TAHA Engineering Toolsby TAHA Knowledge Lab

HVAC & Building Services

COP, EER & kW/TR Converter

Convert cooling efficiency between COP, EER and kW/TR, or work it out from cooling capacity and electrical input power.

Inputs

Calculate from
A box labelled air conditioner or chiller in the centre. An arrow from the left labelled cooling Q enters it from the cooled space. An arrow from the top labelled electrical input P enters it. An arrow to the right labelled Q plus P leaves it to the outdoors.air conditioneror chillercooling Qfrom the spaceelectrical input PQ + Prejected outdoorsCOP = Q ÷ P
A cooling unit takes heat Q from the room or chilled water using electrical input P, and rejects Q + P outdoors. COP = Q ÷ P; EER = Q in Btu/h ÷ P in W; kW/TR = P in kW ÷ Q in tons. Diagram not to scale.

Heat removed from the cooled space or water, at the same operating condition as the input power.

Total power of the unit at that condition — compressor, fans, pumps and controls, as the rating standard defines it.

Result

COP (W/W)
3.333
EER
11.37Btu/(W·h)
kW/TR
1.055kW/TR
Cooling capacity in kW
10kW
Cooling capacity in Btu/h
34,121.4BTU/h
Cooling capacity in tons
2.84345TR
Working
COP = Q ÷ P = 10 kW ÷ 3 kW = 3.3333 EER = COP × 3.41214 = 11.374 Btu/(W·h) kW/TR = 3.51685 ÷ COP = 1.0551 kW/TR (= 12 ÷ EER)

The efficiency is COP 3.333 = EER 11.37 Btu/(W·h) = 1.055 kW/TR.

Educational estimate — check the assumptions below.

About this calculator

Cooling equipment efficiency is quoted in three common ways. All three compare the cooling output with the electrical input at one operating condition:

  • COP (coefficient of performance) — cooling ÷ input in the same unit (W/W). Higher is better.
  • EER (energy efficiency ratio, US) — Btu/h of cooling per watt of input. Higher is better. EER = 3.412 × COP.
  • kW/TR — kW of input per ton of refrigeration, used mainly for chillers. Lower is better. kW/TR = 3.517 ÷ COP = 12 ÷ EER.

These are exact conversions of the same ratio, so they are valid only when they describe the same operating point.

Formula

COP = Q ÷ P    EER = Q (Btu/h) ÷ P (W) = 3.41214 × COP    kW/TR = P (kW) ÷ Q (TR) = 3.51685 ÷ COP = 12 ÷ EER

Q = cooling capacity, P = electrical input power. 1 W = 3.41214 Btu/h; 1 TR = 12 000 Btu/h = 3.51685 kW.

EER is not SEER or IEER. SEER (and SEER2), IEER and the European SEER are seasonal or part-load weighted ratings, measured at several outdoor temperatures and loads by a rating standard. They cannot be calculated from a single COP, EER or kW/TR value, and this calculator does not convert them. Note also that the European “EER” (EN 14511) is a W/W ratio — the same as COP here — not the US Btu/(W·h) EER.

Worked example

  • From test data: 10 kW of cooling with 3 kW of input → COP = 10 ÷ 3 = 3.33; EER = 3.33 × 3.412 = 11.37; kW/TR = 3.517 ÷ 3.33 = 1.055.
  • Chiller: 0.6 kW/TR → COP = 3.517 ÷ 0.6 = 5.86; EER = 20.0.
  • Power for a capacity: a 1.5 TR (5.28 kW) unit with EER 12 (COP 3.52) needs 18 000 Btu/h ÷ 12 = 1.50 kW at its rated condition.

Assumptions and limitations

  • Capacity and power must be measured or rated at the same operating condition. Efficiency changes with outdoor temperature, indoor conditions and part load.
  • EER here is the US definition, Btu/h per W at one rated condition. SEER, SEER2, IEER and European SEER are seasonal or part-load ratings and cannot be derived from one operating point.
  • For a heat pump in heating mode, the heating COP is heat output ÷ input. It is a different number from the cooling COP and is not covered here.
  • Input power should include everything the rating standard includes (compressor, fans, controls; for chillers usually the compressor only — check the data sheet).
  • COP values above 20 are rejected as unrealistic; values above 10 or below 1.5 show a warning to check the inputs.

References

  • AHRI Standard 210/240 (unitary air conditioners: EER, SEER2) and AHRI 340/360 (commercial unitary: EER, IEER); AHRI 550/590 (chillers: COP, kW/ton, IPLV).
  • EN 14511 (EER and COP at rated conditions, W/W) and EN 14825 (seasonal SEER, SCOP).
  • Definition: 1 ton of refrigeration = 12 000 Btu/h; 1 Btu (IT) = 1055.05585262 J.