Power Conversion Formulas
Complete formulas for converting between different power units including watts, horsepower, BTU per hour, and specialized power measurements.
⚡ Power Unit Overview
Electrical
Watt (W): Base SI unit
Kilowatt (kW): 1,000 W
Megawatt (MW): 1,000,000 W
Mechanical
Horsepower (HP): 746 W
Metric HP: 735.5 W
ft⋅lbf/s: Foot-pounds per second
Thermal
BTU/hr: Heat transfer rate
Calories/sec: Thermal power
Tons of refrigeration: Cooling
Specialized
dBm: Decibel-milliwatts
MIPS: Computing power
Lumen/W: Luminous efficacy
🔄 Basic Power Conversion Formulas
Electrical Power Conversions
Watts to Kilowatts
Example: 2,500 W
2,500 W = 2.5 kW
Kilowatts to Megawatts
Example: 5,500 kW
5,500 kW = 5.5 MW
Electrical Power Formula
Example: 120V, 15A
120V × 15A = 1.8 kW
Mechanical Power Conversions
Horsepower to Watts
Example: 10 HP
10 HP = 7,457 W = 7.46 kW
Watts to Horsepower
Example: 3,000 W
3,000 W = 4.02 HP
🔥 Thermal Power Conversions
BTU/hr Conversions
BTU/hr to Watts
Example: 12,000 BTU/hr
12,000 BTU/hr = 3.52 kW
Watts to BTU/hr
Example: 5,000 W
5,000 W = 17,060 BTU/hr
BTU/hr to HP
Example: 10,000 BTU/hr
10,000 BTU/hr = 3.93 HP
Refrigeration & HVAC Units
Tons of Refrigeration
Example: 5 tons cooling
5 tons = 17.6 kW = 60,000 BTU/hr
Boiler Horsepower
Example: 100 BHP boiler
100 BHP = 981 kW
⚙️ Advanced Power Calculations
Mechanical Power Formulas
Rotational Power
Torque: 200 Nm, Speed: 1800 rpm
In HP:
Motor output: 50.6 HP
Pump Power
Q=500 GPM, H=100 ft, η=75%
In kW:
Pump requires: 16.8 HP
Electrical Power Calculations
Three-Phase Power
480V, 50A, PF=0.85
In HP:
Motor load: 35.3 kW
Power Factor Correction
100 kW, PF: 0.7→0.95
Need 69 kVAR capacitors
📊 Power Conversion Reference Table
| Power Source | Watts (W) | HP | BTU/hr | kW |
|---|---|---|---|---|
| Hair Dryer | 1,800 | 2.41 | 6,142 | 1.8 |
| Microwave Oven | 1,000 | 1.34 | 3,412 | 1.0 |
| Car Engine (Small) | 74,570 | 100 | 254,400 | 74.6 |
| Industrial Motor | 373,000 | 500 | 1,272,876 | 373 |
| Wind Turbine (Large) | 2,000,000 | 2,682 | 6,824,000 | 2,000 |
🔬 Specialized Power Units & Applications
RF & Communications Power
dBm to Watts
Example: 30 dBm
30 dBm = 1 Watt
Watts to dBm
Example: 0.001 W (1 mW)
1 mW = 0 dBm
Solar & Renewable Power
Solar Panel Rating
Standard Test Conditions (STC)
Irradiance: 1,000 W/m²
Cell temperature: 25°C
Air mass: 1.5
300W panel efficiency: ~18%
Panel area:
300W panel ≈ 1.67 m²
Wind Power Formula
Wind: 12 m/s, rotor: 50m dia
Air density: ρ = 1.225 kg/m³
Area:
Cp = 0.4 (realistic)
Wind power: 829 kW