# Signal-to-Noise (SNR) Ratio calculator

This Signal-to-Noise Ratio calculator converts signal and noise voltage levels to a deciBel (dB) ratio. To use this tool simply enter the levels and select the appropriate units.

## Formula

SNR (dB) = 20*Log10(S/N)

Note that since the signal and noise values are represented as voltage levels, there’s a square or 20*Log relationship to convert to power ratio.

## Example Calculations

• If the signal and noise voltage levels are the same, the SNR is 0 dB
• For a signal level of 9V and Noise level of 3V, the SNR is 9.54 dB

## Can SNR be negative?

Yes, SNR can be a negative value. This is the case when the noise is greater than the signal. Practically this means that the signal is buried in the noise.

A related question is:

Can the signal be detected if the SNR is negative?

The answer is Yes. Use this calculator to see that with 10 MHz of bandwidth and an SNR value of -10 dB, a throughput of over 1 Mbps cane be achieved.

An example of this is with Direct Sequence Spread Spectrum Systems such as Code Division Multiple Access (CDMA), a signal can be below the noise and still be detected.

## Is High SNR better than Low SNR?

In general, a high SNR is always better than low SNR. However there is a limit for every modulation scheme beyond which a higher SNR makes no difference to performance.

For instance, BPSK modulation requires an SNR of 7 dB for an error rate lower than 10-5. In this case improving the SNR to 10 dB will not provide any benefit if your BER requirement is the same.

## How to convert from SNR to volt?

SNR is a ratio expressed in decibel or dB. It is a relative quantity and as such does not have units. You can use this calculator to convert from dB to linear signal-to-noise voltage ratio.

## How to measure SNR?

One method to measure SNR voltages is to use an oscilloscope shown in the picture below.

The first step is to measure the RMS value of the signal and noise

Modern oscilloscopes like the one above have built-in Math functions to do this. It essentially performs this RMS computation.

Let’s call this VS+N

The next step is to measure the RMS voltage of the signal alone

In the video below, Mark Schnittker shows how to measure the signal voltage in a very noisy signal. Here are the steps:

• Input the signal to be measured to Channel 1 of the scope
• Input the clean reference signal to Channel 2 of the scope and trigger using this signal
• Average the noise on Channel 1 (using 128 averages in this case)
• You should now be able to see the sine wave that has a fixed phase relationship with the signal on channel 2
• Measure the root-mean-square (RMS) voltage value

Let’s call this value VS

The final step is to do the math

The RMS noise voltage is VN = VS+NVS

The SNR is then given by VS/VN

This is a linear value and can be converted to the dB equivalent using the calculator on this page.