Power Units: Converting Watts, Horsepower, BTU/hr, and Calories per Second

Power measures the rate at which work is done — one watt equals one joule of energy transferred per second. James Watt defined the horsepower unit in 1782, calculating that a brewery horse could lift 550 pounds one foot in one second (33,000 ft·lbf per minute), giving 1 hp = 745.7 W. Today, power conversion spans engineering (watts, kilowatts, megawatts), automotive (horsepower), HVAC (BTU per hour), and nutrition (calories per second). Every conversion factor traces back to the SI watt, which has been defined since 1960 in terms of the kilogram, meter, and second. Understanding these relationships enables cross-disciplinary comparison of engines, heaters, appliances, and human metabolic output.

Key Takeaways

• 1 W = 1 J/s.
• 1 hp (mechanical) = 745.7 W. 1 PS (metric) = 735.5 W.
• 1 BTU/hr = 0.293071 W.
• 1 cal/s = 4.1868 W.

1. The watt: the fundamental SI unit
2. Conversion factors and reference table
3. Horsepower: mechanical, metric, and electrical
4. BTU per hour and HVAC applications
5. Practical power conversion examples
6. Frequently Asked Questions

The watt: the fundamental SI unit

Definition. The watt (W) is the SI derived unit of power, defined as one joule per second. Named after Scottish engineer James Watt, it was adopted by the 11th General Conference on Weights and Measures (CGPM) in 1960 as part of the International System of Units. One watt is equivalent to 1 kg·m²/s³ in base SI terms.

Kilowatt, megawatt, gigawatt. The metric prefixes scale the watt: 1 kW = 1,000 W (household appliance); 1 MW = 1,000,000 W (power plant output); 1 GW = 1,000,000,000 W (large power station). The power of the average US household is approximately 1.2 kW; a typical nuclear reactor produces about 1 GW.

Electrical vs mechanical power. In electrical systems, power = voltage × current (P = V × I). A 120 V circuit drawing 10 A delivers 1,200 W = 1.2 kW. In mechanical systems, power = force × velocity (P = F × v). A person pushing with 100 N at 2 m/s produces 200 W.

Conversion factors and reference table

Core conversion relationships:

• 1 kW = 1,000 W
• 1 MW = 1,000 kW = 1,000,000 W
• 1 hp (mechanical) = 745.6999 W
• 1 hp (metric / PS) = 735.4988 W
• 1 hp (electrical) = 746 W
• 1 BTU/hr = 0.293071 W
• 1 cal/s = 4.1868 W
• 1 ft·lbf/s = 1.355818 W

Power Unit Conversion Reference

Worked example: converting 2.5 kW to hp.

2.5 kW = 2,500 W. 2,500 ÷ 745.7 = 3.35 hp. A 2.5 kW electric motor produces approximately 3.35 mechanical horsepower.

Worked example: converting 150 hp to kW.

150 hp × 745.7 = 111,855 W ÷ 1,000 = 111.9 kW. A 150 hp car engine delivers about 112 kW of mechanical power.

Horsepower: mechanical, metric, and electrical

James Watt's original definition. In 1782, James Watt needed a way to market his improved steam engine to buyers who were currently using horses for power. He measured that a brewery horse could lift 550 lb through 1 ft in 1 second, giving 550 ft·lbf/s. Multiplying by 60 gave 33,000 ft·lbf/min — the definition that survives today as mechanical horsepower.

Metric horsepower (PS). The metric system uses Pferdestärke (PS) — literally 'horse strength' — defined as 75 kgf·m/s = 735.4988 W. The 1.4% difference between mechanical hp (745.7 W) and metric PS (735.5 W) means a 100 hp engine is actually 98.6 PS, and vice versa. German and Japanese automakers typically quote PS; US and UK automakers quote hp.

Electrical horsepower. Electrical horsepower is defined as exactly 746 W and is used for electric motor ratings. The US National Electrical Code uses this value for motor sizing calculations. In practice, the difference between mechanical (745.7) and electrical (746) horsepower is negligible — 0.04%.

Worked example: comparing car specs.

A German car advertises 200 PS. In hp: 200 × 735.5 ÷ 745.7 = 197.3 hp. An American car with 200 hp would be 200 × 745.7 ÷ 735.5 = 202.8 PS. The difference is less than 2% and usually lost in drivetrain losses.

Worked example: converting boiler horsepower.

One boiler horsepower (hp(S)) = 34.5 lb/hr of steam at 212 °F = 9,809.5 W. A boiler rated at 100 hp(S) produces 100 × 9,809.5 = 980,950 W ≈ 981 kW of heat output.

BTU per hour and HVAC applications

The British Thermal Unit. One BTU is the energy required to raise one pound of water by one degree Fahrenheit at sea level. When expressed per hour (BTU/hr), it becomes a power unit. The conversion: 1 BTU/hr = 0.293071 W. An HVAC system rated at 12,000 BTU/hr (1 ton of cooling) produces: 12,000 × 0.293071 = 3,516.9 W = 3.52 kW.

Worked example: converting an AC unit rating.

A window air conditioner is labeled 10,000 BTU/hr. In kW: 10,000 × 0.293071 = 2,931 W = 2.93 kW. In hp: 2,931 ÷ 745.7 = 3.93 hp. The electrical input power will be lower than the cooling output due to the coefficient of performance (COP) — typically 2.5 to 4.0 for modern units.

Worked example: comparing heater costs.

A 1,500 W space heater and a 5,000 BTU/hr heater: 5,000 × 0.293071 = 1,465 W. The 1,500 W heater delivers slightly more heat but uses 2.4% more electricity. At $0.12/kWh running 8 hours/day: 1,500 W = 1.5 × 8 × 0.12 = $1.44/day. 5,000 BTU/hr = 1.465 × 8 × 0.12 = $1.41/day.

Practical power conversion examples

Worked example: human metabolic power.

A person consuming 2,500 kcal per day of food energy. 2,500 kcal × 4,184 J/kcal = 10,460,000 J per day. Average power: 10,460,000 ÷ 86,400 s = 121.1 W. A human at rest produces about 100 W; during exercise, 300–500 W; a trained cyclist can sustain 400 W for an hour.

Worked example: solar panel array.

A solar panel rated at 400 W peak (under STC). Array of 20 panels: 20 × 400 = 8,000 W = 8 kW. In hp: 8,000 ÷ 745.7 = 10.7 hp. Annual energy (assuming 4.5 peak sun hours/day): 8 kW × 4.5 × 365 = 13,140 kWh.

Worked example: electric vehicle motor.

An EV motor rated at 150 kW. In hp: 150,000 ÷ 745.7 = 201 hp. In PS: 150,000 ÷ 735.5 = 204 PS. The same motor can be described as 150 kW, 201 hp, or 204 PS depending on the market.

Worked example: power plant output.

A natural gas turbine generates 250 MW. In hp: 250,000,000 ÷ 745.7 = 335,255 hp. In BTU/hr: 250,000,000 ÷ 0.293071 = 853,000,000 BTU/hr. The turbine consumes approximately 8,500 MMBTU/hr of natural gas (at ~30% thermal efficiency) to produce this 250 MW output.