# How to Solve dBm Watts Power Formula Calculator

This dBm Watts Power formula calculator can calculate dBm (decibel-milliwatts) from watts power and can calculate the watts power from dBm. The measurement of dBm is a special case of dB Watts Power, where the wattage is compared to 1mW (milliwatt) of power. When a dBm value is positive it means the output power is larger than 1mW, and when a dBm value is negative it means that the output power is smaller than 1mW. The dBm Watts calculator can be used for any system you want to measure power on a logarithmic scale. If you need to calculate dB from the ratio of wattages or quantities of power, you should use the dB Watts Power Formula Calculator instead. If you need to calculate dB from the comparison of two voltages or amplitudes, use the dB Volts Formula Calculator instead.

The calculator below finds the decibel-milliwatts (dBm) for a given power in watts.

dBm Watts Calculator
 Watts Out MW (megawatts) kW (kilowatts) W (watts) mW (milliwatts) uW (microwatts) nW (nanowatts) pW (picowatts) Decibel-milliwatts dBm

## dBm Watts Formula

The formula used to perform the Wattage to dBm calculation is below. Remember to convert all units to watts when using the dB Watts Formula. As mentioned above, this formula is specifically for dBm (decibel-milliwatts). If you are measuring the decibel gain of a system from a specific input to output power, you are probably looking for the dB Watts Power Formula Calculator instead.

dBm Watts Formula:
$\fn_jvn&space;\small&space;dBm=10log\left&space;(&space;\frac{P}{0.001}&space;\right&space;)$
where:
• dBm = Decibels
• P = Power (watts)

## Solution Examples:

We will use the formula above to work out a few real-world example problems. You can always check your work with this calculator. As you work through these example problems and play around with the numbers, you will see how more significant increases in power cause dBm value to increase more slowly. This is the beauty of using a logarithmic scale such as decibel-milliwatts to measure power because it allows you to use a single scale to measure a wide range of power.

### Example #1:

For this example, we measure a power level of 2 watts. We need to determine what the power quantity is in dBm (decibel-milliwatts). To find this, we must use the formula provided above, and enter the values as shown.

$\inline&space;\dpi{200}&space;\fn_jvn&space;\tiny&space;dBm=10log\left&space;(&space;\frac{P_{out}}{0.001}&space;\right&space;)=10log\left&space;(&space;\frac{2}{0.001}&space;\right&space;)=10log\left&space;(&space;2000&space;\right&space;)\approx&space;10\cdot&space;3.301\approx&space;33.01&space;dBm$

By using the conversion formula, we have found that our measurement of 2 watts can also be written as a power level of 33.01dBm.

### Example #2:

For this next example, we are measuring power with instrumentation that displays dBm (decibel-watts). The instrumentation reads 40dBm, but you want to know what the power level is in watts. How many watts is this?

The formula that was provided above solves for dBm, so we will need to use algebra to rearrange the variables to solve for the wattage P.

$\inline&space;\dpi{200}&space;\fn_jvn&space;\tiny&space;dBm=10log\left(&space;\frac{P}{0.001}&space;\right&space;)&space;\Rightarrow&space;\frac{dB}{10}=log\left(&space;\frac{P}{0.001}&space;\right&space;)\Rightarrow&space;10^{\frac{dB}{10}}=\frac{P}{0.001}\Rightarrow&space;0.001\cdot&space;10^{\frac{dB}{10}}=P$

So now that we have found the formula for for P (wattage), we can plug in the dBm value of 40dBm and solve for power in wattage.

$\fn_jvn&space;\small&space;P=0.001\cdot&space;10^{\frac{dB}{10}}=0.001\cdot&space;10^{\frac{40}{10}}\approx&space;0.001\cdot&space;10^{4}\approx&space;0.001\cdot&space;10000\approx&space;10W$

The result is that if you are measuring a signal level of 40dBm, it is a 10 watt power level.