Power Converter
Power — Watts, Horsepower and More
Quick ways to estimate power and avoid common mistakes. From watts and kilowatts to horsepower, BTU/h, and VA, get answers fast.
Foundations of Power
Electrical Power
Real power (W) does work; apparent power (VA) includes reactive components.
- P = V × I × PF
- PF (power factor) ∈ [0..1]
- 3‑phase ≈ √3 × V × I × PF
Horsepower Family
Historic comparison to a horse’s work rate; multiple variants exist.
- hp(mech) ≈ 745.7 W
- hp(metric) ≈ 735.5 W
- Boiler hp is much larger
Thermal Power
HVAC and engines rate heat flow in BTU/h, kcal/s, tons of refrigeration.
- 1 kW ≈ 3,412 BTU/h
- 1 TR ≈ 3.517 kW
- Check time basis
- Convert via watts (W) to avoid mistakes
- Horsepower differs by variant; quote which one
- VA needs PF to get W
Where Each Unit Fits
Home & Appliances
Appliances label power in W/kW; energy bills in kWh.
- Kettle ~2 kW
- Microwave ~1.2 kW
- Laptop ~60–100 W
Engines & Vehicles
Engines advertise hp or kW; electrics use kW.
- 1 kW ≈ 1.341 hp
- Drivetrains list peak and continuous
HVAC & Thermal
Cooling/heating often shown in BTU/h or tons of refrigeration (TR).
- 1 TR ≈ 12,000 BTU/h
- Heaters in kW or BTU/h
RF & Audio
Small powers use dBm (reference 1 mW).
- 0 dBm = 1 mW
- +30 dBm = 1 W
- Amplifier headroom matters
Quick Math
Power Factor Explainer
Real vs apparent power
- PF = real power / apparent power
- P (W) = V × I × PF
- PF 0.8 means 20% is reactive; higher PF reduces current
Three-Phase Cheats
Quick 3‑phase rules
- VLL = √3 × VLN
- P ≈ √3 × VLL × I × PF
- Example: 400 V, 50 A, PF 0.9 → ≈ 31 kW
Electrical Basics
Instant estimate for electrical loads
- Single‑phase: P = V × I (watts)
- Example: 120 V × 10 A = 1,200 W = 1.2 kW
- Three‑phase: P ≈ √3 × V × I × PF
Scaling & HP
Convert between W, kW and horsepower
- 1 kW = 1,000 W
- 1 hp (mechanical) ≈ 745.7 W
- 1 kW ≈ 1.341 hp
Thermal Conversion
HVAC quick factor
- 1 BTU/h ≈ 0.2931 W
- 1 kW ≈ 3,412 BTU/h
dBm Cheats
Radio/power level shortcuts
- 0 dBm = 1 mW
- 10 dBm = 10 mW; 20 dBm = 100 mW; 30 dBm = 1 W
- dBm = 10·log10(P[mW])
How Conversions Work
- W ÷ 1,000 → kW; kW × 1,000 → W
- hp(mech) × 745.7 → W; W ÷ 745.7 → hp(mech)
- BTU/h × 0.293071 → W; W × 3.41214 → BTU/h
Common Conversions
| From | To | Factor | Example |
|---|---|---|---|
| kW | W | × 1,000 | 1.2 kW = 1,200 W |
| hp(mech) | kW | × 0.7457 | 150 hp ≈ 112 kW |
| kW | BTU/h | × 3,412 | 2 kW ≈ 6,824 BTU/h |
| TR | kW | × 3.517 | 2 TR ≈ 7.03 kW |
| dBm | mW | 10^(dBm/10) | 20 dBm = 100 mW |
Quick Examples
Common Mistakes to Avoid
- kW vs kWh: power (rate) vs energy (amount)
- Horsepower variants: mechanical ≠ metric ≠ boiler
- VA vs W: apparent vs real power (depends on power factor)
- BTU vs BTU/h: unit of energy vs unit of power
- Per‑second vs per‑hour: always check the time basis
- dB math: use 10× for power (not 20×)
Everyday Benchmarks
| Thing | Typical power | Notes |
|---|---|---|
| Human (resting) | ~100 W | Metabolic rate |
| LED bulb | 8–12 W | Modern lighting |
| Laptop | 60–100 W | Under load |
| Microwave | 1.0–1.2 kW | Cooking power |
| Electric kettle | 1.8–2.2 kW | Fast boil |
| Room AC | 1–3 kW | By size/SEER |
| Compact EV motor | 100–200 kW | Peak rating |
Amazing Power Facts
Why Horsepower?
James Watt coined 'horsepower' to market steam engines by comparing them to horses. One horse could lift 33,000 pounds one foot in one minute.
Human Power
The average human body at rest generates about 100 watts of heat — enough to power a bright LED bulb. During intense exercise, power output can exceed 400 watts!
VA vs W Mystery
A 1 kVA UPS may only deliver 800 W of real power if the power factor is 0.8 — the rest is 'imaginary' reactive power!
Solar Power Density
The Sun delivers about 1,000 W per square meter to Earth's surface on a clear day — enough to power a microwave from just one square meter of solar panels!
Lightning Strike
A lightning bolt can deliver up to 1 billion watts (1 GW) of power for a microsecond — but the total energy is surprisingly small, around 250 kWh.
dB Intuition
+3 dB ≈ doubles power; +10 dB = 10× power. So 0 dBm = 1 mW, 30 dBm = 1 W, and 60 dBm = 1 kW!
Heart Power
The human heart generates about 1-5 watts continuously — pumping blood throughout your entire life requires roughly the same energy as lifting a small car 1 meter every minute!
Ton of Refrigeration
A 'ton of refrigeration' equals the cooling power needed to freeze one ton of ice in 24 hours: 12,000 BTU/h or about 3.5 kW. It has nothing to do with the AC unit's weight!
Records & Extremes
| Record | Power | Notes |
|---|---|---|
| Large hydro plant | > 20 GW | Nameplate (e.g., Three Gorges) |
| Utility‑scale gas plant | ~1–2 GW | Combined cycle |
| Petawatt laser (peak) | > 10^15 W | Ultra‑short pulses |
The Evolution of Power Measurement: From Horses to Gigawatts
Power measurement evolved from comparing steam engines to workhorses in the 1700s to managing gigawatt-scale renewable energy grids today. This journey reflects humanity's growing energy demands and technological sophistication.
The Steam Age: Birth of Horsepower (1770s-1880s)
James Watt needed a way to market his steam engines by comparing them to the horses they would replace. His experiments led to the definition of horsepower that we still use today.
- 1776: James Watt observes horses lifting coal from mines
- Calculation: One horse lifts 33,000 pounds one foot in one minute
- Result: 1 horsepower ≈ 746 watts (later standardized)
- Marketing genius: Sold engines rated in 'horse power' units
- Legacy: Different countries created their own hp variants (mechanical, metric, boiler)
The Electrical Revolution (1880s-1960)
The invention of practical electrical power generation and distribution created the need for a new unit. The watt, named after James Watt, became the international standard.
- 1882: Edison's Pearl Street Station generates 600 kW in NYC
- 1889: International Electrical Congress adopts the watt (W)
- Definition: 1 watt = 1 joule per second = 1 volt × 1 ampere
- 1960: SI system confirms watt as the official power unit
- Grid expansion: Power plants scale from kilowatts to megawatts
Modern Power Complexity (1960s-1990s)
As electrical systems became more sophisticated, engineers discovered that not all power does useful work. This led to the concepts of real vs. apparent power.
- Real power (W): Does actual work, measured in watts
- Apparent power (VA): Total power including reactive components
- Power factor: Ratio of real to apparent power (0 to 1)
- 1990s: Power Factor Correction (PFC) becomes standard in electronics
- Impact: Improved grid efficiency, reduced waste heat
- Modern requirement: Most devices must have PF > 0.9
The Renewable Energy Era (2000s-Present)
Wind and solar power brought megawatt and gigawatt scales to everyday energy discussions. Power measurement now spans from nanowatts in IoT sensors to gigawatts in national grids.
- Residential solar: Typical system 5-10 kW
- Wind turbines: Modern offshore turbines reach 15 MW each
- Solar farms: Utility-scale installations exceed 500 MW
- Energy storage: Battery systems rated in MW/MWh
- Smart grids: Real-time power monitoring from nanowatts to gigawatts
- Future: Terawatt-scale renewable installations planned globally
The Modern Power Spectrum
Today's power measurements span an incredible range, from the nanowatt sensors in your smartwatch to the gigawatt output of nuclear power plants.
- Picowatts (pW): Radio astronomy receivers, quantum sensors
- Nanowatts (nW): Ultra-low-power IoT sensors, energy harvesting
- Microwatts (µW): Hearing aids, fitness trackers
- Milliwatts (mW): LED indicators, small electronics
- Watts (W): Light bulbs, USB chargers
- Kilowatts (kW): Home appliances, electric vehicle motors
- Megawatts (MW): Data centers, wind turbines, small power plants
- Gigawatts (GW): Nuclear reactors, large hydroelectric dams
- Terawatts (TW): Global energy production (~20 TW continuous)
Units Catalog
Metric (SI)
| Unit | Symbol | Watts | Notes |
|---|---|---|---|
| kilowatt | kW | 1,000 | 1,000 W; appliances and EVs. |
| megawatt | MW | 1,000,000 | 1,000 kW; generators, datacenters. |
| watt | W | 1 | SI base for power. |
| gigawatt | GW | 1.000e+9 | 1,000 MW; grid scale. |
| microwatt | µW | 0.000001 | Microwatt; sensors. |
| milliwatt | mW | 0.001 | Milliwatt; small electronics. |
| nanowatt | nW | 0.000000001 | Nanowatt; ultra‑low power. |
| picowatt | pW | 1.000e-12 | Picowatt; tiny RF/optical. |
| terawatt | TW | 1.000e+12 | 1,000 GW; global totals context. |
Horsepower
| Unit | Symbol | Watts | Notes |
|---|---|---|---|
| horsepower (mechanical) | hp | 745.7 | Horsepower (mechanical). |
| horsepower (metric) | hp(M) | 735.499 | Metric horsepower (PS). |
| horsepower (boiler) | hp(S) | 9,809.5 | Boiler horsepower (steam). |
| horsepower (electrical) | hp(E) | 746 | Electrical horsepower. |
| horsepower (water) | hp(H) | 746.043 | Water horsepower. |
| pferdestärke (PS) | PS | 735.499 | Pferdestärke (PS), ≈ metric hp. |
Thermal / BTU
| Unit | Symbol | Watts | Notes |
|---|---|---|---|
| BTU per hour | BTU/h | 0.293071 | BTU per hour; HVAC standard. |
| BTU per minute | BTU/min | 17.5843 | BTU per minute. |
| BTU per second | BTU/s | 1,055.06 | BTU per second. |
| calorie per hour | cal/h | 0.00116222 | Calorie per hour. |
| calorie per minute | cal/min | 0.0697333 | Calorie per minute. |
| calorie per second | cal/s | 4.184 | Calorie per second. |
| kilocalorie per hour | kcal/h | 1.16222 | Kilocalorie per hour. |
| kilocalorie per minute | kcal/min | 69.7333 | Kilocalorie per minute. |
| kilocalorie per second | kcal/s | 4,184 | Kilocalorie per second. |
| million BTU per hour | MBTU/h | 293,071 | Million BTU per hour. |
| ton of refrigeration | TR | 3,516.85 | Ton of refrigeration (TR). |
Electrical
| Unit | Symbol | Watts | Notes |
|---|---|---|---|
| kilovolt-ampere | kVA | 1,000 | Kilovolt‑ampere. |
| megavolt-ampere | MVA | 1,000,000 | Megavolt‑ampere. |
| volt-ampere | VA | 1 | Volt‑ampere (apparent power). |
Imperial
| Unit | Symbol | Watts | Notes |
|---|---|---|---|
| foot-pound force per hour | ft·lbf/h | 0.000376616 | Foot‑pound force per hour. |
| foot-pound force per minute | ft·lbf/min | 0.022597 | Foot‑pound force per minute. |
| foot-pound force per second | ft·lbf/s | 1.35582 | Foot‑pound force per second. |
Scientific / CGS
| Unit | Symbol | Watts | Notes |
|---|---|---|---|
| atmosphere cubic cm per minute | atm·cc/min | 0.00168875 | atm·cc per minute. |
| atmosphere cubic cm per second | atm·cc/s | 0.101325 | atm·cc per second. |
| atmosphere cubic foot per minute | atm·cfm | 47.82 | atm·cubic foot per minute. |
| erg per second | erg/s | 0.0000001 | Erg per second (CGS). |
| joule per hour | J/h | 0.000277778 | Joule per hour. |
| joule per second | J/s | 1 | Joule per second = watt. |
| kilojoule per hour | kJ/h | 0.277778 | Kilojoule per hour. |
| kilojoule per minute | kJ/min | 16.6667 | Kilojoule per minute. |
| kilojoule per second | kJ/s | 1,000 | Kilojoule per second. |
| lusec | lusec | 0.0001333 | Leak unit: micron‑liters/s. |
Power Conversion Best Practices
Conversion Best Practices
- Know your context: Use W/kW for precision, hp for engines, BTU/h for HVAC
- Specify horsepower variant: Mechanical hp (745.7 W) ≠ Metric hp (735.5 W) ≠ Boiler hp
- Power factor matters: VA × PF = W (for electrical systems, PF ranges 0-1)
- Time basis is critical: Power (W) vs Energy (Wh) — don't confuse rate with amount
- Check unit consistency: Ensure all units in calculation use same time basis (per second, per hour)
- Use scientific notation: For values < 1 µW or > 1 GW, scientific notation improves readability
Common Mistakes to Avoid
- Confusing kW (power) with kWh (energy) — rate vs amount, completely different quantities
- Mixing horsepower types: Mechanical hp (745.7 W) ≠ Metric hp (735.5 W) — 1.4% error
- Using VA as W: Apparent power (VA) ≠ Real power (W) unless power factor = 1.0
- BTU vs BTU/h: Energy unit vs Power unit — time matters! (like confusing kWh with kW)
- Wrong dB formula: Power uses 10 log₁₀, voltage uses 20 log₁₀ — don't mix them
- Forgetting three-phase: Single-phase P = V × I × PF, but 3-phase P = √3 × VLL × I × PF
Power Scale: From Quantum to Cosmic
Representative Power Scales
| Scale / Power | Representative Units | Typical Uses | Examples |
|---|---|---|---|
| 1 × 10⁻¹⁵ W | Femtowatt (fW) | Quantum optics, single photon detection | Single photon energy flux |
| 1 × 10⁻¹² W | Picowatt (pW) | Radio astronomy receivers, quantum sensors | Voyager 1 signal at Earth ≈ 1 pW |
| 1 × 10⁻⁹ W | Nanowatt (nW) | Ultra-low-power IoT sensors, energy harvesting | RFID tag passive power ≈ 10 nW |
| 1 × 10⁻⁶ W | Microwatt (µW) | Hearing aids, fitness trackers, pacemakers | Pacemaker ≈ 50 µW |
| 1 × 10⁻³ W | Milliwatt (mW) | LED indicators, laser pointers, small electronics | Laser pointer 1-5 mW |
| 1 × 10⁰ W | Watt (W) | Light bulbs, USB chargers, small appliances | LED bulb 10 W, USB charger 20 W |
| 1 × 10³ W | Kilowatt (kW) | Home appliances, EV motors, residential solar | Microwave 1.2 kW, car engine 100 kW |
| 1 × 10⁶ W | Megawatt (MW) | Data centers, wind turbines, small power plants | Wind turbine 3-15 MW |
| 1 × 10⁹ W | Gigawatt (GW) | Nuclear reactors, large dams, grid infrastructure | Nuclear reactor 1-1.5 GW |
| 1 × 10¹² W | Terawatt (TW) | National grid totals, global energy production | Global power use ≈ 20 TW average |
| 1 × 10¹⁵ W | Petawatt (PW) | High-energy laser systems (ultra-short pulses) | National Ignition Facility laser ≈ 500 TW peak |
| 3.828 × 10²⁶ W | Solar luminosity (L☉) | Stellar astronomy, astrophysics | Sun's total power output |
Frequently Asked Questions
VA vs W — what’s the difference?
VA is apparent power (volts × amps). Multiply by power factor to estimate watts (real power).
Which horsepower should I use?
Mechanical hp for engines (≈745.7 W), metric hp for PS; boiler hp is a steam rating, not comparable.
What does 1 ton of refrigeration mean?
Cooling power equal to melting 1 short ton of ice per day: ≈ 12,000 BTU/h or ≈ 3.517 kW.
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