Mixed Air Calculator

What the mixed air calculator does

When two streams of air at different temperatures blend together, the result settles at a temperature in between, closer to whichever stream makes up more of the mix. This calculator finds that mixed temperature from the temperature and proportion of each stream.

Below is what mixed air temperature is, why it is a weighted average, the equation behind it, and a worked example.

How to use it

1. Enter the temperature of the first stream and its proportion of the total mix as a percentage.
2. Enter the temperature and proportion of the second stream. The two proportions should add up to 100 percent.
3. Press Calculate for the mixed air temperature, or Reset to clear it.

What mixed air temperature is

Mixed air temperature is the temperature reached when two airstreams combine into one. If you blend warm air with cool air, the mixture ends up somewhere between the two, and exactly where depends on how much of each you started with. A mix that is mostly warm air ends up warm; a mix that is mostly cool air ends up cool. The mixed temperature is the single temperature the combined stream settles at.

The principle behind it is the conservation of energy. When the two streams meet, the warmer one gives up heat and the cooler one takes it on, until both reach a common temperature. No energy is lost in the blending, it is simply shared out, and the final temperature is the one at which the heat carried by both streams is evenly distributed through the whole mixture. This calculator works out where that balance falls.

A weighted average, not a simple one

The mixed temperature is an average of the two stream temperatures, but a weighted one, which is the important subtlety. A plain average would assume equal amounts of each stream, but mixing rarely works that way. If three-quarters of the mix is warm air and only a quarter is cool, the result sits much closer to the warm temperature, because the warm stream brings far more air and far more heat to the blend.

So each stream's temperature counts in proportion to how much of it there is. The larger stream pulls the mixed temperature toward itself, while a small stream nudges it only slightly. This is why the proportions matter as much as the temperatures, and why the calculator asks for both. Getting the weighting right is the whole point: the answer is the proportion-weighted average of the two temperatures.

The equation it uses

The mixed temperature is each stream's temperature multiplied by its proportion, summed together:

T_mix = T₁ × (P₁ ÷ 100) + T₂ × (P₂ ÷ 100)

Here T₁ and T₂ are the two stream temperatures and P₁ and P₂ are their proportions as percentages, which should add up to 100. Each temperature is weighted by its share of the mix, and the two weighted values add to give the result. When the two streams are equal halves, this reduces to the ordinary average of the two temperatures; when they are unequal, the result leans toward the larger share. This assumes the two streams are the same kind of air, so that mixing by proportion matches mixing by energy.

Where mixing happens in practice

Air mixing is a routine part of building ventilation. Most air-conditioning systems blend fresh outdoor air with recirculated indoor air before conditioning it, bringing in enough outside air to keep the indoor air healthy while reusing already-conditioned indoor air to save energy. The temperature of that blend, the mixed air temperature, is what the heating or cooling coils then have to work on, so knowing it is the starting point for sizing the system.

On a cold day, for instance, a system might mix a small fraction of frigid outdoor air with a large fraction of warm return air, and the mixed temperature tells the designer how much heating is still needed to reach the target. The same idea appears wherever airstreams join, from blending hot and cold flows in industrial processes to combining ducts in a ventilation network. This calculator gives the resulting temperature for any such blend.

Units and precision

The calculator takes the two stream temperatures in kelvin and their proportions as percentages, and returns the mixed temperature in kelvin. For the result to be a true energy-weighted mix, the two proportions should add up to 100 percent, representing the complete blend. The calculation is exact for streams of the same type of air. The mixed temperature is shown to several decimal places.

A worked example

Suppose one stream is at 300 kelvin and makes up 60 percent of the mix, while the other is at 290 kelvin and makes up the remaining 40 percent.

The mixed temperature is T_mix = 300 × 0.60 + 290 × 0.40 = 180 + 116 = 296 kelvin. The result sits closer to 300 than to 290, because the warmer stream is the larger share of the blend. Had the proportions been reversed, the mix would have landed closer to 290 instead.

Questions people ask

How do you calculate mixed air temperature?

Multiply each stream's temperature by its proportion of the mix and add the results, T_mix = T₁(P₁/100) + T₂(P₂/100), with the proportions adding up to 100 percent.

Why is it a weighted average?

Because each stream contributes heat in proportion to how much air it brings. The larger stream pulls the mixed temperature toward its own, so the temperatures are weighted by their shares rather than averaged equally.

Why should the proportions add up to 100?

Because the two streams together make up the whole mixture. Proportions summing to 100 percent represent the complete blend, which is what makes the weighted average correspond to the true energy balance.

Where is mixed air temperature used?

Mainly in building ventilation, where fresh outdoor air is blended with recirculated indoor air. The mixed temperature is what the heating or cooling system must then work on, so it is the starting point for sizing the equipment.

References

A quick note on where the science comes from. Mixing airstreams by an energy balance to find the resulting temperature is standard heating and cooling engineering, set out in the ASHRAE Handbook of Fundamentals and described by the Engineering ToolBox. It follows directly from the conservation of energy.

1. ASHRAE, Handbook of Fundamentals, air mixing and psychrometric processes. https://www.ashrae.org/technical-resources/ashrae-handbook
2. Engineering ToolBox, Mixing Humid Air. https://www.engineeringtoolbox.com/mixing-humid-air-d_694.html
3. Wikipedia, Psychrometrics (mixing of air streams). https://en.wikipedia.org/wiki/Psychrometrics