Primary formula
v_e = sqrt(2GM / r).
Physics calculator
Escape Velocity Calculator
Calculate ideal escape velocity from a central body's mass and radius using the simplified gravitational formula.
Last reviewed: July 21, 2026Physics formula engine v3.0.0
Physics calculator
Escape 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 escape 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. Radius from centre is greater than zero. The body is treated as spherical and isolated.
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 Escape Velocity Calculator does
Use this calculator for introductory gravitation and space examples where atmosphere and propulsion details are ignored.
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_e = sqrt(2GM / 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_e is escape velocity
- G is gravitational constant
- M is central mass
- r is distance from the centre
Worked examples
Use the examples below to check expected order of operations and unit handling before applying the tool to your own values.
- Earth approximation gives about 11186 m/s
- Escape speed increases with mass
- Escape speed decreases as radius increases.
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 instead of distance from the centre.
- Forgetting kilometre-to-metre conversion.
- Treating escape velocity as launch speed through atmosphere.
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.
- Radius from centre is greater than zero.
- The body is treated as spherical and isolated.
- Atmosphere, thrust, rotation, multi-body effects and mission constraints are not included.
- Real launch vehicles follow trajectories, not a single instant-speed rule.
Frequently asked questions
How is escape velocity calculated?
Escape Velocity Calculator uses v_e = sqrt(2GM / r). The result is calculated from the values and units entered in the form.
What radius should I enter?
Use this calculator for introductory gravitation and space examples where atmosphere and propulsion details are ignored. Central mass is greater than zero.
Why does escape velocity use 2GM over r?
Use this calculator for introductory gravitation and space examples where atmosphere and propulsion details are ignored. Central mass is greater than zero.
Does escape velocity include atmosphere?
Escape Velocity Calculator uses an idealized classroom physics model. Atmosphere, thrust, rotation, multi-body effects and mission constraints are not included.
Is escape velocity the same as orbital velocity?
Escape 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.
What units are supported?
Escape Velocity Calculator converts compatible inputs to SI internally, then displays the selected output unit. v_e is escape velocity; G is gravitational constant; M is central mass; r is distance from the centre.
Can I use Earth mass and radius?
Use this calculator for introductory gravitation and space examples where atmosphere and propulsion details are ignored. Central mass is greater than zero.
Does object mass affect escape velocity?
Use this calculator for introductory gravitation and space examples where atmosphere and propulsion details are ignored. Central mass is greater than zero.
Does rotation change real launch requirements?
Use this calculator for introductory gravitation and space examples where atmosphere and propulsion details are ignored. Central mass is greater than zero.
When should I use Orbital Velocity Calculator?
Use this calculator for introductory gravitation and space examples where atmosphere and propulsion details are ignored. 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.