What Are the Units of Power in Physics?

A primary International System (SI) of Units of Power in physics is the Watt (W). The Watt isn’t alone as a Unit of Power; horsepower, megawatt, gigawatt, decibel-milliwatts, British thermal units, and foot-pound also have their place in the discussion.

A simple formula explains the concept of Power in physics: Power(P) equals Work(W) divided by time(t) or (P=W/t). What exactly are the units of Power in physics? Do they matter at all today? Let’s start our exploration by taking a look at James Watt.

James Watt

We can’t talk about the units of Power without first discussing James Watt. Watt is the father of the industrial revolution. A discussion about the units of Power in physics is only complete with understanding Watts’s contribution.

James Watt was born in 1736 in Scotland and died in 1819 in England. Watt was an inventor and instrument maker. Watt’s mother taught him Latin, Greek, and mathematics as a child. Watt’s father, a shipbuilder, and house builder, taught him how to use hand tools and build models.

At 17 years old, Watt studied mathematical instrument making (sextants, scales, quadrants, compasses) in Glasgow. When he completed his training, he opened his store in London.

Watt Improves the Steam Engine

While working to repair a model Newcomen steam engine in 1763, Watt identified a significant design weakness. Condensation occurs inside the steam cylinder causing thermal energy loss. Solids or liquids changing state (Gas to a liquid, solid to a liquid, liquid to a gas, or liquid to a solid) create latent heat. The amount of heat required to convert a pound of water into steam on a steam engine is latent heat.

Watt recognized that the condensation inside the steam chamber prevented the engine from operating fully by reducing the chamber’s temperature. As the temperature in the chamber increases, steam is created. Condensation inside the chamber decreases the temperature, and more energy is required to heat the steam chamber back up. The process repeats over and over.

Steam Engine + Condenser = Big Improvement

Watt designed a condenser chamber that was located outside the steam cylinder. The condenser collected the cooled (or spent) steam for condensation. The condenser allows the primary steam chamber to remain at a high temperature and not be cooled down by condensation.

This invention doubled the amount of energy produced by the engine and set the stage for the industrial revolution.

Horsepower

Watt needed a method to quantify the ability of his new invention. Enter the Goat Brewhouse. The Brewhouse brewed its beer onsite.

Twenty horses lived onsite in a barn. Six horses worked once each day. A harness is attached to each horse at the start of their shift. The harness was attached to a spoke-shaped shaft in the center of a mill room.

The horses walked in a circle, the shaft spun, and grindstones attached to the shaft ground up the malt. Beer production required ground-up malt, so the horses stayed busy year-round.

Horsepower Calculations

Watt wanted to prove to the brewhouse that a steam engine would be more effective than horses. After a great deal of observation (and hopefully a few beers) and a whole lot of complicated math, Watt calculated the Power of a horse based on its walking pace (speed) and how much weight it’s pulling (force).

The steam engine moved into the stable, and the horses headed for the pasture. Would the steam engine perform better than the horses? Within a year, beer production increased by 50% (90,000 to 143,000 barrels of suds.) A new unit of measurement, horsepower, was born. After one year, the steam engine had completely replaced the horses. A new day was dawning.

Industrial Revolution

Watt’s steam engine and Edison’s electrical generator came together in the late 1800s. Their union allowed for large-scale generation of electricity. Within a few years, the streets of New York had electric lamp illumination.

Units of Power Standardization

Electricity hasn’t been around all that long. It’s easy to forget. It’s been here our entire lives, but in the scope of humanity on earth, it’s brand spanking new. Before 1881 electricians used different terms and dissimilar measurement equipment (wire, gold leaf, straw) to determine electrical charges.

Measurement results in England had different measurement units than in America. France was different than Germany too. The measurement devices might create different measurement results on the same electrical device.

Working effectively together across different languages, cultures, and geographic locations requires an international system of units. If we can’t speak the same mathematical language, we can’t communicate.

First International Congress of Electricians

In 1881, Paris, France, hosted the first international exhibition about electricity. Two hundred and fifty engineers and scientists from twenty-eight countries attended the exhibition. Together they created the First International Congress of Electricians and acted as a “congress.” Their congress needed to address electrical units and standards.

After tremendous discussion and arguments, the standardization progress for electricity began. After three months, the members agreed on the following items:

1. A unit of current intensity is called the “ampere.”
2. Resistance units will be called “ohm.”
3. Capacity units will be called the “Farad.”

The Second International Congress of Electricians

In 1882, members of the Congress of Electricians proposed that the term “Watt” be used instead of “ampere.volt.” At the Second meeting of the International Congress of Electricians in 1893, the term “Watt” was approved.

The congress named a unit of power after James Watt in recognition of his contributions to science (He IS the father of the industrial revolution!),

Units of Power in Physics

Abbreviations for the units of Power are everywhere in our everyday life. How many of the abbreviations below do you recognize? Let’s take a quick look at each unit.

Horsepower

Generally, horsepower is a term we use in relation to cars and trucks, “power under the hood.”

Example:  A car engine generates 300 pounds of force and travels at 4 feet per second.  The car’s horsepower is 1200HP (force multiplied by speed.)

Watt

A Watt is a measurement of power. It defines the rate that electricity is being used “right this moment.”

• A LED light bulb uses 10W of electricity when you turn it on.
• An incandescent light bulb uses anywhere from 25-100W.

Megawatt

How much power does a power plant generate? It’s a lot! When we’re talking about Megawatts, we’re talking about how much power an entire city requires.

• New York City uses 11,000 Megawatt-hours of electricity each day.
• 1 Megawatt = 1,000,000 Watts.  Daily NYC energy consumption is 11 billion Watt-hours.

Gigawatt

A Gigawatt is one billion Watts. Gigawatts are (generally) used for power grid requirements or power generation.

• Fun Example: 1 GW is approximately 1.34 million horsepower.
• Practical Example: 1 GW is roughly enough energy to power 750,000 homes.

1 Gigawatt = 1,000,000,000 Watts

Decibel-Milliwatts

A decibel-milliwatt measures the absolute power of large and small radio waves. The closer the dMb logarithmic value is to zero, the better. (It’s a logarithmic scale.)

A cell phone carrier’s signal strength may range from -50 dBm to -120 dBm. We see these signal intensity meters every time we look at the signal strength (AKA the bars) on our cell phones.

• A carrier signal strength of -50 dBm is excellent. You have a good cell phone signal.
• A carrier signal strength of -120 dBm is terrible. You don’t have a good signal.

1 Watt equals 1000mW, which equals 30dBm.

British Thermal Unit

A British Thermal Unit (BtU) is the measurement of the amount of heat required to increase the temperature of one pound of water by one degree Fahrenheit.

• BtUs are a standard measurement used to compare different fuels against each other (natural gas, petroleum).

We run into BTUs when we discuss home heating a cooling. A heater with a higher BtU will heat your house faster. Air conditioners with higher BtUs will cool your house more quickly.

 0.293 Watt equals 1BtU

Foot-Pound

A foot-pound is the amount of work performed, or energy expended, to move a 1-pound object one foot. (One pound of force on a one-pound lever.)

0.22 Watt equals 1 ft-lb/min

The foot-pound is used primarily in the United States in two different applications.

Muzzle Energy

Feet per second defines how fast a bullet exits the barrel of a gun.

Torque

There are two primary “areas” where we’ll run into torque in the US. 

1. The performance specification of an internal combustion automobile engine’s performance will list a torque value. The higher the torque value, the faster your vehicle can accelerate. Heavier cars or trucks require motors with higher torque values to get moving.
2. Defines a “tightness” specification (in ft-lbs) when screwing in a nut, screw, or tightening a bolt.

Non-International System Units of Power

Modern-day measurement standards fall under the category of the International System. The International System is a set of standards for units of measurement.

• The centimeter (length), gram (weight), and second (time) were the foundation of the centimeter-gram-second (cgs) system that developed in 1874.
• The meter (length), kilogram (weight), and second (time) are the baseplate of the International System (SI) of measurement standards.

The SI system of units replaced cgs units in 1971.

erg/s

An erg is a unit of work or energy in the centimeter-gram-second (cgs) system. ergs slowly stopped being a standard unit of measurement after the SI system was agreed to in 1971.

• One erg represents the workforce of one dyne (another unit of force from the cgs system) acting over one cm. A erm is equivalent to 1 X 10-7 joules. 
• One erg/s = 1 X 10-7 W, or 1W= 10,000,000 erg/s

One erg/s equals the work done by a force of one dyne acting through a distance of one centimeter and is equal to 10-7 joule, the standard unit of work or energy.

Conclusion

As you have seen, standardization allows for ease of communication and understanding. Thanks to pioneers like James Watt and the International Congress of Electricians, we have ways to quantify the different aspects of Power. These units of Power surround us in our daily lives, making it possible for us to drive, work, heat our homes, and more.