Case 1
- Speed
- 149896229m/s
1.154701
Open with these valuesLorentz Factor Calculator
Change any value to update the result.
1.154701
Lorentz factor γ: 1.154701Examples
How the result moves
Speed (m/s) → Lorentz factor γYour current valid inputs, with one value varied across the range.
How the result moves
| Speed (m/s) | Lorentz factor γ |
|---|---|
| 120,000,000.00 | 1.091233 |
| 140,000,000.00 | 1.130886 |
| 149,896,229.00Your value | 1.154701 |
| 160,000,000.00 | 1.182491 |
| 180,000,000.00 | 1.250487 |
Enter the speed in metres per second, not as a fraction of c — the calculator divides by 299,792,458 itself. Gamma is 1 at rest, still only 1.0005 at 10,000 km/s, and 7.09 at 99 % of light speed. The field stops one metre per second short of c, where gamma stops being defined.
Worked examples
Case 2
- Speed
- 269813212.2m/s
2.294157
Open with these valuesCase 3
- Speed
- 29979245.8m/s
1.005038
Open with these valuesHow it's calculated
γ = 1 ÷ √(1 − v² ÷ c²)
- StepEnter the speed in metres per second — divide km/h by 3.6.Speed=149,896,229m/s
- StepFor a fraction of light speed, multiply it by 299,792,458 first.Speed=149,896,229m/s
- ResultRead gamma: 1 means no relativistic effect, 2 means clocks run half as fast.1.154701
Reference table
| Speed (m/s) | Share of light speed | Gamma |
|---|---|---|
| 0 | At rest | 1 |
| 10000000 | 3.34 % | 1.000557 |
| 29979245.8 | 10 % | 1.005038 |
| 149896229 | 50 % | 1.154701 |
| 269813212.2 | 90 % | 2.294157 |
| 296794533.42 | 99 % | 7.088812 |
Questions
How do I calculate the Lorentz factor?
Divide the speed by the speed of light, square the result, subtract it from one, take the square root, and divide one by that: γ = 1 / √(1 − (v/c)²). For example, at half the speed of light (v = 149,896,229 m/s) you get γ = 1 / √(1 − 0.25) ≈ 1.1547.
What is the Lorentz factor?
The Lorentz factor (gamma, γ) is the number in special relativity that scales time, length, and mass for a moving object. It is 1 at rest and increases without limit as the speed approaches that of light, capturing how moving clocks run slow and moving objects contract along the direction of motion.
Why can't the velocity reach the speed of light?
Because the term 1 − (v/c)² goes to zero at the speed of light, so γ is divided by zero and becomes infinite. An infinite Lorentz factor would require infinite energy, which is why no object with mass can reach or exceed light speed. The input field here therefore stops one metre per second short of c.
What does the Lorentz factor mean physically?
A γ of 2 means a moving clock ticks half as fast, lengths shrink to half, and relativistic mass doubles compared with the rest frame. At everyday speeds γ is so close to 1 that the effects are unmeasurable, but for particles in accelerators or cosmic rays γ can reach thousands.
What units should I use?
Enter the speed in metres per second, the SI unit used for the speed of light (299,792,458 m/s). The Lorentz factor itself is a pure number with no units. To convert from km/h divide by 3.6, and from a fraction of light speed multiply that fraction by 299,792,458.