Stagnation Temperature Calculator

Calculator Input

Calculation Method

Choose the formula set for your data.

Static Temperature

Enter the undisturbed flow temperature.

Temperature Unit

The result will be shown in all major units.

Mach Number

Use for compressible adiabatic flow.

Specific Heat Ratio (γ)

Air is often approximated as 1.4.

Velocity

Used with specific heat in the energy form.

Velocity Unit

Pick the unit that matches your input.

Specific Heat at Constant Pressure

Needed for the velocity-energy equation.

Specific Heat Unit

Air near room conditions is about 1005 J/kg-K.

Graph Range Limit

Mach limit for Mach mode, scaled range for velocity mode.

Formula Used

Mach number form: T₀ = T \u00d7 [1 + ((\u03b3 - 1) / 2) \u00d7 M²]

Here, T₀ is stagnation temperature, T is static temperature, \u03b3 is the specific heat ratio, and M is Mach number.

Velocity form: T₀ = T + V² / (2c_p)

In this form, V is velocity and c_p is specific heat at constant pressure. Both equations assume adiabatic flow and no external shaft work.

How to Use This Calculator

Select either the Mach method or velocity method.
Enter the static temperature and choose its unit.
For the Mach method, enter Mach number and specific heat ratio.
For the velocity method, enter velocity, velocity unit, specific heat, and its unit.
Set an optional graph range limit for the output chart.
Click the calculate button to show the result above the form.
Review converted temperatures, the temperature rise, and the ratio values.
Use the CSV or PDF buttons to export the results.

Example Data Table

Case	Static Temp	Method	Input Value	Extra Property	Stagnation Temp
Air nozzle test	25 °C	Mach method	M = 2.0	γ = 1.4	245.37 °C
Subsonic duct flow	300 K	Mach method	M = 0.8	γ = 1.4	338.40 K
Wind tunnel run	20 °C	Velocity method	250 m/s	c_p = 1005 J/kg-K	51.09 °C
Hot gas stream	500 K	Velocity method	400 m/s	c_p = 1150 J/kg-K	569.57 K

Frequently Asked Questions

1. What is stagnation temperature?

Stagnation temperature is the temperature a moving fluid would reach if slowed to zero velocity adiabatically. It combines static thermal energy with kinetic energy converted into thermal form.

2. Is stagnation temperature always higher than static temperature?

Yes, for moving flow it is equal to or greater than static temperature. The difference comes from kinetic energy. At zero velocity, stagnation and static temperatures become the same.

3. When should I use the Mach formula?

Use the Mach form when compressible flow data is available as Mach number and specific heat ratio. It is common in aerodynamics, gas dynamics, nozzles, and wind tunnel analysis.

4. When should I use the velocity formula?

Use the velocity form when you know actual flow speed and specific heat. It is useful for engineering energy balances, intake calculations, and moderate-speed gas flow checks.

5. Why does the calculator ask for specific heat ratio?

The Mach equation depends on the thermodynamic behavior of the gas. Specific heat ratio captures that behavior. Air is often approximated with a value near 1.4 under standard conditions.

6. Can I enter Celsius or Fahrenheit?

Yes. The calculator converts Celsius, Fahrenheit, Kelvin, and Rankine internally. For the physics to remain valid, the math is done using absolute temperature after conversion.

7. Does this calculator account for losses?

No. It assumes ideal adiabatic behavior without shaft work or dissipation losses. Real systems may show deviations because of friction, heat transfer, shock effects, or measurement uncertainty.

8. What industries use stagnation temperature calculations?

These calculations are widely used in aerospace, turbomachinery, HVAC research, combustion studies, gas pipelines, engine testing, and high-speed instrumentation design where flow energy matters.