Mach Number
Calculate Mach number from object speed and air temperature. Free online physics calculator with speed comparison chart, flow regime classification, and step-by-step breakdown.
About This Calculator
The Mach Number Calculator computes the Mach number for an object moving through air. The Mach number is a dimensionless quantity that represents the ratio of an object's speed to the local speed of sound. It is widely used in aerospace engineering, fluid dynamics, and aviation to characterize flow regimes — from subsonic commercial flights to hypersonic spacecraft.
The calculator uses the standard formula M = v / c, where v is the speed of the object and c is the speed of sound in air. The speed of sound is calculated from the air temperature using the formula c = 331.3 × √(1 + T / 273.15), where T is the temperature in degrees Celsius. This formula assumes dry air with a specific heat ratio γ = 1.4 and a specific gas constant R = 287.058 J/(kg·K). At 20°C, the speed of sound is approximately 343 m/s.
The calculator supports four speed units: meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), and knots (kn). After calculation, the result displays the Mach number, the speed of sound at the given temperature, the object's speed in m/s, and the flow regime classification: Subsonic (M < 0.8), Transonic (0.8 ≤ M < 1.2), Supersonic (1.2 ≤ M < 5.0), or Hypersonic (M ≥ 5.0). A bar chart compares the object speed against the speed of sound for quick visual reference.
Flow regime classification is critical for aircraft design because the aerodynamic forces change dramatically at transonic and supersonic speeds. Shock waves form above Mach 1, creating wave drag that requires specialized design features like swept wings and area-ruling. Hypersonic flows above Mach 5 additionally involve chemical reactions and thermal dissociation of air molecules, requiring advanced thermal protection systems.
Frequently Asked Questions
What is Mach number?
Mach number is a dimensionless quantity that represents the ratio of an object's speed to the speed of sound in the surrounding medium. It is expressed as M = v/c, where v is the velocity of the object and c is the local speed of sound.
How is Mach number calculated?
Mach number is calculated by dividing the speed of the object by the speed of sound in the medium. The speed of sound in air depends on temperature and is computed using the formula c = 331.3 × √(1 + T/273.15), where T is the air temperature in degrees Celsius.
What is the difference between subsonic, transonic, supersonic, and hypersonic flow?
Subsonic flow occurs at Mach numbers below 0.8, transonic at 0.8 to 1.2, supersonic at 1.2 to 5.0, and hypersonic at Mach 5.0 and above. Subsonic aircraft include commercial airliners, supersonic aircraft include military fighters like the F-16, and hypersonic vehicles include ballistic missiles and the NASA X-15.
What is the Mach number of a typical commercial aircraft?
A typical commercial aircraft like the Boeing 747 or Airbus A330 cruises at Mach 0.84 to 0.86 at an altitude of around 31,000 feet, where the temperature is about -46°C and the speed of sound is approximately 302 m/s.
What is the speed of sound at different temperatures?
The speed of sound in dry air at 0°C is 331.3 m/s. At 20°C (room temperature) it is about 343 m/s, and at 30°C it is about 349 m/s. The speed increases with temperature because warmer air has faster-moving molecules, enabling sound waves to propagate more quickly.
Can Mach number exceed 1?
Yes, Mach numbers greater than 1 indicate supersonic or hypersonic speeds. When an aircraft exceeds Mach 1, it breaks the sound barrier, creating a sonic boom. The Bell X-1 was the first manned aircraft to achieve supersonic flight in 1947, piloted by Chuck Yeager.
What unit is used for Mach number?
Mach number is a dimensionless quantity and has no units. It is simply a ratio of the object's speed to the local speed of sound. This calculator supports input speeds in m/s, km/h, mph, and knots for convenience.