Watt (W) - Unit Information & Conversion

Symbol:W
Plural:watts
Category:Power

🔄 Quick Convert Watt

What is a Watt?

The watt (W) is the SI unit of power, measuring the rate at which energy is transferred or converted. Named after Scottish engineer James Watt, one watt equals one joule of energy per second (1 W = 1 J/s). It is the universal standard for measuring electrical power consumption in appliances, light bulbs, motors, and electronic devices. While horsepower remains popular for engines, the watt dominates electrical and electronic applications worldwide.

History of the Watt

The watt was named in honor of James Watt (1736-1819), the Scottish inventor whose improvements to the steam engine were pivotal to the Industrial Revolution. The unit was officially adopted by the Second Congress of the British Association for the Advancement of Science in 1882, replacing earlier units like "volt-ampere" for electrical power. In 1960, the watt was formally incorporated into the International System of Units (SI) as the standard unit of power. The definition is precise: 1 watt = 1 joule per second = 1 kg⋅m²/s³.

Quick Answer

What is a Watt? A watt (symbol: W) is the SI unit of power—the rate at which energy is used or produced.

The Simple Formula: $$ 1 \text{ Watt} = 1 \frac{\text{Joule}}{\text{second}} $$

Think of it this way:

  • Energy (Joules) is like water in a bucket.
  • Power (Watts) is how fast you pour it out.

Common Examples:

  • LED Bulb: 10 W
  • Laptop Charger: 65 W
  • Microwave: 1,000 W (1 kW)
  • Electric Car Charger: 7,000 W (7 kW)

Quick Comparison Table

Watts Kilowatts Horsepower Typical Device Annual Cost*
1-15 W 0.001-0.015 kW 0.001-0.02 HP LED bulb $1-15
60-100 W 0.06-0.1 kW 0.08-0.13 HP Incandescent bulb $50-90
200-400 W 0.2-0.4 kW 0.27-0.54 HP Desktop computer $175-350
500-800 W 0.5-0.8 kW 0.67-1.07 HP Microwave $440-700
1,000-1,500 W 1-1.5 kW 1.34-2.01 HP Hair dryer $875-1,300
2,000-5,000 W 2-5 kW 2.68-6.7 HP Space heater $1,750-4,400
7,000-11,000 W 7-11 kW 9.4-14.7 HP EV charger (Level 2) $6,100-9,600

*Assumes 8,760 hours/year at $0.10/kWh (continuous operation). Most devices run far less.

Definition

The Physics of Power

Power is the rate at which work is done or energy is transferred.

Mathematical Definition: $$ P = \frac{E}{t} $$ Where:

  • $P$ = Power (Watts)
  • $E$ = Energy (Joules)
  • $t$ = Time (seconds)

Dimensional Analysis: $$ 1 \text{ W} = 1 \frac{\text{J}}{\text{s}} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3} $$

Electrical Definition: For electrical circuits, power is the product of voltage and current: $$ P = V \times I $$ Where:

  • $P$ = Power (Watts)
  • $V$ = Voltage (Volts)
  • $I$ = Current (Amperes)

Example:

  • A device drawing 5 Amps at 120 Volts consumes:
    • $P = 120 \text{ V} \times 5 \text{ A} = 600 \text{ W}$

Watt vs. Watt-Hour (The Confusion)

This is the #1 source of confusion about watts.

  • Watt (W): A unit of power (rate of energy use).
  • Watt-hour (Wh) or Kilowatt-hour (kWh): A unit of energy (total amount of energy used).

The Analogy:

  • Watts are like miles per hour (speed).
  • Watt-hours are like miles (distance).

Example:

  • A 100 W light bulb running for 10 hours uses:
    • $100 \text{ W} \times 10 \text{ h} = 1,000 \text{ Wh} = 1 \text{ kWh}$

Your electricity bill charges you for kWh (energy), not kW (power).

History: James Watt and the Steam Revolution

The Man Behind the Unit

James Watt (1736-1819) was a Scottish instrument maker and inventor. While he didn't invent the steam engine, he made it vastly more efficient, enabling the Industrial Revolution.

His Key Innovation (1769): Watt added a separate condenser to the Newcomen steam engine. This kept the main cylinder hot, reducing fuel consumption by 75%. Suddenly, steam engines became economical for factories, mines, and transportation.

The Irony: Watt also coined the term "horsepower" to market his engines (see our horsepower article). Yet the unit named after him—the watt—would eventually replace horsepower as the global standard for electrical power.

Official Adoption

  • 1882: The British Association for the Advancement of Science officially adopted the "watt" as the unit of electrical power, replacing the awkward "volt-ampere."
  • 1889: The International Electrical Congress endorsed the watt.
  • 1960: The watt was incorporated into the International System of Units (SI) as the standard unit of power.

The Original Definition

The watt was originally defined in relation to the absolute watt, based on mechanical power: $$ 1 \text{ W} = 10^7 \text{ erg/s} $$ (The erg is an obsolete CGS unit of energy.)

Today, the watt is defined in terms of fundamental SI units: $$ 1 \text{ W} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3} $$

Real-World Examples

Household Appliances (Power Consumption)

Appliance Typical Power Daily Usage Daily Energy Monthly Cost*
LED Bulb (60W equiv) 10 W 5 hours 0.05 kWh $0.15
Refrigerator 150 W 24 hours 3.6 kWh $10.80
Laptop 50 W 8 hours 0.4 kWh $1.20
Desktop PC + Monitor 300 W 8 hours 2.4 kWh $7.20
TV (55" LED) 100 W 5 hours 0.5 kWh $1.50
Microwave 1,000 W 0.25 hours 0.25 kWh $0.75
Dishwasher 1,800 W 1 hour 1.8 kWh $5.40
Electric Oven 2,400 W 1 hour 2.4 kWh $7.20
Clothes Dryer 3,000 W 1 hour 3 kWh $9.00
Central AC 3,500 W 8 hours 28 kWh $84.00
Electric Water Heater 4,500 W 3 hours 13.5 kWh $40.50
EV Charger (Level 2) 7,200 W 4 hours 28.8 kWh $86.40

*Assumes $0.10/kWh electricity rate.

Light Bulbs: The Watt Wars

The shift from incandescent to LED bulbs is a perfect case study in power efficiency.

Brightness (Lumens) Incandescent CFL LED Energy Saved (LED vs Incandescent)
450 lm 40 W 9-13 W 6-8 W 80-87%
800 lm 60 W 13-15 W 8-12 W 80-87%
1,100 lm 75 W 18-25 W 13-18 W 76-83%
1,600 lm 100 W 23-30 W 16-20 W 80-84%

Annual Cost Comparison (800 lumens, 3 hours/day):

  • Incandescent (60 W): $6.57/year
  • LED (10 W): $1.10/year
  • Savings: $5.47/year per bulb

Human Power

  • Resting Metabolism: ~100 W (just staying alive).
  • Walking: ~200-300 W.
  • Cycling (Moderate): ~150-250 W.
  • Cycling (Elite Athlete): 300-400 W sustained, 1,000-2,000 W peak.
  • Sprinting: ~1,000-1,500 W (for a few seconds).

Fun Fact: Usain Bolt's peak power during his 100m world record was approximately 2,600 W (3.5 HP).

Industrial & Massive Scale

  • Wind Turbine (Small): 10,000 W (10 kW).
  • Wind Turbine (Large): 3,000,000 W (3 MW).
  • Solar Panel (Residential): 300-400 W per panel.
  • Solar Farm (Utility Scale): 100,000,000 W (100 MW).
  • Nuclear Reactor: 1,000,000,000 W (1 GW).
  • Hoover Dam: 2,080,000,000 W (2.08 GW).
  • Three Gorges Dam (China): 22,500,000,000 W (22.5 GW) - largest power station on Earth.

Common Uses

1. Electrical Appliances

Every electrical device has a power rating in watts, indicating how much electricity it consumes when operating.

  • Low Power (1-100 W): LED bulbs, phone chargers, alarm clocks.
  • Medium Power (100-1,000 W): Laptops, TVs, fans, blenders.
  • High Power (1,000-5,000 W): Microwaves, hair dryers, space heaters, ovens.
  • Very High Power (5,000+ W): Electric water heaters, EV chargers, central AC.

2. Electricity Bills

Your utility company charges you for energy (kWh), not power (kW).

  • Formula: $\text{Cost} = \text{Power (kW)} \times \text{Time (hours)} \times \text{Rate ($/kWh)}$
  • Example: A 1,500 W space heater running 8 hours/day for 30 days:
    • Energy = $1.5 \text{ kW} \times 8 \text{ h/day} \times 30 \text{ days} = 360 \text{ kWh}$
    • Cost = $360 \text{ kWh} \times $0.10/\text{kWh} = $36$

3. Solar Panels & Renewable Energy

Solar panels are rated by their peak power output in watts under ideal conditions (full sun, 25°C).

  • Residential Panel: 300-400 W.
  • 10-Panel System: 3,000-4,000 W (3-4 kW).
  • Daily Energy (sunny location): ~15-20 kWh.

4. Electric Vehicles

EV charging power determines how fast the battery charges.

  • Level 1 (120V outlet): 1,400 W (1.4 kW) - adds ~4 miles/hour.
  • Level 2 (240V charger): 7,200 W (7.2 kW) - adds ~25 miles/hour.
  • DC Fast Charging: 50,000-350,000 W (50-350 kW) - adds 150-1,000 miles/hour.

5. Audio Equipment

Speaker and amplifier power ratings indicate maximum output.

  • Bluetooth Speaker: 5-20 W.
  • Home Theater Receiver: 100-200 W per channel.
  • Concert PA System: 10,000-50,000 W.

Power Factor: The Hidden Complexity

For AC electrical systems (like your home), the relationship between voltage, current, and power is more complex than $P = V \times I$.

The Issue: In AC circuits with inductive or capacitive loads (motors, transformers), the voltage and current are out of phase. This means not all the current contributes to useful work.

Three Types of Power:

  1. Real Power (P): Measured in Watts (W). The actual power doing useful work.
  2. Reactive Power (Q): Measured in Volt-Amperes Reactive (VAR). Power that oscillates back and forth, doing no net work.
  3. Apparent Power (S): Measured in Volt-Amperes (VA). The total power flowing through the circuit.

The Relationship: $$ S = \sqrt{P^2 + Q^2} $$ $$ P = S \times \cos(\phi) $$ Where $\phi$ is the phase angle, and $\cos(\phi)$ is the power factor (PF).

Power Factor Range: 0 to 1 (or 0% to 100%).

  • PF = 1: Perfect efficiency (resistive load, like a heater).
  • PF = 0.8: Typical for motors and fluorescent lights.
  • PF = 0.5: Poor efficiency (large inductive load).

Why It Matters: Utility companies charge industrial customers for low power factor because it wastes transmission capacity.

Conversion Guide

Watts to Kilowatts

The most common conversion.

Formula: $$ \text{kW} = \frac{\text{W}}{1,000} $$

Watts Kilowatts
100 W 0.1 kW
500 W 0.5 kW
1,000 W 1 kW
1,500 W 1.5 kW
5,000 W 5 kW
10,000 W 10 kW

Watts to Horsepower

Used for comparing electrical motors to gas engines.

Formula: $$ \text{HP} = \frac{\text{W}}{745.7} $$

Watts Horsepower
746 W 1 HP
1,000 W 1.34 HP
5,000 W 6.7 HP
10,000 W 13.4 HP
75,000 W 100 HP

Watts to BTU/hr

Used for heating and cooling systems.

Formula: $$ \text{BTU/hr} = \text{W} \times 3.412 $$

Watts BTU/hr
1,000 W 3,412 BTU/hr
3,500 W 11,942 BTU/hr
5,000 W 17,060 BTU/hr

Watt Conversion Formulas

To Milliwatt:

1 W = 1000 mW
Example: 5 watts = 5000 milliwatts

To Kilowatt:

1 W = 0.001 kW
Example: 5 watts = 0.005 kilowatts

To Megawatt:

1 W = 0.000001 MW
Example: 5 watts = 0.000005 megawatts

To Gigawatt:

1 W = 1.0000e-9 GW
Example: 5 watts = 5.0000e-9 gigawatts

To Horsepower:

1 W = 0.001341 hp
Example: 5 watts = 0.006705 horsepower

To Metric Horsepower:

1 W = 0.00136 PS
Example: 5 watts = 0.006798 PS

To Electric Horsepower:

1 W = 0.00134 hp(E)
Example: 5 watts = 0.006702 hp(E)

To BTU per Hour:

1 W = 3.412142 BTU/h
Example: 5 watts = 17.060708 BTU/h

To BTU per Minute:

1 W = 0.056869 BTU/min
Example: 5 watts = 0.284345 BTU/min

To BTU per Second:

1 W = 0.000948 BTU/s
Example: 5 watts = 0.004739 BTU/s

To Foot-pound per Second:

1 W = 0.737562 ft⋅lb/s
Example: 5 watts = 3.687811 ft⋅lb/s

To Foot-pound per Minute:

1 W = 44.253729 ft⋅lb/min
Example: 5 watts = 221.268645 ft⋅lb/min

To Calorie per Second:

1 W = 0.239006 cal/s
Example: 5 watts = 1.195029 cal/s

To Kilocalorie per Hour:

1 W = 0.860421 kcal/h
Example: 5 watts = 4.302103 kcal/h

To Ton of Refrigeration:

1 W = 0.000284 TR
Example: 5 watts = 0.001422 TR

To Erg per Second:

1 W = 10000000 erg/s
Example: 5 watts = 50000000 erg/s

To Joule per Second:

1 W = 1 J/s
Example: 5 watts = 5 J/s

Frequently Asked Questions

Step-by-Step:

  1. Find the power rating (in watts) on the device label.
  2. Estimate daily usage (in hours).
  3. Calculate daily energy: $\text{kWh/day} = \frac{\text{Watts} \times \text{Hours}}{1,000}$
  4. Calculate monthly energy: $\text{kWh/month} = \text{kWh/day} \times 30$
  5. Calculate cost: $\text{Cost} = \text{kWh/month} \times \text{Rate}$ Example: 1,500 W space heater, 6 hours/day, $0.12/kWh
  • Daily energy: $(1,500 \times 6) / 1,000 = 9 \text{ kWh}$
  • Monthly energy: $9 \times 30 = 270 \text{ kWh}$
  • Monthly cost: $270 \times $0.12 = $32.40$

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