Enter a speed in knots (or km/h, m/s, or mph) or a Mach number to convert between them using either ISA altitude or temperature.
Knots to Mach Formula
The following formulas convert a speed in knots to a Mach number and back, using the local speed of sound determined by temperature (entered directly or from ISA altitude).
\mathrm{Mach}=\frac{V}{a},\quad a=\sqrt{\gamma\,R\,T}- γ (ratio of specific heats for dry air) = 1.4
- R (specific gas constant for dry air) = 287.052 J/(kg·K)
- ISA sea level (15 °C): a ≈ 340.3 m/s = 661.5 kn
- Unit link: 1 knot = 0.514444 m/s (1 m/s = 1.94384 kn)
Knots to Mach Conversion Table
| Knots (TAS) | Mach |
|---|---|
| 50 | 0.076 |
| 100 | 0.151 |
| 150 | 0.227 |
| 200 | 0.302 |
| 250 | 0.378 |
| 300 | 0.453 |
| 350 | 0.529 |
| 400 | 0.605 |
| 450 | 0.680 |
| 500 | 0.756 |
| 550 | 0.831 |
| 600 | 0.907 |
| 650 | 0.982 |
| 700 | 1.058 |
| 750 | 1.133 |
| 800 | 1.209 |
| 850 | 1.285 |
| 900 | 1.360 |
| 950 | 1.436 |
| 1000 | 1.511 |
| * ISA sea level approximation: Mach ≈ knots ÷ 661.5. | |
How do you convert knots to Mach? Convert knots to m/s (×0.514444), compute the local speed of sound a = √(γRT) from temperature (or ISA altitude), then Mach = V/a; at ISA sea level, a ≈ 661.5 kn so Mach ≈ knots ÷ 661.5.
How do you convert Mach to knots? Compute V = Mach × a using temperature (or ISA altitude), then convert m/s to knots (×1.94384); at ISA sea level, knots ≈ Mach × 661.5.
Example Problem
Convert 450 knots to Mach at 35,000 ft (ISA).
Use M = V/a. ISA temperature at 35,000 ft (~10,668 m) is T ≈ 218.8 K, so a = √(1.4 × 287.052 × 218.8) ≈ 296.4 m/s.
Convert speed: V = 450 kn × 0.514444 = 231.5 m/s; therefore Mach = 231.5 ÷ 296.4 ≈ 0.781.
