Convert light speed to Mach or Mach to light-speed units using selectable speed of sound references, temperatures, or custom m/s values.
Light Speed to Mach Formula
The following formulas compare a speed with the selected speed of sound a. Temperature references use the ideal dry-air relation a = โ(ฮณRT), with ฮณ = 1.4, R = 287.05 J/(kgยทK), and T in kelvin. This is an arithmetic conversion, not a model of relativistic flight.
- Speed of light: c = 299,792,458 m/s (exact).
- ISA sea level (15ยฐC): a โ 340.3 m/s; at 20ยฐC: a โ 343.2 m/s; at 0ยฐC: a โ 331.3 m/s.
- Relationships: v = Mยทa; fraction of c f = v/c; percent of c = 100ยทf.
- At ISA 15ยฐC in this model: 1c โ Mach 880,985.169; 0.01c โ Mach 8,809.852.
Light Speed to Mach Conversion Table
| Fraction of c | Mach (ISA) |
|---|---|
| 0.000001 | 0.881 |
| 0.00001 | 8.810 |
| 0.0001 | 88.099 |
| 0.001 | 880.985 |
| 0.002 | 1761.970 |
| 0.005 | 4404.926 |
| 0.01 | 8809.852 |
| 0.02 | 17619.703 |
| 0.05 | 44049.258 |
| 0.1 | 88098.517 |
| 0.2 | 176197.034 |
| 0.3 | 264295.551 |
| 0.5 | 440492.585 |
| 1 | 880985.169 |
| * Using the same model as the calculator: a = โ(1.4 ร 287.05 ร 288.15) โ 340.292286865 m/s. Table entries are rounded to three decimal places. | |
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 รท 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 (15ยฐC).
Use the formula: Mach = v รท a with v = 0.05 ร c and a = โ(1.4 ร 287.05 ร 288.15) โ 340.292286865 m/s.
Mach โ (0.05 ร 299,792,458) รท 340.292286865 โ 44,049.258
