Critical Pressure Ratio Calculator

Gas model Custom γ Air (γ≈1.40) Nitrogen (γ≈1.40) Oxygen (γ≈1.40) Carbon dioxide (γ≈1.289) Steam (γ≈1.33) Helium (γ≈1.66) Hydrogen (γ≈1.41)

Preset fills γ automatically on submit.

Heat capacity ratio (γ)

Used when gas model is Custom γ.

Pressure unit PakPaMPabaratmpsi

Applies to all pressure fields.

Stagnation / inlet pressure (P0)

Upstream total pressure before the throat.

Back pressure (Pb) (optional)

Used to test choking: Pb/P0 ≤ P*/P0.

Calculate

For isentropic compressible flow through a converging nozzle, the flow becomes choked when the throat reaches Mach 1. The corresponding critical pressure ratio is:

(P*/P0) = (2/(γ + 1))^(γ/(γ − 1))

• γ is the heat capacity ratio (Cp/Cv).
• P0 is the upstream stagnation (total) pressure.
• P* is the critical back pressure that just causes choking.

1. Select a gas model, or keep Custom γ and enter γ.
2. Enter the stagnation/inlet pressure P0 using your chosen unit.
3. Optionally enter back pressure Pb to test if flow is choked.
4. Press Calculate to show results above this form.
5. Use Download CSV or Download PDF to save outputs.

Values are rounded. Real systems may deviate due to losses and non-ideal effects.

1) Why critical pressure ratio matters

In compressible flow, pressure does not translate to mass flow in a linear way. When a nozzle or orifice accelerates gas toward sonic speed, a threshold appears: once the downstream pressure is low enough, the throat reaches Mach 1 and the mass flow becomes limited by upstream conditions. The key indicator is the critical pressure ratio P*/P0.

2) Choked flow threshold in numbers

For many engineering estimates, air can be modeled with γ≈1.40, producing P*/P0≈0.528. That means if the back pressure is at or below about 52.8% of the inlet stagnation pressure, the flow is choked. For helium (γ≈1.66) the ratio is lower, near 0.487, while steam (γ≈1.33) often gives a higher ratio near 0.546.

3) Role of γ and gas selection

The heat capacity ratio γ = Cp/Cv captures how strongly a gas temperature changes during expansion. Higher γ generally makes the critical ratio smaller, meaning choking can occur at a lower Pb/P0. This calculator includes common presets so you can compare gases quickly without searching property tables.

4) From ratio to critical back pressure

Designers often need a pressure value, not just a ratio. Once P*/P0 is known, critical back pressure follows from P* = (P*/P0) × P0. Example: with P0 = 400 kPa and air, P* ≈ 0.528 × 400 ≈ 211 kPa. Below this, further reducing Pb does not increase mass flow through a purely converging throat.

5) Practical use cases

Critical pressure ratio is used in pneumatic exhaust sizing, regulator selection, safety vent checks, and nozzle performance prediction. In test rigs, it helps confirm whether a measurement is limited by upstream supply or by downstream conditions. It is also a quick screening step before applying full compressible-flow mass flow equations.

6) Units and consistency

The ratio P*/P0 is unitless, so it is stable across unit systems. However, the calculator also reports P* in your selected unit for clarity. Keep P0 and Pb in the same unit, and interpret results as stagnation pressure upstream of the restriction and static back pressure downstream.

7) Assumptions and limitations

The displayed relation assumes isentropic behavior, steady flow, and a converging throat where choking occurs at Mach 1. Real hardware can shift the effective threshold due to friction, heat transfer, boundary layers, and non-ideal gas effects at high pressure or very low temperature.

8) Interpreting the choking check

If you enter Pb, the calculator evaluates Pb/P0 against P*/P0. When Pb/P0 ≤ P*/P0, choking is expected and the throat becomes the controlling section. When Pb/P0 is higher, the flow remains subsonic everywhere and responds more directly to downstream pressure changes.

1) What is the critical pressure ratio?

It is the threshold ratio P*/P0 at which a nozzle throat reaches Mach 1. Below this ratio, the flow becomes choked and mass flow is limited mainly by upstream conditions.

2) Why is γ required?

γ (Cp/Cv) describes gas compressibility during expansion. It controls the isentropic relationship between pressure and Mach number, so it directly sets the critical ratio.

3) Do I need back pressure to use the tool?

No. You can compute P*/P0 and the critical back pressure P* using only γ and P0. Pb is optional for checking whether choking occurs.

4) What does “choked” mean here?

Choked means the throat reaches sonic speed. Once choked, lowering Pb further does not increase mass flow through a purely converging restriction under isentropic assumptions.

5) Is P0 the same as static pressure?

No. P0 is stagnation (total) pressure upstream, including dynamic effects. In many supply lines, it is close to static pressure if velocities are small.

6) Can I use this for liquids?

This relation is for gases in compressible flow. Liquids do not follow the same choking behavior and typically require cavitation or flashing models instead.

7) Why might real results differ from the calculator?

Losses from friction, heat transfer, non-ideal gas behavior, and geometry effects can change the effective threshold. Use this as a first-pass estimate and validate with testing when needed.