Enter light speed or Mach into the calculator to convert to the other value with selectable speed-of-sound conditions.
Light Speed to Mach Formula
The following formulas convert light speed to Mach and back using the selected speed of sound a for the air condition.
\mathrm{Mach} = \dfrac{v}{a}- Speed of light: c = 299,792,458 m/s (exact).
- ISA sea level (15°C): a ≈ 340.3 m/s; at 20°C: a ≈ 343.2 m/s; at 0°C: a ≈ 331.3 m/s.
- Relationships: v = M·a; fraction of c f = v/c; percent of c = 100·f.
- At ISA 15°C: 1c ≈ Mach 880,965; 0.01c ≈ Mach 8,810.
Light Speed to Mach Conversion Table
| Fraction of c | Mach (ISA) |
|---|---|
| 0.000001 | 0.881 |
| 0.00001 | 8.810 |
| 0.0001 | 88.097 |
| 0.001 | 880.965 |
| 0.002 | 1761.930 |
| 0.005 | 4404.826 |
| 0.01 | 8809.652 |
| 0.02 | 17619.304 |
| 0.05 | 44048.260 |
| 0.1 | 88096.520 |
| 0.2 | 176193.040 |
| 0.3 | 264289.560 |
| 0.5 | 440482.600 |
| 1 | 880965.200 |
| * Using ISA sea level: a ≈ 340.3 m/s, so 1c ≈ 299,792,458 / 340.3 ≈ Mach 880,965. | |
How do you convert light speed to Mach? Convert the light-speed value to meters per second (m/s), pick a speed of sound a for the conditions, then compute Mach = v ÷ a.
How do you convert Mach to light speed? Multiply Mach by a to get v, then divide by c for a fraction of c (or multiply by 100 for percent of c); alternatively convert v into km/s, km/h, or mph as needed.
Example Problem
Convert 0.05c to Mach at ISA sea level (15°C).
Use the formula: Mach = v ÷ a with v = 0.05 × c and a ≈ 340.3 m/s.
Mach ≈ (0.05 × 299,792,458) ÷ 340.3 ≈ 44,048.3