Refrigeration Cycle Calculator: COP, Compressor Power and p-h Diagram

The four states of a vapour-compression refrigeration or heat pump cycle from the evaporating and condensing temperatures, with the compressor power, COP and a pressure-enthalpy diagram.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

A refrigeration cycle moves heat from a cold place to a warm place. The refrigerant evaporates at a low pressure, taking heat from the cold side (state 1 is the vapour leaving the evaporator). The compressor raises its pressure and temperature (state 2). The hot vapour condenses at the high pressure and gives its heat to the warm side, leaving as a liquid (state 3). The expansion valve drops the pressure again without adding or removing heat, so the enthalpy stays the same (state 4), and the cycle repeats.

The evaporating and condensing temperatures set the two pressures, because a refrigerant boils at a pressure that depends only on its temperature. The refrigerating effect is the difference in enthalpy between the evaporator outlet and the expansion valve outlet. The mass flow is the cooling wanted divided by that effect, and the compressor power is the mass flow times the enthalpy rise in the compressor. The COP is the cooling divided by the compressor power.

The enthalpy after compression is found from the isentropic (ideal) end state at the condensing pressure, then corrected for the compressor efficiency. All the refrigerant values come from tables made with the CoolProp library, and each interpolation is shown. The pressure-enthalpy chart draws the saturation dome and the cycle on a log pressure scale, the way refrigeration engineers read it.

Formulas used

  • q_e = h_1 - h_4
  • \dot m = Q_e / q_e
  • W = \dot m (h_2 - h_1),\; h_2 = h_1 + \frac{h_{2s} - h_1}{\eta_s}
  • COP = Q_e / W
  • Q_c = \dot m (h_2 - h_3)

Worked example

With the default numbers in the calculator above:

  1. Evaporating and condensing pressures: 292.8 and 1017 kPa
  2. Pressure ratio: 3.472
  3. State 1: compressor inlet (evaporator outlet, superheated): 403 kJ/kg
  4. State 2s: end of isentropic compression (same entropy at p_c): 429.7 kJ/kg
  5. State 2: actual compressor outlet: 441.1 kJ/kg
  6. State 3: condenser outlet (subcooled liquid): 249 kJ/kg
  7. State 4: after the expansion valve (same enthalpy): 249 kJ/kg
  8. Refrigerating effect: 154 kJ/kg
  9. Refrigerant mass flow: 0.06492 kg/s
  10. Compressor shaft power (isentropic efficiency applied): 2.469 kW
  11. Heat rejected in the condenser: 12.47 kW
  12. Coefficient of performance (cooling): 4.05

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why is the real COP lower than this?

The calculator has no pressure drop in the pipes and heat exchangers and no motor, fan or pump power. A real plant also has heat exchangers that need a temperature difference, so the evaporating temperature is lower and the condensing temperature higher than the air or water temperatures.

What is superheat and why is it used?

Superheat is how far the vapour leaving the evaporator is above its boiling temperature. A few kelvin makes sure that no liquid reaches the compressor.

Which refrigerants are included?

R134a, R32, R290 (propane), R1234yf, R1234ze(E), R410A, R404A, R507A and ammonia. CO2 (R744) is left out because its cycle is often transcritical.

Is the compressor discharge temperature a problem?

It can be: compressor makers limit it because oil breaks down when it is too hot. The result shows a warning when the discharge temperature is high.

Related calculators

Further reading: ASHRAE Handbook: Refrigeration and Fundamentals; Cengel and Boles, Thermodynamics: An Engineering Approach; Moran and Shapiro, Fundamentals of Engineering Thermodynamics.

Need a calculator we do not have?

Tell us what you would like to calculate. We read every request and build the most asked-for ones.

We store your request (and your email if you give it) to decide what to build. We do not store the numbers you type into calculators.

Embed this calculator on your own page

Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.

Need this drawn, designed or checked?

Drafting Central is a mechanical engineering and drafting business in Burleigh Waters on the Gold Coast. A calculator gives you the numbers; we can turn them into drawings and designs.

Need help with a real project?

Talk to Drafting Central →

← All engineering calculators