Lorentz Factor Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The Lorentz factor is calculated with γ = 1 ÷ √(1 − v²/c²), where v is the object's speed and c the speed of light. At 80% of the speed of light, γ equals exactly 5/3≈1.667 — meaning time passes 1.667 times more slowly and lengths contract by a factor of 1.667 for that object, as seen from an observer at rest.
Explanation
The Lorentz factor is the central quantity of special relativity: it precisely quantifies by how much the time, space, and apparent mass of a moving object differ from those measured by an observer at rest, an effect completely negligible at everyday speeds (a car, a plane) but which becomes significant at a notable fraction of the speed of light. This factor equals exactly 1 for a stationary object (no relativistic effect), and grows ever faster as speed approaches c, tending toward infinity as v approaches c — it's precisely this unbounded growth that explains why no object with mass can ever reach or exceed the speed of light: it would take infinite energy to accelerate it to that point — a factor γ that also relates directly to the frequency shift already covered by our Doppler effect calculator once a source moves close to the speed of light, and to the kinetic energy an object gains as it approaches relativistic speeds, a regime our kinetic energy calculator only covers in its simpler, non-relativistic form. The Lorentz factor directly underlies the calculation of time dilation (time passes more slowly for a moving object, as seen from a frame at rest) and length contraction (a moving object appears shortened in its direction of travel) — two effects that seem counterintuitive but have been experimentally confirmed countless times, notably through the observation of unstable subatomic particles that "live" longer when moving at high speed in particle accelerators.
Example: a spacecraft at 80% of the speed of light
Inputs
Speed v = 0.8×c (80% of the speed of light).
Calculation
γ = 1 ÷ √(1 − 0.8²) = 1 ÷ √(1 − 0.64) = 1 ÷ √0.36 = 1 ÷ 0.6 ≈ 1.6667.
Result
For this spacecraft, time passes about 1.667 times more slowly, and lengths in its direction of travel appear reduced by the same factor, as seen from an observer who stayed at rest.
Frequently asked questions
Why is the Lorentz factor always greater than or equal to 1?
Because the term v²/c² under the square root is always between 0 (at rest) and 1 (as speed approaches that of light, never reached for a massive object), which keeps the radicand 1−v²/c² always between 0 and 1 — and so does its square root. Dividing 1 by a number between 0 and 1 always gives a result greater than or equal to 1, which mathematically guarantees that γ can never be less than 1, regardless of the speed considered.
Why are relativistic effects imperceptible in everyday life?
Even at the speed of an airliner (about 900 km/h, or v/c≈0.00000083), the term v²/c² is so tiny that the Lorentz factor stays extremely close to 1 (with a difference on the order of 10⁻¹³), making relativistic effects completely undetectable without instruments of extreme precision. It's only at speeds representing a significant fraction of the speed of light — reached by subatomic particles in accelerators, or theoretically by future spacecraft — that these effects become measurable, and then downright dramatic.
Does GPS really use this Lorentz factor?
Yes, indirectly but concretely: GPS satellites move fast enough (about 14,000 km/h) that relativistic time dilation, calculated from the Lorentz factor, must be corrected for in their onboard atomic clocks — without this correction (combined with an opposite effect due to general relativity, related to altitude), positions computed by the GPS system would drift by several kilometers per day, making the system unusable for precise navigation.