Power Units Explained: Watts, Horsepower and BTU per Hour

Power is energy per second, and every industry grabbed its own unit for it: physicists count watts, American motors wear horsepower, German brochures quote PS, heaters are sold in BTU per hour, and air conditioners come in "tons". All of them reduce to one exchange rate against the watt — and the rates are exact.

The watt: one joule per second

The watt is the SI unit of power, defined directly from the joule: one watt is one joule of energy transferred every second. Because the joule is exact, so is every watt-based scale:

1 kW = 1,000 W     1 MW = 1,000 kW    1 GW = 1,000 MW
1 cal/s = 4.184 W  1 kcal/h = 1.16222 W

The kilocalorie per hour is worth a glance: a person burning 2,000 food Calories a day is running at about 2,324 watts — a couple of kilowatts of continuous chemical output, most of it lost as heat. That is why a crowded room warms up: each body is a hundred-watt-class heater that never switches off. The full joule-to-calorie story lives in Energy Units Explained, since power units are just energy units wearing a per-second hat.

Two horsepowers and a fraction

James Watt defined the horsepower in the 1770s to sell his steam engines against draft horses: 550 foot-pounds per second, which works out to exactly 745.699871582 watts. The metric world later created its own version — the Pferdestärke, PS, or "metric horsepower" — set at exactly 75 kilogram-force meters per second, or 735.49875 watts. The gap is small but real:

1 hp  = 745.699871582 W  (550 ft·lbf/s, exact)
1 PS  = 735.49875 W      (75 kgf·m/s, exact)
1 hp  = 1.01386966542 PS

This is why a "200 hp" US car and a "204 PS" European brochure describe the same engine. It also means the two units are not interchangeable when sizing a motor near its limit: a 10 hp motor is 7,457 W of mechanical output, while a 10 PS one is only 7,355 W — about a hundred watts you may or may not have. Foot-pounds per second survive as the bridge unit: 1 ft·lb/s is 1.35582 W, and horsepower is just 550 of those.

BTU per hour and the ton of refrigeration

Heating and cooling kept their own vocabulary. The BTU per hour is the International Table BTU — 1,055.05585262 joules — delivered over an hour:

1 BTU/h = 0.293071 W     1 kW = 3,412.14 BTU/h
1 TR    = 12,000 BTU/h   = 3.51685 kW

A 1,500 W space heater is "5,118 BTU/h" on the box — same machine, different scale. The ton of refrigeration is the best-preserved fossil unit in engineering: the cooling power needed to melt one short ton (2,000 lb) of ice in 24 hours, exactly 12,000 BTU/h or 3.517 kW. It dates from when cooling literally arrived as harvested ice, and it stuck because "3-ton AC" is easier to say than "10.55 kW of cooling". Note that a 3-ton air conditioner does not draw 10.55 kW of electricity — moving heat is cheaper than making it, so at a seasonal efficiency of 3 or so, the electrical draw is nearer 3.5 kW.

Power times time: how the units stack

The single most useful identity in this whole family is energy = power × time. A 1,000 W appliance run for one hour consumes 1,000 watt-hours — one kilowatt-hour. Multiply the watts on the label by the hours you run it and you have the energy, which is what the meter bills. That arithmetic, priced at your tariff, is exactly what the Electricity Cost Calculator does; the torque side of rotating machinery, where watts = newton-meters × radians per second, is covered in Torque Units Explained. The general pattern — each field keeps the unit that fits its numbers — is the same one behind Why Two Measurement Systems.

Try it yourself

Open the Power Converter and check three numbers. First, your car or vacuum cleaner: enter its horsepower and read the watts — a 150 hp engine is about 112 kW of mechanical output. Second, your heater: enter 1,500 W and read 5,118 BTU/h, then compare it to the label on the box. Third, an air conditioner: enter 3 tons of refrigeration and confirm 10.55 kW of cooling and 36,000 BTU/h. Once you can move between the four families — watts, horsepower, BTU/h and tons — every spec sheet in the house reads in one language.