Energy and Power Units: BTU, Kilowatts, Tons and Horsepower

Why this matters

A heat pump is sold in tons, its backup heat in kilowatts, the furnace beside it in BTU per hour, the blower motor in horsepower and the gas it burns in therms. Five units, one house, and the customer asks a simple question: which one makes more heat? Answering it means converting, and the conversion that goes wrong is rarely the multiplication. It is treating a rate as an amount, so a furnace's 80,000 "BTU" gets compared with a heat pump's "12 kWh" as if they were the same kind of number. This card gives the conversions with their checks and keeps the rate-versus-amount line visible on every one.

Rate versus amount, before any number

Every unit here is one of two kinds, and mixing them is the slip the rest of this card is built to catch.

• Energy is an amount. BTU, kilowatt-hours (kWh), therms and ton-hours count how much heat or work has been delivered in total. A bill is in energy units because it counts what you used.
• Power is a rate. BTU per hour (BTU/h), kilowatts (kW), tons and horsepower say how fast energy is delivered. A nameplate is in power units because it says what the equipment does while running.

The bridge between them is time: power x hours = energy. A 2 kW heater running 3 hours delivers 6 kWh. Nothing else turns one into the other. The trap is that "BTU" gets spoken as shorthand for "BTU per hour" on every furnace and air conditioner in the trade, so a nameplate reading "80,000 BTU" almost always means 80,000 BTU/h. Write the "/h" yourself, every time, and the slip has nowhere to hide. What a single BTU physically is, and why the unit exists, is covered in What a BTU Actually Is; this card is the arithmetic around it.

The conversion card

POWER (rates)
1 kW          = 3,412 BTU/h
1 ton         = 12,000 BTU/h
1 ton         = 12,000 / 3,412 = 3.517 kW
1 hp          = 746 W = 0.746 kW
1 hp          = 0.746 x 3,412 = about 2,545 BTU/h
1 MBH         = 1,000 BTU/h  (M = thousand)
1 boiler hp   = about 33,475 BTU/h  (not 1 hp!)

ENERGY (amounts)
1 kWh         = 3,412 BTU
1 therm       = 100,000 BTU
1 therm       = 100,000 / 3,412 = about 29.3 kWh
1 ton-hour    = 12,000 BTU

WORKED
15 kW x 3,412          = 51,180 BTU/h
51,180 / 12,000        = 4.27 tons
4.27 tons x 3.517 kW   = 15.0 kW   (check)

Two lines deserve a second look. Boiler horsepower is an old steam-boiler rating, about 33,475 BTU/h, roughly thirteen times a mechanical horsepower. Read a commercial boiler plate in boiler horsepower as if it were motor horsepower and you undersize it by that factor. And MBH uses the Roman M for thousand, so 80 MBH is 80,000 BTU/h; the same letters in other contexts sometimes mean a million, which is why the unit should be spelled out on anything a customer or another trade reads.

Worked example: strip heat in tons

A 15 kW electric strip heater sits in an air handler as backup heat for a heat pump. The customer wants to know how it compares with the heat pump's nominal 4-ton rating.

• 15 kW x 3,412 BTU/h per kW = 51,180 BTU/h.
• 51,180 BTU/h / 12,000 BTU/h per ton = 4.265 tons, call it 4.3.
• Check from the other side: 4.265 tons x 3.517 kW per ton = 15.0 kW. The units cancel back to kW and the number returns.
• Rough estimate: a kilowatt is about 3,400 BTU/h, so 15 of them is about 51,000, a bit over four tons. Agrees.

So at full output the strip heat matches the heat pump's nominal capacity. Two conditions decide whether that comparison means anything. The heater's 15 kW is at its rated voltage; on 208 V it delivers about three quarters of that, which Resistance Heaters at the Wrong Voltage works through. And the heat pump's 4 tons is a nominal cooling size at rating conditions; its heating output falls as the outdoor temperature drops, which is the whole reason the strip heat is there. The conversion is exact. The comparison is only as good as the conditions on each side, and the sentence telling the customer should name them.

Worked example: a heater, a furnace, and an hour

A homeowner runs a 1,500 W plug-in space heater in a cold room and asks how much heat it puts out compared with the furnace.

• 1,500 W = 1.5 kW. 1.5 kW x 3,412 = 5,118 BTU/h.
• The furnace is rated 80,000 BTU/h input. At 95 percent efficiency its output is 80,000 x 0.95 = 76,000 BTU/h.
• Ratio of outputs: 76,000 / 5,118 = 14.8. The furnace makes about fifteen times the heat of the space heater while each is running.

Now carry time through, because the customer's real question is what each delivers over an evening:

• Space heater, 4 hours: 1.5 kW x 4 h = 6 kWh. In BTU: 6 x 3,412 = 20,472 BTU.
• Furnace, 1 hour of burner time across the same evening: 76,000 BTU/h x 1 h = 76,000 BTU delivered, from 80,000 BTU of gas, which is 0.8 therm.

The heater ran four times as long and still delivered about a quarter of the heat: 20,472 / 76,000 = 0.27. Every figure in that comparison is an amount (BTU, kWh, therm) and every one came from a rate multiplied by hours. A comparison of 5,118 BTU/h against 76,000 BTU would have been a rate against an amount, and no arithmetic could make it mean anything. What either evening costs is a separate question for the utility rate on each bill; the energy is the part this card can settle.

Horsepower: shaft out is not electricity in

A motor's horsepower is what it delivers at the shaft at full load, not what it draws from the wire. The electrical input is larger by the motor's efficiency.

Take a 1/2 hp blower motor at full load with an efficiency of, say, 80 percent (illustrative; the motor's nameplate or data sheet gives the real figure):

• Shaft output: 0.5 hp x 746 W/hp = 373 W.
• Electrical input: 373 W / 0.80 = 466 W.
• If that motor sits in the airstream, all 466 W ends up as heat in the air: 466 W x 3.412 BTU/h per W = 1,590 BTU/h.

Two lessons sit in that. A motor's horsepower times 746 underestimates its power draw, so it underestimates what the circuit and the bill see. And motor heat in an airstream is real heat: on cooling it is load the coil has to remove, on heating it is a small help. Many motors also run below their rated load in service, so the nameplate is a ceiling, and the honest way to know the actual draw is a measurement, not the plate.

Tons, and why a ton is 12,000

A ton of cooling is the rate of heat removal that would melt one short ton (2,000 lb) of ice in 24 hours. Ice takes about 144 BTU per pound to melt, so 2,000 lb x 144 BTU/lb = 288,000 BTU over 24 hours, which is 12,000 BTU/h. That is why the number is round and why it is a rate: it is a day's ice melt divided by the day.

Ton-hours are the energy version, 12,000 BTU each, and they show up in chiller and thermal-storage work. A 3-ton system running flat out for 4 hours moves 3 x 4 = 12 ton-hours, or 144,000 BTU. A sentence that says "3 tons for 4 hours is 12 tons" has dropped the hours and turned an amount back into a rate.

Therms and kilowatt-hours side by side

Gas is billed in therms (100,000 BTU each) or in hundreds of cubic feet; electricity in kWh. Putting them on one scale is a conversion, and its trap is efficiency rather than units.

• 1 therm = 100,000 BTU = 29.3 kWh of energy content.
• A furnace at 95 percent turns a therm into 95,000 BTU of delivered heat.
• A resistance heater turns a kWh into 3,412 BTU, all of it, at the point of use.
• A heat pump delivers more heat than its electrical input, by its coefficient of performance, which varies with outdoor temperature.

So "one therm equals 29.3 kWh" is true of the fuel and false of the comfort, and the sentence that carries it to a customer has to say which one it means. How cubic feet of gas convert to BTU, and how to clock a meter to check a burner's input, are covered in How to Clock a Gas Meter to Check Input.

Efficiency ratios that carry two units

Some ratings divide one power unit by another, and the units inside them are part of the number. EER (energy efficiency ratio) is cooling output in BTU/h divided by electrical input in watts at one rating condition. COP (coefficient of performance) is the same output over input with both in the same unit, so it has no units at all. Converting between them is a units step, not a judgment:

• A 36,000 BTU/h air conditioner rated at an EER of 12 draws 36,000 / 12 = 3,000 W at that condition.
• Its COP: 12 BTU/h per W / 3.412 BTU/h per W = 3.52.
• Check: 3,000 W x 3.412 = 10,236 BTU/h of input; 36,000 / 10,236 = 3.52. Same answer, both units cancelled.

Seasonal ratings (SEER, HSPF and their newer versions) are averaged over a test season and cannot be converted to a draw at any one moment by this arithmetic; quote them as the ratings they are. And every one of these is a rating-condition figure, so the draw you measure on a hot afternoon will not match the plate division, nor should it.

Sanity checks that catch the usual slips

• Write "/h" on every rate. If an answer is in BTU and the question was about a nameplate, you have either multiplied by time or dropped it.
• Bigger unit, smaller number. One ton is about 3.5 kW, and one kW is about 3,400 BTU/h. Converting to a bigger unit should shrink the number; if 15 kW became 180,000 tons, you multiplied where you should have divided.
• Round-trip it. Every conversion on this card has a reverse. Run it and see the starting number come back.
• Which horsepower? Mechanical (746 W) or boiler (about 33,475 BTU/h). The plate's context tells you; a boiler plate is never in mechanical horsepower.
• Input or output? Furnace and boiler plates usually state input; delivered heat is input times efficiency. Say which one the number is before you compare it with anything.

References

• Equipment nameplates and installation manuals for rated input, output and efficiency
• Motor nameplates and manufacturer data sheets for efficiency at load
• See related: What a BTU Actually Is; Common Unit Conversions + Math Formulas; The Sensible Heat Formulas for Air and Water