Bit Error Rate From SNR Calculator

Work out bit error rate from snr instantly with clear inputs, formula shown and shareable results.

About Bit Error Rate From SNR Calculator

Bit error rate follows the Gaussian tail: BER = Q(sqrt(SNR)) for NRZ. PAM4 packs two bits per symbol but its eyes are a third the height, costing about 9.5 dB of SNR — the fundamental trade that makes PAM4 harder despite doubling throughput per baud.

Formula

BER from SNR

BER = Q(sqrt(SNR)); PAM4 suffers a 9.54 dB amplitude penalty versus NRZ

Worked example

With the default values below, Bit Error Rate From SNR Calculator returns Bit error rate of 1.398e-7. Change any input above and every figure here is recalculated in your browser.

Inputs used

Signal to noise ratio: 14 dB
Modulationone of NRZ (2 level), PAM4 (4 level): NRZ (2 level)
Bit rate: 50 Gbit/s

Results

Bit error rate: 1.398e-7
BER exponent: 6.86 1e-x
Errors per second: 6,988.0820 errors/s
Mean time between errors: 0.00 s

Step by step

1Values used
2BER from SNR
3Bit error rate= 1.398e-7
4BER exponent= 6.86 1e-x
5Errors per second= 6,988.0820 errors/s
6Mean time between errors= 0.00 s

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does PAM4 lose 9.5 dB?

Three eyes stacked in the same amplitude means each is one third the height, and 20log10(3) is 9.54 dB of SNR penalty.

Why use PAM4 at all?

It doubles the bits per symbol, halving the Nyquist frequency and therefore the channel loss, which above about 25 GBaud more than compensates for the SNR penalty.