WORKED DEFAULT
Check the calculation with the default inputs
At v = 0.8c, 1 - beta squared is 0.36, its square root is 0.6, and gamma is 1 / 0.6 = 1.6667.
- Square beta0.8^2 = 0.64
- Build the denominatorsqrt(1 - 0.64) = 0.6
- Invertgamma = 1.6667
PHYSICS / SPECIAL RELATIVITY
Lorentz Factor Calculator
Calculate the Lorentz factor from speed expressed as a fraction of the speed of light.
- 01 Calculated in this tab
- 02 Values stay in this browser tab
- 03 Use boundary
METHOD / WORKED EXAMPLE
See when relativistic scaling becomes important
Lorentz factor quantifies how strongly special-relativistic measurements depart from their low-speed approximations for one relative speed.
READ THE RESULT
Interpret the output in context
Gamma is dimensionless and never below one. It stays close to one at ordinary speeds, then rises rapidly as the entered speed approaches c; it is not itself a time, distance, energy, or momentum.
ASSUMPTIONS AND LIMITS
Know where the model stops
- The compared frames are inertial.
- The entered value is v/c, not meters per second.
- Special relativity applies and beta remains below one.
The speed is measured between inertial frames and must remain below the vacuum speed of light.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
COMMON QUESTIONS
Lorentz Factor Calculator FAQs
Why can the speed fraction not equal one?
For an object with rest mass, beta equal to one makes the denominator sqrt(1 - beta squared) equal zero, so gamma is unbounded. The calculator therefore requires a value below one. Photons travel at c, but this massive-particle Lorentz-factor input is not a photon motion model.
Does gamma have a unit?
No. Beta is a ratio of two speeds measured in the same units, so beta and gamma are dimensionless. Gamma becomes a scaling factor only when it is combined with a proper time, proper length, rest mass, or another quantity in a specific relativistic equation.
When is the classical approximation usually close?
When beta is much smaller than one, beta squared is tiny and gamma is very close to one. Whether that difference is negligible depends on the precision and purpose of your work. Inspect gamma rather than relying on a universal speed cutoff, especially for timing or accelerator calculations.
RELATED TOOLS
Continue the calculation
Use boundary
Calculation path
Evaluate the dimensionless relativistic factor shared by time, length, momentum, and energy relations. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
Calculation path
gamma = 1 / sqrt(1 - beta^2)