Mixed Air Temperature Calculator - HVAC and Gas-Mix Formulas

The mixed air temperature calculator blends two gas streams into a single temperature using the flow-weighted average formula from ASHRAE and the Zeroth law of thermodynamics. It accepts either volumetric or molar percentages in composition mode or HVAC cfm flow rates in flow mode and returns the blended result in degrees Celsius. Engineers, HVAC technicians, students, and physics teachers use it to size supply-air temperatures, predict equilibrium states in gas mixtures, and avoid manual arithmetic errors when two streams combine.

• • HVAC supply-air sizing: Estimate the supply-air temperature downstream of an economiser or mixing box by combining the outdoor-air cfm with the return-air cfm at their measured temperatures.
• • Physics class equilibrium problems: Compute the equilibrium temperature when two gas reservoirs of different temperatures are connected and the percentages or flow rates are known.
• • Combustion and process engineering: Back out the temperature of a fuel-air or air-steam blend when the two inlet temperatures and their proportional flow rates are measured.
• • Lab and DIY gas experiments: Predict the temperature of a mixed stream before running an experiment so the user can pre-warm or pre-cool equipment and avoid condensation.

The calculator applies the same flow-weighted average formula regardless of mode; only the proportion units change between percentages and cfm flow rates.

According to Omni Calculator, the gas-mix formula is T = T1*P1 + T2*P2 with P1 plus P2 equal to 100 percent, while the HVAC supply-air version uses Ts = (cfmoa*Toa + cfmra*Tra) divided by (cfmoa + cfmra).

When the mixed stream also needs humidity, enthalpy, or a back-calculated relative humidity, Mixed Air Calculator adds the psychrometric outputs on top of the same blending equation.

The calculator multiplies each source temperature by its proportion, adds the two products, and divides by the total proportion. That flow-weighted average is the blended temperature once the two streams reach thermal equilibrium.

• T1: Temperature of the first stream in degrees Celsius. In HVAC mode this is the outside-air temperature, in composition mode this is gas 1.
• P1: Proportion of the first stream. Percent for composition mode or cubic feet per minute for HVAC flow mode.
• T2: Temperature of the second stream in degrees Celsius. In HVAC mode this is the return-air temperature, in composition mode this is gas 2.
• P2: Proportion of the second stream. Percent for composition mode or cubic feet per minute for HVAC flow mode.
• T_mix: Resulting blended temperature once both streams reach thermal equilibrium.

The numerator is the energy carried into the mix by each stream; the denominator is the total amount of gas moving through. Because the gas constant cancels out, the result does not depend on the absolute mass of either stream, and the Zeroth law says the two streams share one temperature.

According to Wikipedia: Thermodynamic equilibrium, the Zeroth law of thermodynamics justifies treating the mixed stream as one temperature once the two sources combine.

When the supply fan sits at altitude and the standard sea-level reference no longer applies, Altitude Temperature Calculator adjusts the inlet temperatures before they enter the flow-weighted blend.

Four ideas make the flow-weighted average intuitive: thermal equilibrium, flow weighting versus simple averaging, the difference between composition and HVAC flow modes, and the role of proportions.

These four concepts show why the same equation appears in physics textbooks and ASHRAE design guides without modification, and why the same calculator works for both percentage and flow-rate inputs.

When the two streams sit at very different densities because of altitude or temperature, Air Density Calculator converts volumetric cfm to mass flow before applying the weighted average.

Pick the calculation mode, type the two source temperatures and their proportions, and read the mixed temperature from the result panel.

1. 1 Choose Composition or HVAC Flow: Select the mode that matches your data. Use Composition for percent or molar fractions, and HVAC Flow for cfm flow rates from an air-handling unit.
2. 2 Enter the first source temperature: Type T1 in degrees Celsius. For HVAC this is the outside-air temperature; for composition this is gas 1.
3. 3 Enter the first source proportion: Type the percentage from 0 to 100 or the cfm flow rate, depending on the active mode.
4. 4 Enter the second source temperature: Type T2 in degrees Celsius. For HVAC this is the return-air temperature; for composition this is gas 2.
5. 5 Enter the second source proportion: Type the percentage or cfm value. Composition mode expects a sum of 100; HVAC mode expects the design supply cfm.
6. 6 Read the blended temperature: The result panel shows T_mix in degrees Celsius, the active mode, the proportion sum, and the first-source weight so you can verify the inputs at a glance.

A school HVAC unit pulls 200 cfm of 32 degC outdoor air and 1800 cfm of 23 degC return air through the mixing box. After picking HVAC Flow mode and entering the two pairs, the calculator returns a 24.05 degC supply-air temperature with the outdoor-air weight at 10 percent of the total.

If the mixed stream also has to meet a humidity setpoint, Absolute Humidity Calculator converts the relative humidity of each inlet into grams of water per cubic metre before sizing downstream equipment.

This calculator delivers the same flow-weighted answer that ASHRAE expects from a mixing box, and adapts to gas-mix problems without any change to the math.

• • Dual-mode in one form: One tool covers both the ASHRAE supply-air formula and the percentage gas-mix formula, so engineers and students share the same page.
• • Real-time recompute: Results update on every keystroke, which makes it easy to compare outdoor-air cfm values during an economiser tuning session.
• • Validated mode and proportion sum: The active mode and proportion sum are surfaced next to the answer, so mistakes such as entering cfm in composition mode become obvious.
• • Math-free workflow: Removes the mental arithmetic of multiplying and dividing by hand, which is the most common source of setup errors in classroom problems and HVAC field measurements.
• • Linear extension to more streams: Because the formula is linear, the same calculator works for two-stream problems and also flags when an engineer needs to combine three or more streams in series.
• • Negative-temperature safe: Accepts negative outdoor-air temperatures for winter conditions, which the simple average of percentages or flows would not handle cleanly.

The calculator is most useful at the boundary between two streams, before humidity, fan heat, or duct gains are added, which is also where ASHRAE and the Zeroth-law derivation agree on a single result.

For supply air that also has to land inside an indoor humidity range, Vapor Pressure Deficit Calculator translates the mixed temperature into a vapor pressure deficit that controls plant transpiration and occupant comfort.

Three inputs dominate the accuracy of the flow-weighted average: the source temperatures, the proportion split, and the choice of mode. Two assumptions also limit how far the formula can be pushed.

• • The flow-weighted average assumes the two streams reach thermal equilibrium with no external heat input. Real mixing boxes leak heat to ductwork and pick up fan heat, which can shift the measured mixed temperature by a degree or more.
• • Volumetric cfm and percent by volume are not always mass flow. When the two inlet temperatures differ by more than about 20 degC, convert the cfm values to kilograms per second before averaging.
• • Humidity, pressure, and altitude corrections are out of scope here. The full psychrometric version of this calculation is in the related Mixed Air Calculator page.

These factors are why field measurements never quite match the textbook formula, and why ASHRAE tolerances allow a few tenths of a degree around the design value.

According to ASHRAE Handbook, the ASHRAE Handbook (Fundamentals) confirms that the supply-air temperature is the flow-weighted average of the outside-air and return-air streams once they reach thermal equilibrium in the mixing box.

When the site sits above about 1500 metres of elevation, Boiling Point Altitude Calculator helps translate the local barometric pressure into the equivalent altitude before the proportions are interpreted as cfm.