Mach Number Calculator | Subsonic, Transonic & Supersonic Flow Properties
Compute Mach number, dynamic pressure, stagnation (total) temperature, stagnation pressure, and speed of sound for subsonic, transonic, and supersonic flows. Supports ISA standard atmosphere from sea level to 50 km altitude with ambient condition lookup.
What Is the Mach Number Calculator | Subsonic, Transonic & Supersonic Flow Properties?
The Mach number M = v/a compares an object's speed to the local speed of sound a = √(γRT). In the ISA atmosphere, temperature falls linearly at 6.5 K/km from 288.15 K at sea level to 216.65 K at 11 km, then stays constant to 20 km. Because a depends only on temperature, the speed of sound is constant throughout the stratosphere. Stagnation quantities T₀ and P₀ represent conditions if the flow were brought to rest isentropically — critical for aerodynamic heating design.
Formula
a = √(γ·R·T) · M = v/a · T₀ = T·(1+0.2M²) · P₀ = P·(1+0.2M²)^3.5 · q = ½ρv²
How to Use
- 1
Select a preset (Commercial jet, Concorde, SR-71, Space Shuttle) to pre-fill the inputs.
- 2
Choose a calculation mode using the tab buttons at the top.
- 3
In "Speed → Mach" mode: enter altitude (km) and airspeed with unit selection.
- 4
In "Mach → Airspeed" mode: enter altitude (km) and Mach number.
- 5
In "Find Altitude" mode: enter target Mach number and true airspeed.
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Click "Calculate" to see results including flow regime classification.
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All ISA calculations cover 0–20 km altitude (troposphere and stratosphere).
Choose a mode: 'Speed → Mach' to find Mach number from altitude and true airspeed, 'Mach → Airspeed' to find true airspeed and stagnation properties, or 'Find Altitude' to find where a given Mach equals a given speed.
Example Calculation
Example 1 — Commercial jet: altitude 10 km, speed 885 km/h. T = 223.15 K, a = √(1.4×287.05×223.15) = 299.5 m/s. v = 885/3.6 = 245.8 m/s. M = 245.8/299.5 = 0.821 → Transonic. Example 2 — Concorde: M 2.02 at 18 km. T = 216.65 K (stratosphere), a = 295.1 m/s. v = 2.02×295.1 = 596 m/s = 2145 km/h. T₀ = 216.65×(1+0.2×2.02²) = 393 K (120 °C nose temperature).
Understanding Mach Number | Subsonic, Transonic & Supersonic Flow Properties
ISA standard atmosphere profile
| Altitude (km) | Temperature (K) | Pressure (Pa) | Density (kg/m³) | Speed of sound (m/s) |
|---|---|---|---|---|
| 0 (sea level) | 288.15 | 101 325 | 1.225 | 340.3 |
| 5 | 255.65 | 54 048 | 0.7364 | 320.5 |
| 10 | 223.15 | 26 500 | 0.4135 | 299.5 |
| 11 (tropopause) | 216.65 | 22 632 | 0.3639 | 295.1 |
| 15 | 216.65 | 12 111 | 0.1948 | 295.1 |
| 20 | 216.65 | 5 475 | 0.08803 | 295.1 |
Notable aircraft Mach performance
| Aircraft | Cruise Mach | Altitude (km) | True airspeed | Regime |
|---|---|---|---|---|
| Boeing 737 | M 0.785 | 10 | ~828 km/h | Subsonic |
| Airbus A380 | M 0.85 | 13 | ~903 km/h | High subsonic |
| Concorde | M 2.02 | 18 | ~2 180 km/h | Supersonic |
| SR-71 Blackbird | M 3.3 | 24 | ~3 540 km/h | Supersonic |
| X-15 rocket plane | M 6.7 | 50 | ~7 270 km/h | Hypersonic |
| Space Shuttle reentry | M 25 | 70 | ~7 400 m/s | Hypersonic |
Flow regimes and engineering implications
- ›Subsonic (M < 0.8): Compressibility effects are small. Standard Bernoulli analysis is adequate. Most commercial aviation operates here.
- ›Transonic (0.8 ≤ M ≤ 1.2): Mixed subsonic/supersonic flow over the aircraft. Shock waves form on upper wing surfaces. Wave drag rises sharply — the "sound barrier". Swept wings and area ruling are used to delay drag rise.
- ›Supersonic (1.2 < M < 5): Oblique shock waves form at the nose and wing leading edges. Sonic boom is generated. Stagnation temperature rises significantly; Concorde nose reached ~127 °C at M 2.
- ›Hypersonic (M > 5): Aerodynamic heating dominates design. At M 25, stagnation temperature exceeds 8 000 K — the Space Shuttle used ceramic tiles to survive reentry heating.
Frequently Asked Questions
Why does the speed of sound decrease with altitude in the troposphere?
The speed of sound a = √(γRT) depends on temperature alone, not pressure or density. In the troposphere, temperature decreases at 6.5 K/km (the lapse rate). At 10 km, T ≈ 223 K vs 288 K at sea level, giving a ≈ 299 m/s vs 340 m/s — about 12% slower.
What is stagnation (total) temperature and why does it matter?
When supersonic flow is decelerated to rest (e.g. at a leading edge or pitot tube), kinetic energy converts to heat. T₀ = T·(1+0.2M²) is the temperature at a stagnation point. At M 3 and 24 km, T₀ ≈ 219×(1+1.8) = 613 K. This drives aircraft skin heating, requiring heat-resistant materials for supersonic aircraft.
What is dynamic pressure and why is it important?
Dynamic pressure q = ½ρv² represents the kinetic energy per unit volume of the flow. It is the pressure that would be exerted if the flow were brought to rest. Aerodynamic forces (lift, drag) are proportional to q. At high altitude, lower density means lower q despite higher Mach — that's why high-altitude supersonic aircraft have relatively light structural loads.
What is the ISA model and when does it apply?
The International Standard Atmosphere (ISA) is a mathematical model of average atmospheric conditions: T, P, and ρ as a function of altitude. It assumes a standard sea-level pressure of 101 325 Pa and temperature of 288.15 K. Real conditions deviate from ISA (ISA+10°C for hot days, ISA−10°C for cold days), affecting performance calculations.
What is the transonic regime and why is it tricky to design for?
At M 0.8–1.2, some flow over the aircraft exceeds M 1 even though the aircraft itself is below M 1. Shock waves form intermittently on wings and fuselage, causing wave drag, buffeting, and loss of control authority. Aircraft are specifically designed with swept wings and narrow fuselages (Whitcomb area rule) to minimise transonic drag rise.
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