How to Calculate Equation Watts

Watts are SI (metric) units for power, and calculating power usually isn't difficult. There are two ways to do it, though, depending on whether you're talking about mechanical or electrical power.

The watts equation for an electrical circuit takes into account the voltage across the circuit V, measured in volts, and the current I, measured in amps, passing through it. In mechanics, the definition of power is the rate of doing work W. It's defined as W/t, where t is the time it takes for the work to be completed. To get the result in watts, work must be expressed in joules, and time must be expressed in seconds.

What Is a Watt?

The concept of power was introduced by James Watt, the Scottish inventor who is better known for his work on steam engines. He conceived of power as the product of force F and velocity v, and that definition of power is still valid. In other words, if you keep applying a force F to a body while it is moving with a velocity v, the power expended is

P = F × v

Watt did all of his measurements using English units, and he invented the horsepower, which he defined as the power necessary to raise a load of 33,000 pounds one foot every minute.

When the metric system was adopted by the international scientific community, a watt, by virtue of it being a unit of work or energy over time, became equal to a joule per second. Since work W is force F times distance d, a joule is equal to a newton-meter, because newtons are the units of force. That makes 1 watt equal to 1 newton-meter / second.

The Watts Equation in Mechanics

You can use either of the following equations to calculate power in watts, provided all quantities are expressed in in MKS (meters, kilograms, seconds) metric units.

P = F × v \\ P = \frac{W}{t}

If you do your measurements on the CGS (centimeters, grams, seconds) system, force is expressed in dynes and work in ergs. You must convert these to newtons and joules to get the result in watts. Here are the conversion factors:

1 dyne = 10 −5 newtons

1 erg = 10 −7 joules

You can also express your result in kilowatts (kw). The kilowatt formula is 1 kw = 1,000 watts.

Watts as Units of Electrical Power

The power formula for a circuit with a voltage V and current I is

P = V × I

You can use Ohm's law to express either voltage or current in terms of the resistance R in the circuit: V = I × R. Doing so allows you to express power as a function of either voltage and current or voltage and resistance.

P = I^2 × R \\ P = \frac{V^2}{R}

After making your measurements, you don't have to do the calculations yourself. You can use an online calculator. There is one such calculator in Resources.

To get the result in watts, you must express voltage in volts, current in amperes and resistance on ohms. Thus, the watt can be expressed in these units:

1 watt = 1 volt-amp = 1 amp2-ohm = 1 volt2 / ohm.

References

About the Author

Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.

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