Watt's Law

Watt’s Law is an electrical relationship that is helpful in sizing the capacity of circuits and services. You will commonly see two forms of Watt’s Law. There are two forms because the law is different for single-phase power, which is the type of power provided to most homes and small businesses, and three-phase power, which is the type of power provided to large commercial and industrial facilities.

For single-phase service:

watts = volts x amps x power factor

For the more complex three-phase electrical system, watts = volts x amps x power factor x the square root of 3. For simplicity the square root of 3 is shown as the math value of 1.732.

watts = volts x amps x power factor x 1.732

Using Watt’s Law, you can answer the practical question “Why can’t I run my heater and coffee pot without the circuit breaker tripping?” The important question in this situation really is how many amps does a circuit with a 1650-watt electric heater and a 350-watt coffee maker draw if both appliances are operating at the same time. 

If you look at the rating on the nameplate of the appliance you will find the wattage each requires to operate. By adding the two together, you can see that a total of 2,000 watts is needed to run both appliances. Since we know the watts required, and we know that the appliances operate at 120 volts, if we also know the power factor of this load, we can calculate the amps. To determine the power factor, let’s look at how an electric heater operates. Since this is a resistive load, the power factor will be 1. The coffee pot is also a resistive load, so its power factor will also be 1.

For a single-phase service like this one, Watt’s Laws tells us that amps equals watts divided by the product of volts and power factor. Because the power factor for both appliances is 1, we can effectively ignore power factor in this particular equation. So we simply take 2,000 watts and divide by 120 volts for a total of 16.7 amps drawn when both appliances are operating. 

Think about what would happen if both appliances are turned on and the circuit has a 15-amp fuse or circuit breaker. Because the amps would exceed 15, the fuse or breaker would operate to shut off the electricity and protect the wire from overheating. In this case, the circuit simply wasn’t sized to handle this amp load.

This concept is applied to size-specific circuits ranging from those within your house to service feeds into buildings to neighborhood distribution feeders.