Enter a speed or a value relative to the speed of light to convert between common units and a fraction or percent of c.
M/s to Speed of Light Formula
The following formulas convert speed to a fraction or percent of the speed of light and back.
r = \frac{v}{c}- c (speed of light) = 299,792,458 m/s (exact)
- 1 km/s = 1,000 m/s.
- 1 km/h = 0.277777… m/s.
- 1 mph = 0.44704 m/s.
- 1 ft/s = 0.3048 m/s.
- 1 knot = 0.514444 m/s.
M/s to Speed of Light Conversion Table
| Fraction of c | Speed (m/s) |
|---|---|
| 0.001 | 299,792.458 |
| 0.010 | 2,997,924.580 |
| 0.050 | 14,989,622.900 |
| 0.100 | 29,979,245.800 |
| 0.200 | 59,958,491.600 |
| 0.300 | 89,937,737.400 |
| 0.500 | 149,896,229.000 |
| 0.900 | 269,813,212.200 |
| 0.990 | 296,794,533.420 |
| 1.000 | 299,792,458.000 |
| * c = 299,792,458 m/s (exact). | |
How do you convert m/s to a fraction or percent of c? Divide by c: r = v ÷ 299,792,458 for fraction of c; %c = 100 × v ÷ 299,792,458 for percent of c.
How do you convert a fraction or percent of c to m/s? Multiply by c: v = r × 299,792,458 or v = (%c ÷ 100) × 299,792,458.
Example Problem
Convert 90,000 km/s to percent of the speed of light.
First convert to m/s: v = 90,000 × 1,000 = 90,000,000 m/s.
Use the formula r = v ÷ c: r = 90,000,000 ÷ 299,792,458 ≈ 0.3002 c ≈ 30.02% of c.