Power Converter
High-precision calculator for mechanical work rate, electrical drivetrains, and HVAC thermal conditioning. Translate between SI Watts, Kilowatts (kW), Mechanical Horsepower (hp), European Metric PS, and Tons of Refrigeration (TR).
Power Configuration
1 W = 1 J/s = 1 N⋅m/s • SI StandardLoading power constant...
745.7 Watts (W) = 1 Mechanical Horsepower (hp)
Automotive Engine & EV Drivetrain Analysis
Imperial hp vs. European Metric PS vs. Electric Vehicle kWWhy European and US horsepower figures differ: German, Italian, and French manufacturers often quote engine power in Pferdestärke (PS) or cavalli (cv). Because 1 PS = 735.498 W while 1 Imperial hp = 745.700 W, an engine marketed at 400 PS in Europe is certified as 394.5 hp in North America.
HVAC Thermal Heating & Cooling Capacity
Residential Air Conditioning Sizing (1 Ton = 12,000 BTU/hr = 3.517 kW)Step-by-Step Conversion Arithmetic
Simultaneous Multi-Unit Power Grid
Real-time converted values across all 16 major SI metric, mechanical, electrical, and HVAC thermal power units
How to Convert Power Units
In physics and engineering, the SI unit of power is the Watt (W), representing an energy transfer rate of 1 Joule per second (1 W = 1 J/s). Standard conversion identities include: 1 Mechanical Horsepower (hp) = 745.69987 Watts; 1 Metric Horsepower (PS) = 735.49875 Watts; 1 Kilowatt (kW) = 1,000 Watts ≈ 1.341 hp; and 1 Ton of Refrigeration (TR) = 12,000 BTU/hr = 3,516.85 Watts.
1. The SI Watt: Rate of Energy Transfer & Base Dimensions
The Watt (symbol W) is the coherent derived unit of power in the International System of Units (SI), defined as one Joule of energy transferred or converted per second:
1 Watt = 1 Joule / second. In SI base units: 1 kg⋅m²⋅s⁻³. It measures the instantaneous velocity of physical work.
1 Watt = 1 Volt × 1 Ampere (1 V⋅A). In resistive DC circuits: P = I²R = V²/R (Joule heating rate).
1 Watt = 1 Newton × 1 meter/second (1 N⋅m/s). The rate of work done moving an object at 1 m/s against a 1 N opposing force.
2. The Anatomy of Horsepower: Mechanical (hp) vs. Metric (PS)
The term "horsepower" encompasses multiple distinct engineering standards across North America and Europe:
| Standard Name | Symbol | Exact Definition | Watt Equivalent | Primary Domain |
|---|---|---|---|---|
| Mechanical Horsepower | hp or hp(I) | 550 ft⋅lbf / second | 745.69987 W | US & UK automotive (SAE Net), aerospace |
| Metric Horsepower (PS) | PS, cv, ch, pk | 75 kgf⋅m / second | 735.49875 W | German DIN 66036, European vehicle registration |
| Electrical Horsepower | hp(E) | Exactly 746 Watts | 746.00000 W | NEMA electric motor nameplates & pumps |
| Boiler Horsepower | hp(S) | Evaporates 34.5 lbs water/hr at 212°F | 9,809.50 W | Industrial boiler capacity (approx. 13.15 hp) |
Because 1 hp = 1.01387 PS, an imported European performance sports car rated at 600 PS in Germany produces 591.8 hp under North American SAE J1349 net testing standards.
3. Automotive Engineering: Combustion Torque vs. EV Kilowatts
In internal combustion engines (ICE), dynamometers measure engine crankshaft torque (τ) and rotational speed (RPM), then calculate horsepower algebraically:
Why 5,252? One horsepower equals 33,000 ft⋅lb/min. In rotational motion, one revolution is 2π radians. Dividing 33,000 by 2π (6.283185) yields exactly 5,252.113. Consequently, on every dyno graph plotted with identical scales, horsepower and torque curves always cross at 5,252 RPM.
In modern Electric Vehicles (EVs), electric motors deliver instantaneous peak torque at zero RPM, and power output is governed by inverter current and battery pack DC bus voltage:
4. HVAC Sizing & Thermal Dynamics: BTU/hr and Refrigeration Tons
Residential and commercial air conditioning systems across the Americas use the Ton of Refrigeration (TR) and BTU per hour (BTU/hr):
- 1 Ton of Refrigeration (TR): Exactly 12,000 BTU/hr = 3,516.85 Watts (3.517 kW) of thermal heat extraction.
- Residential Sizing Rule of Thumb: In temperate climates, modern well-insulated homes require approximately 1 Ton of cooling capacity per 400 to 600 square feet of conditioned living area.
- SEER Rating (Seasonal Energy Efficiency Ratio): Evaluates air conditioner efficiency by dividing total cooling output in BTUs over a cooling season by total electrical energy consumed in Watt-hours: SEER = BTU / Wh. A modern SEER 18 unit uses significantly fewer electrical Watts than an older SEER 10 system.
5. Comprehensive Multi-Unit Power Conversion Reference Matrix
The table below documents exact mathematical factors for converting any standard power unit directly into SI Watts (W):
| Unit Name | Symbol | Category | Watt Equivalent (W) | hp Equivalent |
|---|---|---|---|---|
| Watt | W | SI Base | 1 | 0.001341 |
| Kilowatt | kW | SI Metric | 1,000 | 1.341022 |
| Megawatt | MW | SI Metric | 10⁶ | 1,341.02 |
| Gigawatt | GW | SI Metric | 10⁹ | 1,341,022 |
| Mechanical Horsepower | hp | Mechanical | 745.69987 | 1.000000 |
| Metric Horsepower | PS | Automotive | 735.49875 | 0.986320 |
| Electric Horsepower | hp(E) | Electrical | 746.00000 | 1.000402 |
| Boiler Horsepower | hp(S) | Thermal | 9,809.50 | 13.15475 |
| BTU per hour | BTU/hr | HVAC | 0.293071 | 3.9301 × 10⁻⁴ |
| Ton of Refrigeration | TR | HVAC | 3,516.853 | 4.716178 |
| Calorie per second | cal/s | Thermal | 4.184 | 0.005611 |
| Foot-pound/second | ft⋅lbf/s | Mechanical | 1.355818 | 0.001818 |
| Erg per second | erg/s | CGS | 10⁻⁷ | 1.341 × 10⁻¹⁰ |
6. Industrial Megawatts to Planetary Terawatts: The Kardashev Scale
Astrophysicists and macro-energy economists categorize energetic civilizational progress using powers of ten:
1 MW = 1,000,000 Watts. Modern offshore wind turbines generate 10 MW to 15 MW each; high-speed electric trains (TGV/Shinkansen) draw 8 MW to 12 MW during peak acceleration.
1 GW = 1,000 MW. The Three Gorges Dam in China possesses a world-record hydroelectric capacity of 22.5 GW. Standard nuclear power plants generate 1 GW to 3 GW per station.
1 TW = 1,000 GW. Total global human instantaneous primary power consumption is approximately 19 TW (of which ~2.5 TW is grid electricity). Total solar power intercepted by Earth is ~173,000 TW.
7. Step-by-Step Worked Conversion Problems
An electric vehicle motor produces 225 Kilowatts (kW). What is its mechanical horsepower and European metric PS rating?
Step 1: Convert Kilowatts to Base SI Watts
Power = 225 kW × 1,000 W/kW = 225,000 Watts
Step 2: Divide by Mechanical Horsepower Factor (745.69987 W)
Mechanical Horsepower = 225,000 ÷ 745.69987 ≈ 301.73 hp
Step 3: Divide by Metric Horsepower Factor (735.49875 W)
Metric Horsepower = 225,000 ÷ 735.49875 ≈ 305.92 PS
A central heat pump provides 36,000 BTU/hr of cooling. How many Tons of Refrigeration and thermal Kilowatts does this deliver?
Step 1: Convert BTU/hr into Tons of Refrigeration (12,000 BTU/hr per Ton)
Cooling Capacity = 36,000 BTU/hr ÷ 12,000 BTU/(hr⋅Ton) = 3.00 Tons (TR)
Step 2: Convert to Watts Using the BTU/hr to Watt Constant (0.293071 W)
Power in Watts = 36,000 × 0.29307107 W ≈ 10,550.56 Watts
Step 3: Convert to Kilowatts
10,550.56 ÷ 1,000 = 10.55 kW of thermal cooling rate
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