Mixed-air temperature calculator
Mixing 2 kg/s of air at 10 °C with 2 kg/s at 30 °C gives a blend at 20 °C. Enter the temperature and mass flow of each stream to get the adiabatic mixed-air temperature, with no specific heat needed. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- T1
- 10
- M1
- 2
- T2
- 30
- M2
- 2
- Mixed air temperature
- 20
- Mixed temperature
- 20
- Total mass flow
- 4
- Stream 1 fraction
- 0.5
A mixed-air temperature calculator answers a standard HVAC question: if two air streams meet and mix adiabatically, what temperature does the combined stream leave at? Enter the temperature and mass flow rate of each stream; the tool returns the mixed-air temperature as the mass-flow-weighted average T_mix equals (m1 T1 plus m2 T2) over (m1 plus m2). Because both streams are air, the same specific heat appears in the numerator and the denominator and cancels, so you do not supply a heat-capacity input. Zero total mass flow is likewise rejected so the solver never divides by zero. Economizer mixing boxes, outdoor-air plus return-air blending, and two-branch supply junctions all need that same conserved-energy result without opening a full psychrometric suite.
What mixed-air temperature means for two air streams
When two dry air streams mix in a duct, mixing box, or air-handling-unit plenum and exchange no heat with the surroundings, energy conservation plus equal specific heat reduces the leaving temperature to a mass-flow-weighted average. Stream i carries an enthalpy rate equal to its mass flow times cp times its temperature; adding both streams and dividing by the combined mass flow times the same cp cancels cp and leaves T_mix equal to (m1 T1 plus m2 T2) over (m1 plus m2).
That is the HVAC mixed-air formula used for outdoor-air plus return-air blending, economizer mixing boxes, and two-branch supply junctions. Temperature units must match for both streams—Celsius with Celsius, kelvin with kelvin, or Fahrenheit with Fahrenheit—because the formula is affine-invariant on a single linear scale but is not a unit converter. Mass-flow units must also match between m1 and m2, for example kilograms per second with kilograms per second, or pounds per hour with pounds per hour.
If one stream has zero mass flow and the other is positive, mixed air is simply the remaining stream.
Practical tips, limits, and related searches
Keep inputs inside the published absolute range so products of mass flow and temperature cannot overflow into a non-finite numerator that the solver must reject. Use the same temperature scale for both streams and convert beforehand if your source data mixes Celsius and kelvin. Volume flow in cubic metres per second or cubic feet per minute is not a mass flow: convert with density on the client first if your meters report volumetric airflow, then send kilograms per second or pounds per hour.
Prefer this capability when both streams are air, you already have two temperatures and two mass flows, and you only need the adiabatic mixed-air temperature.
What you can do with it
AHU outdoor-air plus return-air blend
Enter outdoor-air and return-air temperatures with their mass flows to get the mixed-air temperature into the cooling coil before a full psychrometric run.
Homework checks for HVAC mixing boxes
Students enter two stream temperatures and mass flows from textbook mixed-air problems and compare the mass-flow-weighted T_mix against a deterministic result before submitting.
FAQ
What formula does the mixed-air temperature calculator use?
Under adiabatic mixing of two air streams with equal specific heat, T_mix = (m1·T1 + m2·T2) / (m1 + m2). That is the mass-flow-weighted average of the two stream temperatures.
What happens if a mass flow rate is negative?
Negative mass flow is not physically valid in this two-stream model.
Do I need specific heat or humidity as inputs?
No. Both streams are treated as air with the same specific heat, so cp cancels. Humidity and condensation are outside this mixed-air temperature model.
Do temperature units matter?
Both temperatures must use the same linear scale (°C with °C, K with K, or °F with °F). The calculator does not convert between temperature units.
Is the mixed-air temperature calculator free?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/phys/mixed-air \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"t1":10,"m1":2,"t2":30,"m2":2}'const res = await fetch("https://api.kit.forhosting.com/phys/mixed-air", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"t1": 10,
"m1": 2,
"t2": 30,
"m2": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/mixed-air",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"t1": 10,
"m1": 2,
"t2": 30,
"m2": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/mixed-air", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"t1":10,"m1":2,"t2":30,"m2":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"t1":10,"m1":2,"t2":30,"m2":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/mixed-air", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"t1": 10,
"m1": 2,
"t2": 30,
"m2": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.mixed_air",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Negative mass flow is rejected with a clear invalid_input error because reverse flow has no meaning in this two-stream mixing model.
What mixed-air temperature means for two air streams
Teachers, commissioning scripts, and automated graders care about the negative-mass-flow rejection as much as the success path: a learner who types a minus sign by accident should see an explicit invalid_input message rather than a silently nonsensical temperature. If both mass flows are zero, the mixed temperature is undefined and the solver returns invalid_input instead of dividing by zero. The check path recomputes the weighted average with the same fixed rounding used for published fields, so a successful response always ships a mixed_air_temperature you can assert in tests or worksheets.
How to call the API and what comes back
Mass flow rates must not be negative; the combined mass flow m1 plus m2 must be positive so both streams cannot be shut at once. Send a JSON body with four required finite numbers: t1 (aliases T1, temp1, temperature1, and stream1_temp), m1 (aliases mass_flow1, mdot1, and flow1), t2 (aliases T2, temp2, temperature2, and stream2_temp), and m2 (aliases mass_flow2, mdot2, and flow2). Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded t1, m1, t2, and m2, sets mixed_air_temperature and mixed_temperature to the same rounded T_mix, total_mass_flow to m1 plus m2, stream_1_fraction to m1 over the total, formula to the string T_mix equals (m1 T1 plus m2 T2) over (m1 plus m2), method to mass_flow_weighted_average, message to a short English summary, and steps to an ordered array of substitution lines. Failed validation—missing fields, non-finite numbers, values outside absolute limits, negative mass flow, or zero total mass flow—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price. Prefer sending JSON numbers rather than pre-formatted strings when you control the client; numeric strings are accepted only when they match a strict finite numeric pattern.
Practical tips, limits, and related searches
When teaching or commissioning, pair examples: equal mass flows at ten and thirty degrees yield a midpoint of twenty; unequal flows weight the result toward the larger stream; one stream at zero flow returns the other stream's temperature; and a deliberately negative mass flow demonstrates the hard invalid_input path. This landing targets people searching for a mixed air temperature calculator, HVAC two-stream mixing, or outdoor-air plus return-air blend temperature; it is not a two-substance calorimetry tool that asks for independent specific heats, not a psychrometric chart that tracks humidity ratio, and not a unit converter for temperature alone. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send bad flows. Round-trip checks are easy: recompute the mass-flow-weighted average by hand and confirm it equals the published mixed_air_temperature within the same twelve-decimal rounding, and confirm that swapping labels one and two leaves T_mix unchanged.
Integration use cases
Unit tests for student HVAC solvers
Generate known-good equal-flow, unequal-flow, and one-stream-zero cases plus deliberate negative-mass-flow rejections for coding kata expected values.