Normal Shock Calculator
Calculate downstream Mach and static pressure, density and temperature ratios across a perfect-gas normal shock.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use mass, momentum and energy conservation across a stationary one-dimensional normal shock with constant gamma.
M2²=(1+(γ−1)M1²/2)/(γM1²−(γ−1)/2); p2/p1=1+2γ(M1²−1)/(γ+1)
Worked example
For M1=2 and γ=1.4, M2=√(1/3)≈0.577350269, pressure ratio 4.5, density ratio 8/3 and temperature ratio 1.6875.
Assumptions and input details
Supersonic upstream perfect gas with constant heat capacities, normal shock only. Real-gas high-temperature chemistry, oblique shocks, boundary layers and actual geometry are excluded; large Mach inputs are mathematical extrapolations of this model.
References: NASA: compressible-flow equations, Report 1135
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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