How can a heat pump give 3–4 kWh of heat per kWh of electricity?

It does not turn electricity into heat; it uses the compressor to move heat from outdoor air into the house. The theoretical limit is the Carnot COP = T_hot / (T_hot − T_cold), about 9.3 for 35 °C water and 2 °C outside. Real machines reach 40–60% of that, so COP 3–4 is typical. A resistance heater is always COP 1.

Why does heat pump efficiency drop in cold weather?

The bigger the temperature lift from outdoor air to supply water, the more work the compressor does per unit of heat, so COP falls. Around 0 °C humid air also frosts the outdoor coil, and reverse-cycle defrosting costs roughly another 10%. Cold-climate models and low-temperature emitters like underfloor heating help.

What size air conditioner do I need?

An averagely insulated room needs roughly 150 W of cooling per square metre, so a 2.5 kW (about 8500 BTU/h) unit suits 10–15 m² and 3.5 kW suits about 15–22 m². Add capacity for top floors, west-facing windows, kitchens or many occupants. In China units are sold by “匹”: 1 匹 ≈ 2.5 kW, 1.5 匹 ≈ 3.5 kW, 2 匹 ≈ 5 kW.

Is a heat pump cheaper to run than a gas boiler?

It depends on the price ratio. Natural gas gives about 10 kWh per cubic metre and a boiler is about 90% efficient, so gas heat costs the gas price divided by 9 per kWh. Heat-pump heat costs the electricity price divided by SCOP. The tool shows the break-even COP; whenever your expected SCOP is above it, the heat pump wins.

Can I cool my kitchen by leaving the fridge door open?

No — the room gets warmer. The fridge pulls heat from the air in front of it and dumps that heat, plus the compressor's electrical energy, out of the condenser at the back into the same room. The net effect is extra heat equal to the compressor power. An air conditioner cools because its condenser sits outside.

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❄️Heat Pump & Air Conditioner Calculator - Refrigeration Cycle, COP, Heating Cost

Heat pumps and air conditioners do not make heat or cold — they use electricity to move heat from a colder place to a warmer one, which is why one kilowatt-hour can deliver three or four of heat. This tool animates the compressor, condenser, expansion valve and evaporator loop, sketches the cycle on a P–h diagram with approximate refrigerant properties, compares Carnot and realistic COP against outdoor temperature, and works out whether a heat pump, resistance heater or gas boiler is cheapest and what size AC a room needs.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Heat Pump & Air Conditioner Calculator

1In Refrigeration cycle pick a refrigerant and heating or cooling mode, set indoor and outdoor temperatures, and watch the loop, state points and COP
2In COP vs outdoor temp set the supply temperature to compare underfloor heating with radiators and the Carnot limit
3In Heating cost enter floor area or annual heat demand and your energy prices to compare yearly cost and CO₂
4In AC sizing enter room size, insulation and sun exposure to get the cooling load, unit size and running cost by efficiency grade

FAQ

How can a heat pump give 3–4 kWh of heat per kWh of electricity?: It does not turn electricity into heat; it uses the compressor to move heat from outdoor air into the house. The theoretical limit is the Carnot COP = T_hot / (T_hot − T_cold), about 9.3 for 35 °C water and 2 °C outside. Real machines reach 40–60% of that, so COP 3–4 is typical. A resistance heater is always COP 1.
Why does heat pump efficiency drop in cold weather?: The bigger the temperature lift from outdoor air to supply water, the more work the compressor does per unit of heat, so COP falls. Around 0 °C humid air also frosts the outdoor coil, and reverse-cycle defrosting costs roughly another 10%. Cold-climate models and low-temperature emitters like underfloor heating help.
What size air conditioner do I need?: An averagely insulated room needs roughly 150 W of cooling per square metre, so a 2.5 kW (about 8500 BTU/h) unit suits 10–15 m² and 3.5 kW suits about 15–22 m². Add capacity for top floors, west-facing windows, kitchens or many occupants. In China units are sold by “匹”: 1 匹 ≈ 2.5 kW, 1.5 匹 ≈ 3.5 kW, 2 匹 ≈ 5 kW.
Is a heat pump cheaper to run than a gas boiler?: It depends on the price ratio. Natural gas gives about 10 kWh per cubic metre and a boiler is about 90% efficient, so gas heat costs the gas price divided by 9 per kWh. Heat-pump heat costs the electricity price divided by SCOP. The tool shows the break-even COP; whenever your expected SCOP is above it, the heat pump wins.
Can I cool my kitchen by leaving the fridge door open?: No — the room gets warmer. The fridge pulls heat from the air in front of it and dumps that heat, plus the compressor's electrical energy, out of the condenser at the back into the same room. The net effect is extra heat equal to the compressor power. An air conditioner cools because its condenser sits outside.

Features

Animated vapour-compression loop coloured by temperature, with Q_h, Q_c, W and four labelled state points
P–h diagram for R32, R290 and R410A (saturation dome and cycle) with pressure ratio, discharge temperature and quality
Carnot COP, cycle-model COP and fraction-of-Carnot curves, optionally with defrost losses
Yearly cost, cost per kWh of heat and CO₂ for heat pump, resistance and gas, plus the break-even COP
Cooling load from area, height, insulation, sun and occupants in W, BTU/h, tons and Chinese “匹”, with GB 21455 APF grades
Energy flow of a fridge with its door open: the room gains exactly the compressor's power

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