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Oblique Shock Calculator — Shock Angle, Mach & Pressure Rise
Solve the weak attached oblique-shock angle from upstream Mach and flow deflection, then calculate downstream Mach and normal-shock property ratios.
Last updated: September 17, 2026
Results
Formula, example and assumptions
tanθ=2cotβ·(M1²sin²β−1)/(M1²(γ+cos2β)+2); apply normal-shock relations to M1n=M1sinβ.
For M1=3, γ=1.4 and θ=20°, the weak shock angle is about 37.8° and downstream Mach about 2.0.
- Weak attached-shock branch is selected numerically when it exists.
- Perfect-gas, steady two-dimensional inviscid flow is assumed.
Frequently asked questions
What does this Oblique Shock Calculator solve?
Solve the weak attached oblique-shock angle from upstream Mach and flow deflection, then calculate downstream Mach and normal-shock property ratios.
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.