Refrigeration keeps two questions apart, and half the mistakes in this subject come from letting them touch. How much cooling? is a CAPACITY. How cheaply? is an EFFICIENCY. Tonnage answers the first. COP, EER and kW/ton answer the second.

Start with the efficiency, because it is the honest one. $\mathrm{COP} = \dfrac{\dot{Q}}{\dot{W}}$ — read aloud C O P equals Q-dot over W-dot. $\dot{Q}$ is the cooling delivered, a rate, in kilowatts; $\dot{W}$ is the electrical power drawn to deliver it, also in kilowatts; and the dot over a letter means per unit time throughout this chapter. Both sides are powers, so every unit cancels and the COP travels naked. A COP of 5 says five kilowatts of heat move for each kilowatt bought — no law is broken, because the machine MOVES heat rather than making it.

Now the capacity. A ton of refrigeration is a POWER, not a weight: 12,000 BTU per hour, or $3.517\ \mathrm{kW}$. It got its name honestly — it is the rate that would freeze one short ton of water in a day, which is what an ice plant used to sell. So $T = \dfrac{\dot{Q}}{3.517}$, with $T$ the capacity in tons and $\dot{Q}$ the same cooling rate in kilowatts. Nothing in the machine weighs a ton.

Finally the dialect North America prints on nameplates: $\mathrm{EER} = 3.412\,\mathrm{COP}$. EER is deliberately mixed — BTU per hour of cooling over WATTS of input — and 3.412 is simply how many BTU/h live in a watt. Keep the two constants apart. 3.517 kW per ton converts CAPACITIES; 3.412 BTU/h per watt converts EFFICIENCIES. They look alike, they are three percent apart, and swapping them produces an answer that passes every eyeball test and fails the submittal.