Mode
Needed only for kinetic energy output.
m/s
Override for medium effects or sensitivity analysis.
Results
from velocity
β (v/c)
—
γ (Lorentz factor)
—
Time dilation factor (γ)
—
Length contraction factor (1/γ)
—
Relativistic kinetic energy (optional mass)
—
Velocity
—
Example data
| Velocity | β | γ | 1/γ |
|---|
Examples are computed at page load using c = 299792458 m/s.
Saved rows
| # | Timestamp | Mode | Velocity (m/s) | β | γ | 1/γ | KE (J) |
|---|
Formula used
Lorentz factor: γ = 1 / √(1 − β²), where β = v/c.
Time dilation: moving clocks tick slower by factor γ.
Length contraction: lengths along motion contract by 1/γ.
Velocity from target γ: v = c · √(1 − 1/γ²).
Relativistic kinetic energy (optional mass m): K = (γ − 1) m c².
Energy is shown in joules and electronvolts.
Assumes inertial frames and constant velocity. For
v ≥ c, γ is undefined. Use custom c for refractive media experiments cautiously.
How to use this calculator
- Select a mode: compute from velocity, or from a target γ.
- Enter velocity and pick units, or enter target γ (≥ 1).
- Optionally enter rest mass to view kinetic energy outputs.
- Adjust c or precision if needed, then click Compute.
- Click Add to table to record results for export.
- Export results to CSV or PDF for documentation or sharing.
Reference data for γ calculations
γ vs β quick reference
| β | v (m/s) | v (km/s) | γ | 1/γ |
|---|
Computed using current c and precision settings.
Velocity needed for target γ
| γ (target) | β = v/c | v (m/s) | v (km/s) | % of c |
|---|
Derived from v = c·√(1 − 1/γ²).
Real‑world speeds and γ
| Scenario | Speed (m/s) | β | γ | 1/γ |
|---|
Speeds are representative; γ recalculates if c is changed.