Time Dilation and Length Contraction Calculator
Lorentz factor at a given fraction of light speed, with the stretched time, the shortened length and the kinetic energy.
Results
Lorentz factor
2.294157
Dilated time
2.294157
a
Contracted length
43.588989
m
Speed
269,813,212
m/s
Energy
129.4157
% mc²
What this tool does
Below about 10 % of light speed the factor is barely above one and relativity can be ignored; above 90 % it climbs steeply, and it runs away entirely as you approach c. That runaway is why nothing with mass ever reaches light speed: the energy needed goes to infinity.
Formula
γ = 1 ÷ √(1 − v²/c²) ; Δt = γ Δt₀
Variables
| Symbol | Meaning | Unit |
|---|---|---|
vc | Speed as a fraction of light | % c |
t0 | Time on board | a |
l0 | Rest length | m |
GA | Lorentz factor | — |
DT | Dilated time | a |
LC | Contracted length | m |
V | Speed | m/s |
KE | Energy | % mc² |
Worked example
- Speed as a fraction of light90 % c
- Time on board1 a
- Rest length100 m
- Lorentz factor2.294157
- Dilated time2.294157 a
- Contracted length43.588989 m
- Speed269,813,212 m/s
- Energy129.4157 % mc²
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
Frequently asked questions
Is this measurable or just theory?
It is measured every day. Muons created high in the atmosphere reach the ground only because their clocks run slow at the speed they travel, and satellite navigation would drift by kilometres within a day if the correction were left out. The effect is small at everyday speeds but never zero.