# Power Converter

Created by Davide Borchia
Last updated: Jul 07, 2022

They say knowledge is power, and money is power: our power converter can't tell you if this is true, but it can help you convert power among its various measurement units.

Here you will learn:

• What is power (in physics);
• What is a watt: the fundamental power unit;
• The multiples and submultiples of the watt;
• The conversion of power from horsepowers to watts; and
• Other power units of measurements.

## What is power?

Power is the rate of energy transfer, or in other words, the amount of work done in a time unit. From its definition, we can easily infer its dimensions: energy/time.

Found more about the relationship between these quantities at our work and power calculator

As energy assumes many forms, depending on the context in which we define it, power reflects this variability. We can define many forms of power:

• Electric power;
• Mechanical power;

## The units of measurement of power: what is a watt?

In the International System, the power is measured in watts, $\text{W}$. The watt is a derived unit, defined as:

$1\ \text{W} = \frac{1\ \text{J}}{1\ \text{s}}$

Where:

• $\text{J}$ are joules, the measurement unit of energy; and
• $\text{s}$ are seconds.

🔎 The name watt comes from James Watt, a Scottish inventor instrumental in the industrial revolution. Watt introduced important technology relative to engines and steam power: it makes sense that we remember him when measuring power.

The watt measures directly the rate of mechanical work, when it assumes the dimensions:

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

In an electromagnetic context, the watt defines the work performed by a current of $1\ \text{A}$ flowing in a potential difference of $1\ \text{V}$. We define the electrical power as:

$1\ \text{W} = 1\ \text{A}\cdot 1\ \cdot{V}$

## The multiples and submultiples of the watt

As for all the other SI units, the watt readily adapts to different contexts (low or high powers) by the careful use of multiples and submultiples.

When we are talking of the power consumption of many electronic devices, we can use the submultiples of the watt:

• The milliwatt, $\text{mW}$;
• The microwatt, $\text{μW}$; and the
• The nanowatt, $\text{nW}$.

The conversion of power units from the watt to its submultiples follows the powers on ten:

\begin{align*} 1\ \text{W}=1\cdot10^3\ \text{mW}\\ 1\ \text{W}=1\cdot10^6\ \text{μW}\\ 1\ \text{W}=1\cdot10^9\ \text{nW} \end{align*}

We can go even smaller: the picowatt, femtowatt, and attowatt. But the scope of these units is pretty limited.

Most commonly, the submultiples of the watt find use in electronic applications: the power of a typical laser pointer is $5\ \text{mW}$, while computing and sensing both use powers in the nanowatt.

When we need to consider a , we can rely on the multiples of the watt:

• The kilowatt, $\text{kW}$;
• The megawatt, $\text{MW}$;
• The gigawatt, $\text{GW}$;

And so on, with the terawatt, the petawatt, and so on.

Here are the conversions for the multiples of the watt:

\begin{align*} 1\ \text{kW}=1\cdot10^3\ \text{W}\\ 1\ \text{MW}=1\cdot10^6\ \text{W}\\ 1\ \text{GW}=1\cdot10^9\ \text{W} \end{align*}

An electric kettle has a power of $2\ \text{kW}$. Power plants usually have an output of megawatts to gigawatts. The largest power plant, the Three Gorges Dam in China, has a capacity of $22.5\ \text{GW}$.

We can, of course, define other watt multiples: the terawatt, petawatt, and so on, but apart from very niche applications, and astronomy, there's no need to dwell for long on them. Just a couple of examples:

• In 2012, the National Ignition Facility (NIF) in the US shot a laser pulse with power $500\ \text{TW}$. The catch here is the duration of the pulse: with a few nanoseconds, the total energy of the pulse was $1.85\ \text{MJ}$, roughly $440\ \text{kcal}$, the energy of a big bar of chocolate.
• The Tsar Bomba, the most powerful nuclear device ever detonated, exploded with a power of about $5$ yottawatt, a power comparable to the output of the Sun, which is slightly less than $400\ \text{YW}$.
• The most powerful supernova ever discovered by astronomers shined with the power of, quite literally, a billion suns: ASSASN-15lh (don't mind the name) produced a power in the order of $10^38$ watts. Don't even try to understand this number!

## At full steam: the horsepower

The measurement of power is intimately connected to industrialization: with the advent of machines, power outputs became stable and reliant, and humans promptly learned how to measure it.

With which measurement unit, you ask? Something quickly understandable and relatable for the people of the time, the nineteenth century: the power of a horse!

The definition of horsepower draws from the physical definition of power as the ratio of work ad time. By calculating the work produced by a horse in a certain unit of time, we can define the power of a horse itself. How?

We need to ask James Watt, which calculated the distance covered by a horse during a task (turning a wheel mill), and multiplied it by the estimated force of a horse. There are two main definitions of the horsepower:

• The mechanical horsepower (or imperial horsepower), $\text{hp(I)}$, by definition equal to $33,000\ \text{ft}\cdot\text{lbf}/\text{min}$, where $\text{lbf}$ is the pound-force, an imperial measurement unit of force.
• The metric horsepower, $\text{hp(M)}$, defined as the power required to lift a mass of $75\ \text{kg}$ for nee metre in one second.

We convert power unit from mechanical horsepower to watts using the following equation:

$1\ \text{hp(I)} \simeq 745.7 \ \text{W}$

The opposite conversion of power units from watts to horsepower is:

$1\ \text{W} = 0.001341\ \text{hp(I)}$

To convert power from metric horsepower to watts and vice-versa, follow these rules:

\begin{align*} 1\ \text{hp(I)} \simeq 735.5 \ \text{W}\\ 1\ \text{W} = 0.0013596\ \text{hp(I)} \end{align*}

🙋 In our power converter you can find other types of horsepower: choose carefully the one you need!

## From uncommon units to watt: conversion of power for specific uses

As mentioned, power can assume various units according to the needs. In our power converter, we choose the following measurement units, spanning heating and cooling related units, food/exercise, and the erg, the CGS (centimeter-gram-second) system unit for energy. Here they are:

• The British thermal unit per hour;
• The kilocalorie per hour;
• The erg per second; and
• The TR (ton of refrigeration).

The conversion from watt to the units mentioned above (and some more) follows the next table:

$\text{BTU}/\text{h}$

$\text{kcal}/\text{h}$

$\text{kcal}/\text{mi}$

$\text{erg}/\text{s}$

$\text{TR}$

$1\text{W}$

$3.412$

$0.8604$

$0.01434$

$10,000,000$

$0.00028435$

Davide Borchia
SI units
mW
W
kW
Horsepower
hp(l)
hp(M)
Others
BTU/h
kcal/h
erg/s
TR
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