Almost every air handling unit blends two streams before it does anything else. Return air comes back from the space at whatever condition the space is in, outside air arrives at whatever the weather is doing, and the mixed condition entering the coil is what the coil actually has to deal with. Get that mixed point wrong and every downstream calculation — coil capacity, reheat, dehumidification load — inherits the error.
This mixed air calculator from Arb Digital takes the flow, dry-bulb temperature and relative humidity of two streams and returns the blended condition. It does the mixing on a mass basis rather than a volume basis, which is the physically correct approach and which matters more than people expect when the two streams are at very different temperatures. It also detects the case where mixing two unsaturated streams produces saturated air, which is a real and frequently overlooked outcome.
What This Mixed Air Calculator Does
For each stream the tool computes the saturation vapour pressure at its temperature, converts relative humidity into a humidity ratio in kilograms of water per kilogram of dry air, works out the moist-air density, and from that converts your volumetric flow into a mass flow. It then mixes the two on that mass basis: the humidity ratio and the specific enthalpy of the blend are each the mass-weighted average of the two inputs.
From the mixed enthalpy and mixed humidity ratio it recovers the mixed dry-bulb temperature, and from the mixed humidity ratio and the barometric pressure it recovers the vapour pressure, and hence the relative humidity and dew point of the blend. The result hero gives the mixed temperature, the grid gives humidity, moisture content, dew point and the mass share contributed by the second stream, and the note reports the enthalpy and the total mass flow.
The mass-versus-volume distinction is the reason this page exists as something other than a weighted average. Air at 35 °C is roughly four per cent less dense than air at 22 °C, so a hot outside-air stream contributes about four per cent less mass than its volumetric share implies. On a small fresh-air fraction the error is negligible; on a system running fifty per cent outside air in a hot climate it is worth having right, and it always errs in the same direction.
How to Use It
- Set the units before typing the numbers. Temperature in Celsius or Fahrenheit, flow in cubic metres per hour, litres per second or CFM. All four inputs of a kind share the same unit.
- Use dry-bulb temperatures. These are ordinary thermometer readings. If you have wet-bulb rather than relative humidity, convert first; the wet-bulb temperature is not interchangeable with dry-bulb.
- Enter the real flow rates, not the design ones. Damper positions rarely match their schedules, and the mixed condition follows what the fan is actually moving.
- Adjust the barometric pressure for altitude. At 1,500 m the pressure is roughly 84 per cent of sea level, and the humidity ratio corresponding to a given temperature and relative humidity rises accordingly.
- Check whether the blend is saturated. If the note reports condensation, the mixed point has crossed the saturation line and some water has left the air as mist. The reported temperature and humidity then describe the saturated state after that has happened.
The Method and a Worked Example
Saturation vapour pressure comes from the August–Roche–Magnus expression, eₛ = 6.112 exp(17.67T/(T+243.5)) in hectopascals with T in Celsius, which is accurate to a fraction of a per cent between roughly −40 and +50 °C. Vapour pressure is that value multiplied by the relative humidity. The humidity ratio is W = 0.62198e/(p − e), and the specific enthalpy is h = 1.006T + W(2501 + 1.86T) in kilojoules per kilogram of dry air. Moist-air density comes from applying the ideal gas law separately to the dry and vapour components.
Take the default: 1,000 m³/h of return air at 24 °C and 50 % RH mixed with 300 m³/h of outside air at 32 °C and 60 % RH. The return stream has a humidity ratio of about 9.29 g/kg, an enthalpy near 47.8 kJ/kg and a density of 1.181 kg/m³, giving 1,181 kg/h. The outside stream is at about 18.04 g/kg, 78.4 kJ/kg and 1.144 kg/m³, giving 343 kg/h. Mass-weighting the two gives a mixed humidity ratio near 11.26 g/kg and a mixed enthalpy near 54.7 kJ/kg, which recovers a mixed dry-bulb of about 25.8 °C at roughly 54 % relative humidity with a dew point near 15.9 °C. Note that the outside air is 23.1 % of the volume but only 22.5 % of the mass. The National Weather Service humidity calculator publishes the relationships between relative humidity, dew point and wet bulb that underlie this method.
Why Temperature Mixes Almost Linearly and Humidity Really Does
Humidity ratio is a genuine mass ratio, so it mixes exactly linearly on a mass basis. The same is true of specific enthalpy. Dry-bulb temperature does not, quite, because the specific heat of moist air depends slightly on how much moisture it contains. The difference is small — usually a few hundredths of a degree — but the correct procedure is to mix enthalpy and humidity ratio and then recover the temperature, which is what this tool does rather than averaging the temperatures directly.
Relative humidity is the quantity that emphatically does not mix linearly, and assuming it does is the most common error in this whole area. Relative humidity is a ratio to a saturation value that itself changes exponentially with temperature, so the mixed relative humidity depends on the mixed temperature as well as on the two input humidities. Two streams at 50 % and 60 % relative humidity can mix to anything from below 50 % to fully saturated, depending entirely on their temperatures. A weighted average of the two percentages is not an approximation of the answer, it is a different quantity.
On a psychrometric chart this is easy to see. The mixed condition lies on the straight line joining the two state points, at the position that divides it in inverse proportion to the mass flows. The saturation curve, however, bends. A straight line between two points below the curve can pass above it, and that is exactly the fogging case.
When Mixing Two Dry Streams Makes Fog
Take warm humid air at 30 °C and 85 % relative humidity and mix it in equal mass with cold air at 8 °C and 95 % relative humidity. Neither stream is saturated. The blend, however, sits above the saturation curve: the mixed humidity ratio exceeds what the mixed temperature can hold, and the excess leaves the air as visible mist. This is why your breath is visible on a cold day, why aircraft contrails form, and why a cooling coil face can fog when a hot damper opens suddenly.
The calculator detects this by comparing the mixed humidity ratio with the saturation value at the mixed temperature. When it exceeds it, the tool reports the blend as saturated, states how much water per kilogram of dry air must condense, and reports the corrected temperature after the latent heat released by that condensation has warmed the air slightly. Reporting a relative humidity above 100 % would be arithmetically defensible and physically meaningless, so it does not do that.
In building services the practical consequence is water where it is not wanted: on duct interiors, on the upstream face of a filter, or dripping from a mixing box. The dew point calculator is the quick way to check whether a surface is cold enough for the same thing to happen by contact rather than by mixing, and the relative humidity calculator converts between the humidity measures for a single air state.
How This Differs From the Adjacent Arb Digital Tools
This page blends two air states into one. The psychrometric calculator characterises a single air state, giving wet bulb, dew point, humidity ratio, enthalpy and specific volume from any consistent pair of inputs; use it when there is only one condition to describe, and use this page when two streams meet. The dew point calculator and the relative humidity calculator each convert between two humidity measures without any mixing at all. The heat index calculator answers a comfort question rather than a thermodynamic one.
On the airflow side, the air changes per hour calculator relates a flow rate to a room volume, which is usually how the minimum outside-air figure is set in the first place, and the SCFM calculator handles the standard-versus-actual flow distinction that appears whenever compressed air or altitude is involved. The fan calculator covers the fan laws relating speed, flow and power, and the temperature converter deals with unit changes. Coherent SI use throughout is worth the discipline; the NIST summary of SI units is a good reference for the base and derived quantities involved.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Averaging the two relative humidities — relative humidity is a ratio to a temperature-dependent saturation value, so it does not mix linearly and a weighted average of the percentages is simply a different number.
- Weighting by volume instead of mass — the hotter stream is less dense and contributes less mass than its flow share suggests. The error grows with the temperature difference between the streams.
- Using wet-bulb temperature in the dry-bulb boxes — the two agree only in saturated air, and substituting one for the other biases every result on the page.
- Leaving pressure at sea level for a high-altitude site — humidity ratio depends on barometric pressure, so an unadjusted value misstates the moisture load.
- Ignoring a saturated result — if mixing pushes the blend past saturation, water leaves the air. Treating the excess as though it were still vapour overstates the latent load on the coil downstream.
Related Free Tools From Arb Digital
Describe a single air state with the psychrometric calculator, or convert between humidity measures with the dew point calculator and the relative humidity calculator. Size ventilation with the air changes per hour calculator and the fan calculator, handle standard flow with the SCFM calculator, and estimate fabric losses with the heat loss calculator. Comfort is covered by the heat index calculator and units by the temperature converter. The full free online tools hub lists everything Arb Digital has published.
Frequently Asked Questions
Only if the two streams carry equal mass flows and similar moisture. In general the blend must be weighted by mass flow, and the correct procedure mixes enthalpy and humidity ratio first and recovers the temperature from those, because the specific heat of air varies slightly with its moisture content.
Because mass is conserved and volume is not. Air expands as it warms, so a hot stream occupies more space per kilogram. Weighting by volume systematically overstates the contribution of the hotter stream, and the error grows with the temperature difference.
Yes. The mixed condition lies on the straight line between the two states on a psychrometric chart, while the saturation curve bends. A straight line between two points below the curve can pass above it, and the excess moisture then leaves the air as visible mist.
It is the mass of water vapour carried by each kilogram of dry air. Unlike relative humidity it does not change when the air is heated or cooled without adding or removing water, which makes it the quantity that mixes linearly and the one to track through a system.
Yes. The humidity ratio depends on barometric pressure as well as on temperature and relative humidity, so a site at altitude carries more moisture per kilogram of dry air at the same temperature and relative humidity. Set the pressure box to the local value.
The saturation vapour pressure formula used here is accurate to a fraction of a per cent between roughly minus forty and plus fifty degrees Celsius. Outside that range, and particularly well below freezing where sublimation over ice applies, a different formulation is needed.
No. It models an adiabatic mixing of two streams and nothing else. Fan motor heat, duct heat gain and leakage all shift the real condition at the coil face, and each has to be added separately.
This tool is provided for educational and study use. It applies standard adiabatic mixing relations and is not a substitute for full psychrometric analysis or professional HVAC design.
