloiedUpdated April 16, 2026

This free online orbital velocity calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Central Body Mass (kg)

Earth by default

Orbit Radius (m)

Distance from center

Results

Orbital Velocity

7672.32 m/s

How to Use This Calculator

Enter your input values

Fill in all required input fields for the Orbital Velocity Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

Read the results

The Orbital Velocity Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Orbital Velocity Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

•Use the Orbital Velocity Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
•Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
•Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
•Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Orbital Velocity Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the orbital velocity required for a circular orbit around a massive body using v = √(GM/r). Determine satellite speeds, orbital periods, and understand Keplerian orbital mechanics. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Orbital Velocity Calculator

The Orbital Velocity Calculator determines the speed required for an object to maintain a circular orbit around a celestial body at a given altitude. For Earth orbit, this is about 7.8 km/s (17,400 mph) at low altitude — over 20 times the speed of a commercial airliner. This calculator uses Newton's law of universal gravitation to compute the velocity where gravitational pull equals the centripetal force needed for circular motion. Understanding orbital velocity is fundamental to space exploration: it's why rockets need to accelerate to extreme speeds to reach orbit, why satellites at different altitudes travel at different speeds, and why the International Space Station orbits at 17,500 mph to stay in orbit.

The Math Behind It

Orbital velocity is determined by balancing two forces: gravitational attraction pulling the satellite toward the central body, and the centripetal force required for circular motion. **Derivation**: Setting gravitational force equal to centripetal force: - F_gravity = GMm/r² - F_centripetal = mv²/r Setting them equal and solving for v: - GMm/r² = mv²/r - GM/r = v² - **v = √(GM/r)** Note that the mass of the satellite (m) cancels out — orbital velocity depends only on the central body's mass and the orbit radius. **Key Values**: | Orbit | Altitude | Velocity | |-------|----------|----------| | Low Earth Orbit (LEO) | ~400 km | 7.67 km/s | | ISS | 408 km | 7.66 km/s (27,600 km/h) | | Medium Earth Orbit | 2,000 km | 6.9 km/s | | GPS Satellites | 20,200 km | 3.87 km/s | | Geostationary (GEO) | 35,786 km | 3.07 km/s | | Moon's orbit | 384,400 km | 1.02 km/s | **Key Insight**: Higher orbits mean SLOWER velocities. This is counterintuitive — to move 'up' to a higher orbit, you actually need less speed. But getting there requires more energy (to raise altitude against gravity), so rockets must accelerate first, then let the object 'fall' into the higher orbit. **Escape vs Orbital Velocity**: - **Orbital velocity**: v_orbit = √(GM/r) — circular orbit - **Escape velocity**: v_escape = √(2GM/r) = √2 × v_orbit Escape velocity is always √2 ≈ 1.414 times the orbital velocity at the same altitude. From Earth's surface, orbital velocity is ~7.9 km/s and escape velocity is ~11.2 km/s. **Orbital Period**: For circular orbits, period T = 2πr/v = 2π√(r³/GM). This is Kepler's Third Law — the period squared is proportional to the semi-major axis cubed. **Applications**: 1. **Satellite Deployment**: Engineers must accelerate satellites to the exact orbital velocity at their target altitude. Too slow and they fall back; too fast and they climb higher. 2. **ISS Operations**: The ISS travels at ~7.66 km/s, completing an orbit every ~90 minutes. Astronauts see ~16 sunrises per day. 3. **Geostationary Orbit**: At 35,786 km altitude, orbital period equals 24 hours, so satellites appear stationary from Earth. This is used for communications satellites and weather observation. 4. **Interplanetary Missions**: Hohmann transfer orbits use orbital mechanics to efficiently travel between planets. **Earth Constants**: - Earth mass: 5.972 × 10²⁴ kg - Earth radius: 6.371 × 10⁶ m - Earth surface orbital velocity: 7.91 km/s (if atmosphere weren't in the way) - Gravitational constant G: 6.674 × 10⁻¹¹ N·m²/kg² **Orbital Decay**: Low Earth orbit satellites (below ~600 km) experience atmospheric drag that slowly reduces their velocity, causing them to spiral down. The ISS requires periodic reboosts to maintain altitude. Higher orbits (above 1000 km) experience negligible drag and can last millennia.

Formula Reference

Orbital Velocity

v = √(GM/r)

Variables: G = 6.674×10⁻¹¹ N·m²/kg², M = mass of central body, r = orbit radius from center

Worked Examples

Example 1: International Space Station

ISS orbits Earth at ~408 km altitude. Calculate orbital velocity.

Step 1:Radius = Earth radius + altitude = 6,371,000 + 408,000 = 6,779,000 m

Step 2:v = √(6.674×10⁻¹¹ × 5.972×10²⁴ / 6,779,000)

Step 3:v = √(3.986×10¹⁴ / 6,779,000)

Step 4:v = √(5.878×10⁷)

Step 5:v ≈ 7,666 m/s = 7.67 km/s

The ISS must maintain ~7.67 km/s (27,600 km/h, 17,150 mph) to stay in orbit.

Example 2: Moon's Orbit

Calculate the Moon's orbital velocity around Earth (384,400 km average).

Step 1:r = 384,400,000 m

Step 2:v = √(6.674×10⁻¹¹ × 5.972×10²⁴ / 3.844×10⁸)

Step 3:v = √(1.037×10⁶)

Step 4:v ≈ 1,018 m/s = 1.02 km/s

The Moon orbits at about 1 km/s — 7.5 times slower than the ISS despite being the same satellite logic.

Common Mistakes & Tips

!Using altitude instead of total distance from center. The formula requires distance from the central body's center, not its surface.
!Forgetting that higher altitude means slower velocity. Many assume the opposite.
!Confusing orbital velocity with escape velocity. Orbital is √(GM/r); escape is √(2GM/r).
!Applying this formula to elliptical orbits. Elliptical orbits have variable velocity — slowest at apogee, fastest at perigee.

Related Concepts

Escape Velocity

Speed to break free from gravity entirely.

Gravitational Force

The underlying force that defines orbits.

Kepler's Third Law

Relates orbital period to distance.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Centripetal Force Calculator

Escape Velocity Calculator

Kepler's Third Law Calculator

Frequently Asked Questions

Why do satellites at higher altitudes move slower?

At higher altitudes, gravity is weaker, so less centripetal force is needed. Less force means less velocity (since F = mv²/r). Mathematically, orbital velocity ∝ 1/√r — doubling the distance divides velocity by √2. This means geostationary satellites (~36,000 km up) orbit at only 3 km/s while the ISS (~400 km up) orbits at nearly 8 km/s.

What would happen if the ISS slowed down?

It would fall to a lower orbit. Gravity would pull it down, increasing its speed and energy as it descends. Without thrust, it eventually enters thicker atmosphere and burns up or crashes. This is why the ISS requires periodic reboosts — atmospheric drag slows it slightly, and if unchecked, it would deorbit within months.

How fast does the Earth orbit the Sun?

Earth orbits the Sun at about 29.78 km/s (107,200 km/h or 66,600 mph). Using the orbital velocity formula with the Sun's mass (2×10³⁰ kg) and Earth's distance (1.496×10¹¹ m): v = √(GM_sun/r) ≈ 29.78 km/s. This is why we don't feel our incredible motion — it's constant and uniform.

Can satellites orbit at any altitude?

In principle, yes. In practice, low altitudes (below ~300 km) experience too much atmospheric drag to be sustainable. Very high altitudes approach the Moon's gravitational influence, causing instability. Typical orbits range from 200 km to 40,000 km, with specific 'zones' (LEO, MEO, GEO) used for different purposes.