Performance coefficient calculator
A refrigerator that removes 400 J of heat from its cold side using 100 J of work has a COP of 4. Enter the heat absorbed and the work supplied and get the coefficient of performance of a fridge or heat pump. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Heat absorbed
- 400
- Work
- 100
- Cop
- 4
This performance coefficient calculator returns the dimensionless COP of a refrigerator or a heat pump when you know the heat absorbed at the cold side and the work supplied to the compressor or drive. The defining ratio is COP equals heat absorbed divided by work, the same Q over W identity used in first-year thermodynamics, HVAC homework, and laboratory write-ups. Energies may be joules, kilowatt-hours, or any other consistent pair; the coefficient itself carries no unit.
What the performance coefficient is and how COP = Q/W is defined
The coefficient of performance, often shortened to COP and sometimes searched as performance coefficient, is the figure of merit for machines that move heat rather than convert heat into shaft work. A refrigerator, freezer, or air conditioner is judged by how much heat it can pull from a cold space for each unit of compressor or electrical work you pay for. A heat pump is judged by how much heat it delivers to a warm space for the same work.
In both cases the energy-ratio definition is useful heat over work. For a refrigerator Q is the heat absorbed from the cold box. For a heat pump you may enter the heat absorbed at the outdoor coil if that is the quantity you measured, or the useful heating load if that is the numerator your problem statement uses; the engine applies the same closed form either way and does not silently add work to the numerator.
It does not convert units, look up refrigerants, integrate a vapor-compression cycle, or apply the Carnot temperature bound from two absolute temperatures. Those are different search intents and belong on other pages. What this page answers is the two-energy COP that appears when a worksheet, a lab, or a first-order design check gives only heat absorbed and work.
Where a performance-coefficient lookup belongs in study, lab, and software
Students meet COP equals Q over W when a thermodynamics chapter introduces refrigeration cycles, when a problem gives cooling load and compressor work and asks for the performance coefficient, or when a contest item contrasts refrigerator COP with heat-engine efficiency, which is a different ratio and a different landing. Teachers can pre-generate answer keys for modest energy pairs without trusting opaque calculator apps that silently invert numerator and denominator or treat zero work as a special infinity case.
University HVAC labs reduce measured evaporator heat and electrical work to a single COP before they discuss Carnot limits, refrigerant charts, or multi-stage cycles. First-order engineering checks use the energy-based coefficient when only heat absorbed and work are known, as a sanity bound before a detailed vapor-compression model is built. Product and education tools call the same contract when a learner types two energies and the user interface must show a dimensionless COP rather than a hand-waved percent.
Developers seed deterministic test vectors for cooling demos, normalize user-entered loads before a process sketch, or satisfy programming-challenge statements that demand COP = Q/W without re-deriving the division in every language. Pair it with Carnot-efficiency helpers when you need temperature-based upper bounds, and with heat-engine efficiency tools when the machine produces work instead of moving heat.
What you can do with it
Homework and lab checks
Compute COP = Q/W from heat absorbed and compressor work before grading refrigeration worksheets or HVAC laboratory reports.
Design bounds and tutoring software
Normalize user-entered heat absorbed and work into a dimensionless COP for process sketches, interactive lessons, and first-order HVAC checks.
FAQ
What does the performance coefficient calculator cost?
It is free in your browser on this page.
Why does a zero work input fail instead of returning infinity?
COP is defined as heat absorbed divided by work.
Do a refrigerator and a heat pump use the same formula here?
Yes. Both use COP = Q/W. Enter the heat that belongs in the numerator of your problem: cooling absorbed for a refrigerator, or the useful heat your heat-pump statement specifies.
Is the performance coefficient the same as thermal efficiency?
No. Thermal efficiency is work over heat input for an engine that produces work. The performance coefficient is useful heat over work for a machine that moves heat, and it is often greater than one.
Can I enter kilowatt-hours instead of joules?
Yes, as long as heat and work use the same unit, because the coefficient is a plain ratio with no unit. The calculator does not convert units, so mixing joules with kilowatt-hours gives a wrong result.
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/performance-coefficient \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"heat_absorbed":400,"work":100}'const res = await fetch("https://api.kit.forhosting.com/phys/performance-coefficient", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"heat_absorbed": 400,
"work": 100
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/performance-coefficient",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"heat_absorbed": 400,
"work": 100
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/performance-coefficient", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"heat_absorbed":400,"work":100}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"heat_absorbed":400,"work":100}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/performance-coefficient", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"heat_absorbed": 400,
"work": 100
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.performance_coefficient",
"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_energy | 1000000000000000 |
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
Work must be non-zero: a vanishing denominator would make the ratio undefined, so the engine rejects that case with invalid_input instead of Infinity.
What the performance coefficient is and how COP = Q/W is defined
This calculator takes heat_absorbed as the numerator Q and work as the denominator W, then returns COP equals Q divided by W as a dimensionless number. The response echoes the cleaned inputs, reports cop, restates the formula COP = Q / W, labels the unit as dimensionless, and tags the method as performance_coefficient so a notebook can store the number without inventing a percent scale. Because work sits in the denominator, a zero work input makes the ratio undefined: the engine fails with invalid_input instead of returning Infinity or NaN. That failure is the honest classroom statement that you cannot quote a performance coefficient when no work was supplied. Identical inputs always produce identical JSON because the path is pure floating-point arithmetic with no clock, no random seed, and no network call.
Input contract, zero-work rejection, and the shape of the response
Magnitudes above the documented energy ceiling are rejected so a stray unit conversion cannot overflow the isolate. Work may be negative, which is unusual for a driven refrigerator but is mathematically defined and can flag a sign error in a logged data series. Heat absorbed may be any finite value, including zero, which simply yields a COP of zero. A classic check is four hundred units of heat absorbed and one hundred units of work, which yields COP equal to four. Keep both energies in matching units so the ratio is truly dimensionless. POST a JSON body with two required finite numbers. heat_absorbed is Q, the heat taken up at the cold side or the useful heat you treat as the COP numerator, in joules or any energy unit you prefer. Aliases Q, Q_c, Qc, heat, cooling, and q_absorbed are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. work is W in the same energy unit, with aliases W, work_input, and work_in. Both fields may arrive as JSON numbers or as decimal strings; missing fields, empty strings, NaN, Infinity, and non-numeric text fail with invalid_input naming the field, and those failures are not billed. The critical edge is a vanishing denominator: when the absolute value of work is zero within a tiny epsilon, the request fails with invalid_input and a message that the performance coefficient COP = Q/W is undefined when work is zero, so callers never receive Infinity. On success the body includes the echoed heat_absorbed and work rounded to twelve decimal places for stable goldens, the dimensionless cop, the formula string COP = Q / W, a unit hint of dimensionless, and method performance_coefficient. Pair the free browser form with the priced API when you need the identical mathematical result inside an automated pipeline; each successful API call costs $0.002 and failed validation does not consume balance.
Where a performance-coefficient lookup belongs in study, lab, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic test fixtures
Generate reproducible performance coefficients for unit tests, cooling demos, and continuous-integration assertions on energy ratios.
Technical questions
Which energy units should heat_absorbed and work use?
Any consistent pair — joules, kilowatt-hours, BTU, or another energy unit. The coefficient is dimensionless and does not depend on the unit as long as both numbers share it.