Coefficient of Performance Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

Share Print Save

Thermal calculations often look simple until absolute temperature, sign convention, phase, or heat-transfer mode changes the meaning. Coefficient of Performance Calculator keeps the page’s coefficient of performance tied to the quantities and assumptions used by this specific thermodynamic relation.

What this calculator does

The Coefficient of Performance Calculator brings together Type of process, Hot reservoir temperature (Tₕ), Cold reservoir temperature (T꜀), COP — refrigerator, COP — heat pump around the page’s coefficient of performance. The formula section below identifies which values actually drive that result and which fields are supporting or derived quantities, so you can check the page without assuming every visible box is an independent input.

How to use it

The main fields on this page are Type of process, Hot reservoir temperature (Tₕ), Cold reservoir temperature (T꜀), COP — refrigerator, COP — heat pump. Enter the quantities you actually know, keep their units consistent, and leave derived/output-style fields blank unless the formula explicitly allows solving in the opposite direction. For a clean check of coefficient of performance, change one driving quantity at a time and confirm that the result moves in the direction predicted by the equation.

How the calculation works

For an ideal reversible refrigerator, COP_R = Tc/(Th−Tc); for a heat pump, COP_HP = Th/(Th−Tc). The page calculates both and returns the one selected by the process control.

Example

For example, start with the page’s populated scenario: Type of process = refrigerator; Hot reservoir temperature (Tₕ) = 300; Cold reservoir temperature (T꜀) = 270. Apply the equation above using the units shown on the page, then compare the calculated coefficient of performance with the displayed result. As a second check, change one physical input while holding the others fixed and confirm that the direction of change makes sense for this formula.

How to interpret the result

Interpret coefficient of performance within the stated thermodynamic model, unit system, and sign convention. Check whether temperatures are absolute where required and whether the process is idealized, because those details can matter more than the last decimal place.

Limitations and notes

Ideal thermal equations omit some combination of heat loss, contact resistance, temperature-dependent properties, radiation/convection coupling, phase behavior, and nonuniform temperature. Recheck units and process assumptions before using the result for equipment or safety decisions. For Coefficient of Performance Calculator, keep that general caution tied to the exact fields and equation shown here rather than carrying assumptions over from a different calculator.