What the Signal-to-Noise Ratio Calculator does
This calculator works out signal-to-noise ratio from levels in volts, watts or dBm, using the right logarithm rule for each, and converts between SNR, SINAD, THD+N and effective number of bits. It also computes the thermal noise floor for a bandwidth and temperature from the Boltzmann constant rather than quoting the rounded -174 dBm/Hz.
The unit you measure in decides the rule. Volts use 20 log and watts use 10 log, so the same pair of numbers gives two different SNR figures - and getting that wrong is the single most common error in noise arithmetic.
How to use it
- Choose the units your measurements are in, then enter the signal and noise levels. In dBm the SNR is simply the difference.
- Read the SNR in decibels, as a power ratio and as a voltage ratio, plus the effective number of bits that noise level corresponds to.
- Enter a bit depth to compare against an ideal converter, or a measured SINAD from a data sheet to get the real ENOB.
- Enter a THD figure to see how much distortion drags SNR down to SINAD - powers add, so the decibels do not.
- For a radio or a sensor front end, set the bandwidth, temperature and noise figure to get the floor your signal has to sit above.
Reading the results
ENOB from a SINAD figure is what a converter really achieves, and it is always below the nominal bit depth. A 16-bit converter quoting 78 dB SINAD is delivering about 12.7 effective bits, and the other three bits are noise.
The thermal floor is a hard limit set by physics: -174 dBm per hertz at room temperature. Narrowing the bandwidth is the only way to lower it, which is why a slow measurement is a quiet one.
Noise figure is how much worse than that floor a real receiver is. A 3 dB noise figure means the system's own noise equals the thermal noise it is trying to receive.
Worked example: a 1 V signal with 1 mV of noise
In volts the rule is 20 log10(1 / 0.001) = 60 dB. That is a voltage ratio of 1,000 and a power ratio of 1,000,000. Had the same numbers been watts, the answer would be 10 log10(1000) = 30 dB - the same measurement, half the decibels, because the rule differs.
Sixty decibels corresponds to (60 - 1.76) / 6.02 = 9.7 effective bits. A perfect 10-bit converter manages 61.96 dB, so this signal is at about the limit of what 10 bits can represent: using a 16-bit converter would not improve it, because the noise is in the signal, not in the converter.
For the front end feeding it, the thermal floor in 1 MHz of bandwidth at 290 K is -174 + 60 = -114 dBm. With a 3 dB noise figure the system floor is -111 dBm, so a -95 dBm signal would arrive with 16 dB of headroom above the noise.
Formulas and scoring rules
- SNR from voltages
SNR[dB] = 20 log10(Vsignal / Vnoise)Both RMS, measured across the same impedance.- SNR from powers
SNR[dB] = 10 log10(Psignal / Pnoise)- SNR from dBm
SNR[dB] = signal[dBm] - noise[dBm]A subtraction, because both are already logarithms.- Ideal converter SNR
SNR[dB] = 6.02 N + 1.76For a full-scale sine wave with quantisation noise spread over the Nyquist band.- Effective number of bits
ENOB = (SINAD - 1.76) / 6.02Using SINAD, not SNR, gives the figure a data sheet means.- SINAD from SNR and THD
SINAD = -10 log10(10^(-SNR/10) + 10^(THD/10))Noise and distortion powers add; their decibels do not.- THD+N as a percentage
THD+N[%] = 100 x 10^(-SINAD/20)80 dB SINAD is 0.01%.- Thermal noise power
P = k T Bk = 1.380649e-23 J/K. At 290 K that is -173.98 dBm/Hz, usually quoted as -174.- Johnson noise voltage
V = sqrt(4 k T R B)The open-circuit noise across a resistance; the available power into a matched load is kTB.
SNR, SINAD and ENOB are three different numbers
SNR counts noise only and excludes harmonics of the signal. SINAD counts noise and distortion together, which is why it is always the lower figure and the more honest one. ENOB is SINAD expressed as a bit depth, using the same 6.02 N + 1.76 relationship in reverse.
A data sheet that quotes SNR alone is flattering the part. Look for SINAD, or for SNR and THD together so you can combine them - which this calculator does. The gap between nominal bits and effective bits is often two or three, and on a fast converter running near its maximum input frequency it can be more.
Why bandwidth is the cheapest noise reduction there is
Thermal noise power is kTB: proportional to bandwidth. Halving the bandwidth halves the noise power, a 3 dB improvement, and it costs nothing but time. That is the entire principle behind lock-in amplifiers, narrow-band receivers and long integration times in radio astronomy.
The same applies to oversampling and averaging. Averaging N samples of an uncorrelated noise signal improves SNR by 10 log10(N) dB - 10 dB for a hundred samples - provided the noise really is uncorrelated. It does nothing at all for a systematic offset or for interference at a fixed frequency, which is why a noisy measurement that will not average down usually has a pickup problem rather than a noise problem.
Limitations: what the result does not prove
- SNR figures only compare like with like: both measurements must be RMS, over the same bandwidth, across the same impedance.
- The ideal converter SNR of 6.02 N + 1.76 dB assumes a full-scale sine wave and quantisation noise that is uniform and uncorrelated with the signal. A small signal uses fewer codes and gets a proportionally worse figure.
- The thermal floor is a physical minimum, not a prediction of your system's noise. Real front ends add their own, which is what noise figure measures.
- Nothing here accounts for 1/f noise, interference, ground loops or quantisation effects at low signal levels - the things that usually dominate a real measurement.
Privacy: where your data goes
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Standards and sources
- Texas Instruments - Op amps for everyone design reference - checked 19 Sep 2026
- Analog Devices - Taking the mystery out of the infamous formula SNR = 6.02N + 1.76 dB (MT-001)
- Analog Devices - ADC noise figure, SNR, SINAD and ENOB (MT-003)
Frequently asked questions
How do I calculate signal-to-noise ratio in dB?
From voltages, 20 log10(Vsignal/Vnoise); from powers, 10 log10(Psignal/Pnoise); from dBm levels, just subtract. A 1 V signal with 1 mV of noise is 60 dB. Using the wrong rule gives an answer that is out by a factor of two in decibels.
What is a good signal-to-noise ratio?
It depends entirely on the application. Digital audio aims for 90 dB or more, a 12-bit measurement system for around 70 dB, and a digital radio link may work happily at 10 dB. What matters is whether the SNR is enough for the decision the system has to make.
What is ENOB and how is it different from bit depth?
Effective number of bits is the resolution a converter actually delivers once its noise and distortion are counted: ENOB = (SINAD - 1.76) / 6.02. A 16-bit part with 78 dB SINAD gives about 12.7 effective bits, so the last three bits carry noise rather than information.
What is the difference between SNR and SINAD?
SNR counts noise only; SINAD counts noise and harmonic distortion together. SINAD is always lower and is the figure that determines ENOB. If a data sheet quotes SNR and THD separately, combine them - the calculator above does exactly that.
Where does -174 dBm/Hz come from?
From P = kTB with k = 1.380649e-23 J/K and T = 290 K: 4.004e-21 W per hertz, which is -173.98 dBm. It is the thermal noise available from any resistance at room temperature, and it is the floor every radio receiver works against.
What does noise figure mean?
How many decibels worse than the thermal floor a system's own noise makes it. A 3 dB noise figure means the system adds as much noise as the source produces, halving the signal-to-noise ratio. In a cascade, the first stage's noise figure dominates, which is why the low-noise amplifier comes first.
Does averaging improve signal-to-noise ratio?
Yes, by 10 log10(N) dB for N samples, provided the noise is uncorrelated between samples - 10 dB for a hundred averages, 20 dB for ten thousand. It does nothing for a fixed offset or for interference at a steady frequency, which is the usual reason averaging stops helping.
Why is my measured SNR worse than the converter's data sheet?
Usually everything around the converter rather than the converter itself: reference noise, a noisy supply, clock jitter, an amplifier with its own noise floor, or a source impedance high enough to contribute Johnson noise. Data-sheet figures are measured on an evaluation board designed to eliminate all of those.
Last reviewed by the A2Z.Tools team against the sources listed above.
