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Normal Shock Calculator — Downstream Mach & Property Ratios
Calculate downstream Mach number, static pressure, density and temperature ratios across a normal shock for a perfect gas.
Last updated: September 17, 2026
Results
Formula, example and assumptions
M2²=[1+(γ−1)M1²/2]/[γM1²−(γ−1)/2]; P2/P1=1+2γ(M1²−1)/(γ+1).
For air at M1=2, M2≈0.577, P2/P1=4.5 and ρ2/ρ1≈2.667.
- Upstream flow must be supersonic.
- The shock is stationary, planar and normal to a calorically perfect gas stream.
Frequently asked questions
What does this Normal Shock Calculator solve?
Calculate downstream Mach number, static pressure, density and temperature ratios across a normal shock for a perfect gas.
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.