Convert knots or other true airspeed to Mach using ISA altitude or air temperature, reverse the conversion, and see local sound speed and thermal sensitivity.
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).
- γ (ratio of specific heats for dry air) = 1.4
- R (specific gas constant for dry air) = 287.05287 J/(kg·K)
- ISA sea level (15 °C): a ≈ 340.3 m/s = 661.5 kn
- Unit link: 1 knot = 1852/3600 m/s ≈ 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 (×1852/3600), 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 × (1852/3600) = 231.5 m/s; therefore Mach ≈ 231.5 ÷ 296.4 ≈ 0.781. The model assumes ideal dry air with fixed γ = 1.4 and omits humidity and variable specific heats; it is not a flight instrument.
