Stagnation Properties Calculator

Compute total (stagnation) temperature T₀ and pressure P₀ from static conditions and Mach number via isentropic deceleration to rest.

Compressible Flow · Stagnation

Gas presets — click to fill γ

Inputs

Mach number M (dimensionless)

Specific heat ratio γ (dimensionless)

c_p/c_v — use gas presets above

Static temperature T (K)

T = 250.00 K

Static pressure P (kPa)

Theory

Stagnation (total) property relations:

T₀ = T × [1 + (γ−1)/2 × M²] [stagnation temperature]

P₀ = P × [1 + (γ−1)/2 × M²]^γ/(γ−1) [stagnation pressure]

ρ₀ = ρ × [1 + (γ−1)/2 × M²]^1/(γ−1) [stagnation density]

Where:

T, P, ρ = static (local) properties of the flowing gas
T₀, P₀, ρ₀ = stagnation (total) properties — state if isentropically decelerated to rest
M = Mach number = V/c where c = √(γRT)
ΔT = T₀ − T = (γ−1)/2 × M² × T — dynamic temperature rise from kinetic energy
T₀ is conserved in any adiabatic flow (with or without friction)
P₀ is conserved only in isentropic (reversible adiabatic) flow — drops across shocks and in viscous ducts

Stagnation ratios for air (γ = 1.4) at common Mach numbers:

M	T₀/T	P₀/P	ΔT/T	Regime
0.0	1.000	1.000	0.000	at rest
0.3	1.018	1.064	0.018	subsonic
0.5	1.050	1.186	0.050	subsonic
0.8	1.128	1.524	0.128	subsonic
1.0	1.200	1.893	0.200	transonic
1.5	1.450	3.671	0.450	supersonic
2.0	1.800	7.824	0.800	supersonic
3.0	2.800	36.73	1.800	supersonic

Stagnation temperature T₀ is the key quantity in propulsion — it represents the total energy content per unit mass of the gas stream. T₀ = T + V²/(2c_p), showing it is the static temperature plus the kinetic energy contribution. P₀ is used to quantify losses: any irreversibility (shock, friction) reduces P₀ even if T₀ stays constant.