Primary formula
v = sqrt(GM / r).
Physics calculator
Orbital Velocity Calculator
Calculate ideal circular orbital velocity from central mass and orbital radius using the simplified gravity model.
Last reviewed: July 21, 2026Physics formula engine v3.0.0
Physics calculator
Orbital Velocity Calculator
Enter values, select units and calculate locally. Results use SI internally and show rounded display values.
Decimal.js physics math
Mode
Find ideal circular orbital velocity from mass and radius.
Result and visual stay hidden until you choose Calculate.
Formula and assumptions
Input assumptions
Central mass is greater than zero. Orbital radius is greater than zero. The orbit is circular around an isolated spherical body.
Precision note
Physics calculators convert compatible inputs into SI units before calculating. Decimal.js is used for arithmetic where practical; trigonometric angle factors are rounded for display.
Physics calculation flow
Parse
Read labelled inputs, selected units and calculation mode from the calculator card.
Convert
Convert compatible values to SI base or derived units without calling external services.
Calculate
Apply the selected deterministic mechanics formula and validate against NaN, Infinity and invalid divisors.
Label
Display the result, supporting unit rows, formula steps, warnings and dynamic visual below the input card.
What Orbital Velocity Calculator does
Use this calculator for circular-orbit estimates and classroom gravitation problems.
The calculator is deterministic and runs from manual inputs only. It is a physics formula tool, so it should not be confused with a unit converter that only changes labels after a value is already known.
Formula and variables
v = sqrt(GM / r).
The calculator converts supported units into SI base or derived units for the actual calculation, then formats the result in the selected display unit.
- v is orbital velocity
- G is gravitational constant
- M is central mass
- r is orbital radius from centre
Worked examples
Use the examples below to check expected order of operations and unit handling before applying the tool to your own values.
- Low Earth circular orbit approximation gives about 7672 m/s
- Higher orbit radius lowers circular speed
- Escape velocity at the same radius is sqrt(2) times circular speed.
Unit conversions
Length, time, mass, area, volume, speed, force, pressure, density, frequency, energy and power units reuse the central NexaCalc conversion registry. Acceleration, angle and spring-constant units use the same SI-first convention where applicable.
The displayed conversion rows are supporting context. They do not change the physical assumptions of the selected formula.
Common mistakes
Most errors come from mixing physical quantities that sound similar in everyday language or choosing a unit that belongs to a different dimension.
- Using altitude without adding body radius.
- Confusing escape speed with orbital speed.
- Ignoring noncircular orbits.
Assumptions and limitations
This page is intended for educational and planning calculations, not professional engineering certification.
This calculator uses idealized physics formulas and the input values you provide. Real systems may require additional effects such as friction, drag, rotation, deformation, losses or measurement uncertainty.
- Central mass is greater than zero.
- Orbital radius is greater than zero.
- The orbit is circular around an isolated spherical body.
- Atmosphere, thrust, eccentricity, rotation and third-body effects are not modeled.
- Mission planning requires full orbital mechanics.
Frequently asked questions
How is orbital velocity calculated?
Orbital Velocity Calculator uses v = sqrt(GM / r). The result is calculated from the values and units entered in the form.
What orbital radius should I enter?
Use this calculator for circular-orbit estimates and classroom gravitation problems. Central mass is greater than zero.
Is orbital velocity the same as escape velocity?
Orbital Velocity Calculator is formula-based. Use the related calculator when the question changes physical quantity, and use Conversion tools only when the value is already known.
Why does a higher orbit have lower circular speed?
Use this calculator for circular-orbit estimates and classroom gravitation problems. Central mass is greater than zero.
Does satellite mass matter?
Use this calculator for circular-orbit estimates and classroom gravitation problems. Central mass is greater than zero.
Does this model include atmosphere?
Orbital Velocity Calculator uses an idealized classroom physics model. Atmosphere, thrust, eccentricity, rotation and third-body effects are not modeled.
Can I calculate low Earth orbit speed?
Orbital Velocity Calculator uses v = sqrt(GM / r). The result is calculated from the values and units entered in the form.
What units are supported?
Orbital Velocity Calculator converts compatible inputs to SI internally, then displays the selected output unit. v is orbital velocity; G is gravitational constant; M is central mass; r is orbital radius from centre.
Does this work for elliptical orbits?
Use this calculator for circular-orbit estimates and classroom gravitation problems. Central mass is greater than zero.
When should I use Escape Velocity Calculator?
Use this calculator for circular-orbit estimates and classroom gravitation problems. Central mass is greater than zero.
References
- NIST Special Publication 811, Guide for the Use of the International System of Units. Relevance: SI unit symbols and derived-unit naming. Last verified: July 21, 2026. Source.
- BIPM, The International System of Units SI Brochure. Relevance: SI base and derived units used in mechanics, fluids, waves and optics. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 1. Relevance: introductory formulas for motion, force, work, energy, momentum, fluids, waves and optics. Last verified: July 21, 2026. Source.
- NIST CODATA internationally recommended values. Relevance: physical constants for electricity, modern physics, gravitation and radiation formulas. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 2. Relevance: electric circuits, capacitance, magnetic force and electromagnetic waves. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 3. Relevance: photons, nuclear decay and blackbody radiation concepts. Last verified: July 21, 2026. Source.
Physics references verified for SI units, mechanics, fluids, waves, sound and optics formulas on July 21, 2026.
Educational disclaimer
This calculator provides mathematical results from the values, conventions and methods you enter. Verify important academic, engineering or professional work independently.