Heat Pump COP Calculation

The formula for COP is energy-out/energy-in. The energy-in part is typically just the electric power consumed over the measurement period in Kwh. The energy-out part is the total heat output over the measurement period, usually expressed in btu or Kcal but converted to Kwh so that the COP formula results in a unit-less ratio. For example:

If my one-ton mini split heat pump puts out 10,236 btus in an hour, dividing by 3412btu/kwh = 3kwh of energy (heat) output. If it uses 1 kwh of electricity during that hour, then the COP is 3/1 = 3.

That’s the simple answer. In the case of a mini-split, that includes the power used to run the blowers and fans. In non-integrated units, the power used by the air-handler may not be included in the calculation. There are legitimate reasons on both sides of that argument.

If you have a real-time input for heating-power, and it’s not in watt-hrs(wh), divide to convert (1wh = 3.41btus or .860Kcal), then multiply by the number of posting intervals in an hour (If your feeds are every 30 seconds, multiply by 120). Now you can divide that by the input power feed, to get the average COP over the interval.

Log that to a feed called COP and you are done.

Lets use the first cop=3 example to illustrate.

  • If the unit is putting out 10,236 btus per hour, then the input at 30 seconds intervals would be 85.3 (btus).
  • Dividing by 3.412, would be 25 watt-hrs.
  • Multiplying by 120 intervals/hour would be 3000.
  • Dividing by input power (1000 watts) would be 3 (COP).

All that said, I’m curious how you are measuring the heat output of your heat pump. Most attempts I’ve seen try to measure the air-flow and temperature rise at the condenser. That’s pretty hard with a mini-split and only a little easier with an air-handler. I’ve done some work in the area of airflow measurement so I’d be interested in the details if that’s what you are doing.