# SNR dB to Linear Ratio Calculator

Signal-to-noise ratio is typically expressed as a ratio in dB. Use this calculator to convert from

• dB to linear voltage
• dB to linear power

Signal and Noise Voltage units can be volt, millivolt, microvolt or nanovolt

Signal and Noise Power units can be watt, milliwatt, microwatt, nanowatt

Note that the result of this calculation is a ratio and as such has no units.

## Formula

SNRlinear volt = 10^(SNRdB/20)

SNRlinear power = 10^(SNRdB/10)

## Background

Signal-to-Noise ratio (SNR), is a very important system parameter. Widely used in communication technologies, it provides a measure of how well the system is performing.

Quite simply, the goal of the system design is to maximize the SNR.

## How is SNR measured?

One of the most popular methods of measuring SNR is with the use of a spectrum analyzer – shown in the picture below.

The picture below is a closer look at the screen that shows a signal in the presence of noise.

The 10 MHz signal is at the center of the screen with a green marker indicating its peak value of around +3 dBm. The noise floor is at -50 dBm. Use this calculator to translate dBm to Watt.

In this case the SNR is +3-(-50) = 53 dB. Our post on dBm dB explains this calculation

Since this is a ratio of two power levels, the linear ratio given by the calculator on this page is 199,526. The signal is almost 200,000 times the noise.

The dB scale is a convenient way to measure large differences. For instance the difference between the largest and smallest value measured on the screen of the spectrum analyzer in the picture can be 90 dB. This represents an even larger ratio of 1,000,000,000.

Note: The resolution bandwidth of the analyzer in the picture above, is set to 100 kHz. This means that the noise power of -50 dBm is the total noise integrated over that bandwidth.

If the RBW is reduced, it will reduce the noise power and increase the SNR. Increasing the RBW will increase the noise power and reduce the SNR.

Use this tool to compute the noise power in an arbitrary bandwidth.

For instance the same noise power is equivalent to -40 dBm in a 1 MHz bandwidth and -70 dBm in a 1 kHz bandwidth. With a 1 MHz bandwidth, the SNR is 43 dB. With 1 kHz bandwidth, the SNR is 73 dB. As the resolution bandwidth is increased, for a fixed signal power, the SNR decreases.

The RBW must be taken into account when making SNR measurements with a spectrum analyzer.