Mixing temperature calculator
Mix 100 g at 80 °C with 200 g at 20 °C, both with a specific heat of 4.184, and they settle at 40 °C. Enter two masses, two specific heats and two temperatures to get the shared final temperature with every step shown. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- M1
- 100
- C1
- 4.184
- T1
- 80
- M2
- 200
- C2
- 4.184
- T2
- 20
- Final temperature
- 40
- Equilibrium temperature
- 40
A mixing temperature calculator answers a classic calorimetry question: if you bring two bodies or fluid samples into thermal contact and wait, what single temperature do they settle at? Zero total heat capacity (both masses zero) is likewise rejected so the solver never divides by zero. Lab prep, kitchen-scale intuition checks, and coding-kata expected values all need that same conserved-energy result without opening a full thermodynamics suite.
What thermal equilibrium after mixing means
When two substances that can exchange heat are placed in contact and isolated from the surroundings, energy conservation requires that the heat lost by the warmer body equals the heat gained by the cooler body until both share one common temperature. Setting the sum of those heat terms to zero for two substances yields the closed formula Tf equals the mass-and-heat-capacity weighted average of the two initial temperatures: numerator m1 c1 T1 plus m2 c2 T2, denominator m1 c1 plus m2 c2.
That result is independent of which body starts hotter; the algebra is the same whether you think of heat flowing left-to-right or right-to-left. Temperature units must match for both inputs—Celsius with Celsius, kelvin with kelvin, or Fahrenheit with Fahrenheit—because the formula is affine-invariant on a single linear temperature scale but is not a unit converter. Mass units must also match between m1 and m2, and the specific-heat units must be consistent with those masses and temperatures so that m c has units of energy per temperature.
The check path recomputes the weighted average with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets.
Practical tips, limits, and related searches
Keep inputs inside the published absolute range so products m c T cannot overflow into a non-finite numerator that the solver must reject. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. Use the same temperature scale for both samples and convert beforehand if your source data mixes Celsius and kelvin.
Prefer this capability when you already have two masses, two specific heats, and two initial temperatures and only need the adiabatic equilibrium; if your problem involves melting ice or boiling, solve the latent-heat stages separately first.
What you can do with it
Homework checks for calorimetry problems
Students enter two masses, specific heats, and initial temperatures from textbook mixing problems and compare hand-written Tf and weighted averages against a deterministic result before submitting.
Lab prep and process intuition
Quickly estimate the temperature after blending two process streams or lab samples when specific heats are approximately constant and heat loss is negligible.
FAQ
What formula does the mixing temperature calculator use?
Under adiabatic conditions with constant specific heats and no phase change, Tf = (m1·c1·T1 + m2·c2·T2) / (m1·c1 + m2·c2). That is the heat-capacity-weighted average of the two initial temperatures.
What happens if a mass is negative?
Negative mass is not physically valid in this 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.
Does this handle ice melting or boiling?
No. It assumes constant specific heats and no phase change. Solve latent-heat stages separately if a sample crosses a melting or boiling point.
Is the mixing 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/thermo/final-temperature-mixing \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"m1":100,"c1":4.184,"t1":80,"m2":200,"c2":4.184,"t2":20}'const res = await fetch("https://api.kit.forhosting.com/thermo/final-temperature-mixing", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"m1": 100,
"c1": 4.184,
"t1": 80,
"m2": 200,
"c2": 4.184,
"t2": 20
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/thermo/final-temperature-mixing",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"m1": 100,
"c1": 4.184,
"t1": 80,
"m2": 200,
"c2": 4.184,
"t2": 20
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/thermo/final-temperature-mixing", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"m1":100,"c1":4.184,"t1":80,"m2":200,"c2":4.184,"t2":20}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"m1":100,"c1":4.184,"t1":80,"m2":200,"c2":4.184,"t2":20}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/thermo/final-temperature-mixing", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"m1": 100,
"c1": 4.184,
"t1": 80,
"m2": 200,
"c2": 4.184,
"t2": 20
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "thermo.final_temperature_mixing",
"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.
Limits
max_abs | 1000000000000 |
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 is rejected with a clear invalid_input error because it has no physical meaning in this model.
What thermal equilibrium after mixing means
In the standard constant-specific-heat model without phase change, the heat exchanged by substance i is m_i times c_i times the change in its temperature. Teachers and automated graders care about the negative-mass 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.
How to call the API and what comes back
Masses must not be negative; specific heats must be strictly positive; the combined heat capacity m1 c1 plus m2 c2 must be positive so both masses cannot be zero at once. Send a JSON body with six required finite numbers: m1 (aliases mass1 and mass_1), c1 (aliases specific_heat1, cp1, and heat_capacity1), t1 (aliases T1, temp1, and temperature1), m2 (aliases mass2 and mass_2), c2 (aliases specific_heat2, cp2, and heat_capacity2), and t2 (aliases T2, temp2, and temperature2). 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 m1, c1, t1, m2, c2, and t2, sets final_temperature and equilibrium_temperature to the same rounded Tf, formula to the string Tf equals (m1 c1 T1 plus m2 c2 T2) over (m1 c1 plus m2 c2), 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, non-positive specific heat, or zero total heat capacity—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
When teaching, pair examples: equal masses of the same fluid at eighty and twenty degrees yield a midpoint of fifty; unequal masses weight the result toward the larger sample; different specific heats (for example water versus oil) weight the result toward the higher heat-capacity product; and a deliberately negative mass demonstrates the hard invalid_input path. This landing targets people searching for a mixing temperature calculator, equilibrium temperature after mixing, or two-substance calorimetry online; it is not a multi-body mixer with three or more streams, not a phase-change or latent-heat calculator, 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 masses. Round-trip checks are easy: recompute the weighted average by hand and confirm it equals the published final_temperature within the same twelve-decimal rounding, and confirm that swapping labels one and two leaves Tf unchanged.
Integration use cases
Unit tests for student thermo solvers
Generate known-good equal-mass, unequal-mass, and different-c cases plus deliberate negative-mass rejections for coding kata expected values.