How this instrument works
Coefficient of performance is a ratio, not a percentage: divide the rate of useful heating or cooling a machine delivers by the rate of work spent driving it, COP = Q̇ ⁄ Ẇ — the dots mark that both quantities are rates, measured in watts or kilowatts, not one-off energy totals. Because a heat pump or refrigerator does not manufacture the heat it moves, only relocates heat already present in the air, ground, or water, that ratio routinely runs past 1.0 — something a combustion furnace or resistance heater, both structurally capped near 100 percent, cannot do.
The formula is a first-law energy count, not a description of what happens inside the machine. Electrical work drives a compressor that forces refrigerant through a cycle, and that cycle carries thermal energy from a cold reservoir to a warmer one. The theoretical ceiling on how large COP can get is the Carnot value, T_cold ⁄ (T_hot − T_cold) for cooling mode, built from absolute temperature — so the smaller the lift a system has to climb, the higher a COP it can reach, and the coldest winter days are exactly when a heat pump's lift, and its COP, are at their worst.
COP for heating and COP for cooling are not the same number on one machine, because heating mode also credits the compressor's own work, which ends up as heat in the delivered stream: COP_heating equals COP_cooling plus 1 for the same physical cycle. Any COP printed on a spec sheet was measured at one fixed pair of temperatures, usually a standards-body test condition such as those set by ISO 13256 or AHRI 870, so it is a snapshot rather than a guarantee at every temperature a real installation will actually see.
- Enter the cooling (or heating) output — the rate of thermal effect the machine actually delivers, in watts or kilowatts.
- Enter the work (electrical) input — the real electrical power the compressor draws to produce that output, also in watts or kilowatts.
- Leave both fields as power, not accumulated energy; mixing a rate against a total like kWh will quietly give a wrong ratio.
- Read the coefficient of performance — a figure above 1 means more thermal power delivered than electrical power spent.
- Compare the result against a manufacturer's rated COP measured at the same outdoor and indoor temperatures, not just its headline number.
Worked example — a 3 kW compressor moving 10 kW of heat
Take an air-source heat pump delivering 10 kW of heating output while its compressor draws 3 kW of electrical work — the calculator's own default values, chosen because the ratio is a clean one to check by hand. COP = 10 ⁄ 3 = 3.3333333333, which rounds to 3.33 on a spec sheet: for every 1 kW of electricity paid for, the unit is putting roughly 3.33 kW of heat into the house.
Compare that to a baseboard resistance heater burning the same 3 kW: its COP is 1 by definition, since at best every watt in becomes a watt of heat out, so it delivers only 3 kW total. The heat pump's extra 7 kW is not free energy from nowhere — it is heat already present in the outdoor air, moved indoors by the refrigeration cycle, which is exactly what a COP above 1 means.
Questions
Why can COP be greater than 1 when a percentage efficiency can't?
Because COP isn't measuring energy conversion, it's measuring energy relocation. A heat pump doesn't create the heat it delivers — it pumps existing heat from a colder space to a warmer one, and the electrical work only pays the cost of moving it, not making it. A combustion furnace or resistance heater has no such trick, so its ratio tops out near 1.
What's the difference between COP for heating and for cooling?
In cooling mode, COP compares the heat removed from the cold space to the work spent. In heating mode, COP compares the heat delivered to the warm space to that same work — and because the compressor's own work ends up as heat in the delivered stream too, COP_heating equals COP_cooling plus 1 for one physical machine running the same cycle.
Does a higher COP always mean a more efficient machine?
Only when the comparison is fair. COP is measured at one temperature pair, so a unit rated 4.0 at a mild outdoor temperature is not automatically better than one rated 3.2 at a colder test condition. Compare figures measured at matching indoor and outdoor temperatures, ideally from the same test standard, before trusting the bigger number.
Why does COP fall as the outdoor temperature drops for a heat pump?
Because the compressor has to lift heat across a bigger temperature gap, and the Carnot limit says that costs more work per unit of heat moved. That's why heat pump spec sheets list COP at several outdoor temperatures instead of one figure, and why very cold climates sometimes pair a heat pump with backup resistance heat for the worst days.
Can a real system's COP beat the Carnot limit?
No. The Carnot COP, built from the absolute temperatures of the hot and cold reservoirs, is the thermodynamic ceiling no real cycle can cross. Practical vapor-compression equipment typically reaches somewhere around 40 to 60 percent of that limit, the gap accounted for by compressor losses, heat-exchanger imperfections, and refrigerant pressure drop.
What units should the output and work input fields use?
Either watts or kilowatts — the calculator converts between the two internally, so the fields need not match. What it will not fix for you is comparing a rate against a total, like watts against kilowatt-hours accumulated over an hour; keep both fields as power, not banked energy, or the ratio stops meaning anything.