Stagnation Pressure and Temperature Calculator

Stagnation temperature T0 and stagnation pressure P0 are the temperature and pressure a moving gas would reach if it were brought to rest isentropically (reversibly and without heat loss). They represent the total energy state of the flow, static conditions plus the energy of its motion, and are what a forward-facing Pitot probe or an engine inlet actually measures.

The Isentropic Flow Relations Calculator outputs dimensionless ratios (T0/T, p0/p, etc.) swept across a range of Mach numbers, useful for general coursework and reference tables. This calculator instead takes your real, actual static temperature and pressure at a specific flight condition and computes the actual T0 and P0 numbers in Kelvin and kPa, answering 'what are the real numbers for my altitude and speed' rather than giving a general ratio.

T0 = T × (1 + (γ-1)/2·M²), where T is the static (ambient) temperature in Kelvin, γ is the ratio of specific heats (1.4 for air), and M is the Mach number. The temperature rise T0 - T grows with the square of Mach number, which is why high-speed flight causes so much more aerodynamic heating than low-speed flight.

P0 = P × (1 + (γ-1)/2·M²)^(γ/(γ-1)), where P is the static (ambient) pressure. Because the exponent γ/(γ-1) is 3.5 for air, stagnation pressure rises much more steeply with Mach number than stagnation temperature does.

The stagnation temperature rise scales with M², so doubling Mach number roughly quadruples the temperature rise above ambient. At 11 km altitude (static T = 216.65 K), Mach 0.85 gives a stagnation temperature of about 248 K, only 31 K above ambient, while Mach 2.0 at the same altitude gives about 390 K, a 173 K rise, over five times larger. This is why supersonic and hypersonic vehicles need thermal protection systems that subsonic aircraft do not.

A Pitot-static probe measures stagnation pressure P0 at a forward-facing port (where the flow is brought to rest) and static pressure P at a side port unaffected by the probe's presence. The difference P0 - P, corrected for compressibility using these same formulas, gives the airspeed. At low speed the simple incompressible Bernoulli approximation is close enough, but above roughly Mach 0.3 the full compressible stagnation pressure formula is needed for accurate airspeed.

No, select Celsius as the temperature unit and this calculator converts automatically using T(K) = T(°C) + 273.15. If you already have the static temperature in Kelvin, leave the unit as Kelvin.

Use the International Standard Atmosphere (ISA) values for your target altitude: at sea level, T ≈ 288.15 K and P ≈ 101.325 kPa; at 11 km (typical airliner cruise altitude), T ≈ 216.65 K and P ≈ 22.63 kPa. Standard atmosphere reference tables list these values at any altitude.

Stagnation pressure P0/P = (T0/T)^(γ/(γ-1)), and for air γ/(γ-1) equals 3.5, so the pressure ratio is the temperature ratio raised to the 3.5 power. A modest rise in the temperature ratio compounds into a much larger rise in the pressure ratio, which is why cabin pressurization and structural loads on high-speed aircraft scale so steeply with Mach number.

No, the same stagnation temperature and pressure formulas apply to any compressible gas flow at a known Mach number: gas turbine inlet analysis, high-speed wind tunnel instrumentation, compressor and turbine stage design, and any Pitot-static measurement in a compressible flow, not only aircraft in flight.