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Isentropic Flow Calculator — Mach, Static Ratios & Area Ratio
Calculate ideal-gas static temperature, pressure and density ratios, velocity and nozzle area ratio from Mach number and stagnation conditions.
Last updated: September 17, 2026
Results
Formula, example and assumptions
T/T0=[1+(γ−1)M²/2]⁻¹; P/P0=(T/T0)^(γ/(γ−1)); A/A*=M⁻¹[(2/(γ+1))(1+(γ−1)M²/2)]^((γ+1)/(2(γ−1))).
For air at M=2, T/T0≈0.5556, P/P0≈0.1278 and A/A*≈1.6875.
- Steady one-dimensional adiabatic reversible ideal-gas flow.
- Constant γ and R; shocks, friction and heat addition are excluded.
Frequently asked questions
What does this Isentropic Flow Calculator solve?
Calculate ideal-gas static temperature, pressure and density ratios, velocity and nozzle area ratio from Mach number and stagnation conditions.
Which units should I use?
Use the units printed beside each input. Dimensionless ratios need no conversion; pressure inputs used in gas equations are absolute unless the field explicitly says differential.
Is this suitable for final engineering design?
Use it for transparent first-pass calculations and cross-checks. Final design should verify gas or fluid properties, geometry, loss data, equipment curves and the applicable engineering standard.