The Coefficient of Performance (COP) Calculator rates how efficiently a heat pump, refrigerator, or air conditioner moves heat relative to the energy it consumes. It also computes the Carnot COP — the theoretical ceiling for any device operating between the same two temperatures — so you can see how close real equipment gets to the physical limit.
How the Coefficient of Performance Calculator works
COP = Q/W, where Q is the heat energy moved and W is the work or electrical energy supplied to move it. Because a heat pump or refrigerator relocates existing heat rather than generating it from scratch, COP is routinely greater than 1 — a stark contrast to a resistive electric heater, which converts 100% of its input to heat and therefore has a COP capped at 1.
The calculator also derives the Carnot COP, the maximum possible COP any reversible device could achieve between a hot reservoir (Th) and a cold reservoir (Tc), both in Kelvin. For heating, COP_carnot = Th/(Th − Tc); for cooling, COP_carnot = Tc/(Th − Tc). These are consequences of the second law of thermodynamics, the same principle that sets the Carnot efficiency ceiling for heat engines — just applied in reverse, since a heat pump uses work to move heat against its natural direction of flow.
Inputs and what they mean
Q (heat moved) and W (work input) should be in consistent energy units — joules by default. For real equipment these are usually derived from a manufacturer's rated capacity (heat output or removal, in BTU/h or watts) divided by rated power draw over the same time period; the ratio is the same regardless of units as long as Q and W share them.
Th and Tc are optional and only needed for the Carnot Limit and Heating vs Cooling tabs — they must be absolute temperatures in Kelvin (K = °C + 273.15), with Th strictly greater than Tc. For a home heat pump, Tc is close to the outdoor air temperature and Th is close to the indoor delivery temperature; the calculator uses these to compute the theoretical ceiling your measured COP is being compared against.
Limits and edge cases
COP = Q/W is undefined when W is zero — no energy was supplied, so no ratio exists; the calculator flags this rather than showing an infinite or nonsensical result. The Carnot COP is always an unreachable upper bound: real compressors, refrigerant throttling losses, and imperfect heat exchangers mean actual COP sits well below the Carnot ceiling, typically 25-50% of it for common HVAC equipment. Manufacturer-rated COP, EER, and SEER figures are measured under standardized test conditions and will differ from real-world performance, which varies with outdoor temperature, humidity, and system age — this calculator computes the physics-based ratio from whatever Q and W you supply, not a manufacturer rating lookup.