Boneyard Tools

Coefficient of Performance (COP) Calculator

Work out the coefficient of performance (COP) of a refrigerator, air conditioner or heat pump. COP is the useful heat moved divided by the work put in, so a value of 3 means the machine shifts three joules of heat for every joule of work it consumes. Switch between cooling and heating to label the heat term correctly and read the ratio instantly.

How to calculate the coefficient of performance

  1. Pick a Mode: 'Cooling (refrigerator)' for a fridge or air conditioner, or 'Heating (heat pump)' for a heat pump.
  2. In cooling mode the heat field reads 'Heat removed (Qc)'; in heating mode it reads 'Heat delivered (Qh)'. Enter that value in joules.
  3. Enter the work input W in joules in the second field.
  4. Read the coefficient of performance in the highlighted result box; it updates as you type.
  5. Click Copy to copy the labeled result, for example 'COP (cooling) = 3'.

Examples

Refrigerator (cooling)

Mode cooling, Qc = 3000 J, W = 1000 J
COP = 3

Heat pump (heating)

Mode heating, Qh = 4000 J, W = 1000 J
COP = 4

Heat pump with more work per unit heat

Mode heating, Qh = 4500 J, W = 1500 J
COP = 3

Frequently asked questions

What is the coefficient of performance formula?

COP equals the heat transferred divided by the work input. In cooling mode use the heat removed from the cold space (Qc); in heating mode use the heat delivered to the warm space (Qh). Both divide by the same work W.

Does the mode change the math?

The division is identical in both modes; the mode only changes which heat you enter and how the result is labeled. Cooling uses Qc and heating uses Qh, so switch the mode to match the machine you are analysing.

What is a good COP value?

Air conditioners and refrigerators typically show a cooling COP of about 2 to 4, while air-source heat pumps often reach a heating COP of 3 to 5. Ground-source systems can go higher. In every case a bigger number means more heat moved per joule of work.

Why can COP be greater than 1?

COP is not a thermal efficiency capped at 100 percent. A heat pump moves heat that already exists rather than generating it, so it can deliver several times more heat energy than the electrical work it draws, giving values well above 1.

How are heating and cooling COP related?

For the same machine the heating COP is the cooling COP plus 1, because the heat delivered equals the heat removed plus the work input (Qh = Qc + W). A unit with a cooling COP of 3 therefore has a heating COP of about 4.

What units should I use?

Enter both heat and work in joules; the tool divides them so the COP is dimensionless. If you have power in watts measured over the same time, the ratio is the same, since the shared time cancels out. Just keep both fields in matching units.

Why do I get an error or no result?

Both fields must be filled with finite numbers, and both the heat and the work must be greater than zero. Zero or negative work would mean dividing by zero or worse, so the tool asks for positive values before it computes.

How is COP different from EER or SEER?

COP is dimensionless and uses SI units. EER divides cooling output in BTU per hour by input in watts, so it is roughly 3.41 times the cooling COP. SEER is a seasonal average of EER across a range of conditions.

Is my input sent anywhere?

No. The calculation runs entirely in your browser with a single division, so the heat and work values you type never leave your device and nothing is stored or uploaded.

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