Normal Shock Calculator
Type into any box, a pitot reading included, and the rest of the shock follows, at any γ.
Every jump across a normal shock rises or falls monotonically with M₁, so any one of them fixes the whole shock. There is no second root to choose here.
Results
| Quantity | Value every white box is an input |
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Isentropic state either side
| Upstream | Downstream |
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What this is computing
A normal shock is a discontinuity a few mean free paths thick that a supersonic flow cannot avoid. Mass, momentum and energy all cross it unchanged; entropy does not, and that one-way rise is what fixes the direction and makes every jump below a function of M₁ alone.
Stagnation temperature is unchanged because the shock is adiabatic; stagnation pressure is not, and its loss is the entropy rise wearing different units. Every jump here is monotonic in M₁, so any one of them fixes the whole shock — which is why this page has no branch to choose.
Only one direction is allowed
Nothing in mass, momentum or energy forbids running the shock backwards — an expansion shock satisfies all three. The second law forbids it, and this is the one place in the subject where entropy does visible work rather than bookkeeping.
Density saturates, pressure does not
Pressure and temperature climb without limit as M₁ grows, but the density ratio cannot pass (γ+1)/(γ−1) — 6 for air — and M₂ falls to a floor of 0.378 rather than to zero. A shock compresses a fixed amount however hard you hit it.
Why a pitot probe needs this page
A probe in supersonic flow reads the stagnation pressure behind its own bow shock, so the incompressible formula is not merely inaccurate, it is measuring a different quantity. And the loss is severe: p₀₂/p₀₁ is 0.721 at M₁ = 2 but 0.062 at M₁ = 5, which is why supersonic inlets use several oblique shocks instead of one normal one.