The signal-to-noise ratio calculator above turns a pair of measurements into an SNR expressed both as a plain ratio and in decibels. It asks one question first, and the whole answer hangs on it: was the quantity you measured a power or an amplitude? Power ratios convert to decibels with ten times the base-ten logarithm. Amplitude ratios — volts, currents, sound pressures, ADC counts — convert with twenty times it. Get the two mixed up and every figure you publish is out by a factor of two in dB, which is a factor of four in power.
Arb Digital publishes free engineering calculators that make the ambiguous choice explicit rather than hiding it behind a default. This page therefore shows the answer under the convention you selected and, in the fourth grid box, the answer the other convention would have given. Seeing both at once is the fastest way to catch the error that this subject generates more than any other.
What This Signal-to-Noise Ratio Calculator Does
The hero figure is the SNR in decibels under the convention you picked. Beneath it, the linear ratio is the raw quotient of signal to noise, which is what the decibel figure is a logarithmic restatement of. Keeping both in view matters because people reason badly about decibels: 40 dB sounds like a modest number and is in fact a hundred-to-one amplitude ratio.
The SINAD box repeats the calculation with distortion and spurious content added to the noise in the root-sum-square sense, because uncorrelated contributions add in power rather than in amplitude. The effective-number-of-bits box converts that SINAD into the resolution an ideal converter would need to be that clean. The last box is the teaching one: the same inputs under the other logarithmic convention, so a misread measurement announces itself immediately.
How to Use It
- Decide what your instrument actually reports. An oscilloscope, a voltmeter and a sound level meter's pressure reading are amplitudes. A power meter, a spectrum analyser reading in dBm and an optical detector calibrated in watts are powers.
- Enter signal and noise in the same unit. Millivolts against millivolts, watts against watts. Because only the ratio is used, mixing scales silently corrupts the result.
- Use RMS values, not peak. Noise has no meaningful peak, so a peak signal against an RMS noise inflates the ratio by whatever crest factor your waveform happens to have.
- Add distortion only if you measured it. Leaving it at zero gives plain SNR; entering a harmonic level gives SINAD as well, which is the honest figure for anything that will be listened to or demodulated.
- Record the bandwidth. An SNR quoted without the bandwidth it was measured over is not a reproducible number, which is why the tool reports the implied noise density alongside it.
The Formula: How SNR Is Calculated
As a plain ratio, SNR is signal divided by noise. The decibel form depends on which quantity you have. For powers, SNRdB = 10 log10(Psignal ÷ Pnoise). For amplitudes, SNRdB = 20 log10(Asignal ÷ Anoise). The factor of two exists because power is proportional to the square of amplitude, and squaring inside a logarithm becomes a multiplication by two outside it. Stanford's CCRMA course notes on decibels set this out compactly, and the NIST Guide to the SI, Special Publication 811 covers the formal status of the decibel as a logarithmic ratio rather than a unit.
SINAD extends the idea by replacing the noise term with the total of noise and distortion. Because those contributions are uncorrelated, they combine in power: the effective amplitude denominator is the square root of the sum of the squares of the noise and the distortion amplitudes. The effective number of bits follows from the ideal-quantiser relation ENOB = (SINADdB − 1.76) ÷ 6.02, where the 6.02 is twenty times the log of two and the 1.76 comes from the uniform distribution of quantisation error.
Work the defaults through by hand. A signal of 1.5 units against noise of 0.015 units is a ratio of exactly 100. As amplitudes that is 20 log10(100) = 40.00 dB. Read as powers instead, the same pair would give 10 log10(100) = 20.00 dB, which is the value the fourth box reports. Adding a distortion amplitude of 0.008 gives a combined noise-and-distortion amplitude of √(0.015² + 0.008²) = √0.000289 = 0.017 exactly. The SINAD ratio is 1.5 ÷ 0.017 = 88.235, so SINAD = 20 log10(88.235) = 38.91 dB, and the effective number of bits is (38.91 − 1.76) ÷ 6.02 = 6.17.
Where This Page Stops and the Cascade Page Starts
Arb Digital also publishes a noise figure calculator, and the two pages answer different questions. That page takes a chain of amplifiers and mixers, each with its own gain and noise figure, and applies the Friis cascade relation to work out how much the chain as a whole degrades the ratio passing through it. An output SNR appears there, but it is a by-product: it is predicted from stage parameters and a thermal noise floor, not measured.
This page starts from measurement. You have two numbers off an instrument and you want them expressed correctly and comparably. Nothing here knows or cares what produced the noise. If you are designing a receiver front end and choosing which low-noise amplifier goes first, the cascade page is the right tool. If you have a scope trace, a spectrum plot or a data file and you want the ratio it implies, this one is. The same distinction separates this page from the resistor noise calculator, which predicts a thermal noise voltage from resistance, bandwidth and temperature rather than reading one off a screen.
A third neighbour is the decibel calculator, which is the right page when the question is about decibel arithmetic in the abstract rather than about a signal and its noise floor.
The Mistake That Halves or Doubles Every Answer
The 10 log versus 20 log error is not rare. It is the single most common defect in published SNR figures, and it survives review because the wrong answer is still a plausible-looking number in a plausible-looking unit. Nothing about 20 dB looks wrong when the truth is 40 dB.
There is a reliable way to avoid it. Ask what physical quantity the instrument is proportional to. A voltmeter, an ADC code, a microphone's output and a photodiode's photocurrent are all amplitude-like; they scale linearly with the field or the pressure or the current. A bolometer, a thermal power meter, an optical power meter and anything already reading in dBm are power-like. If you can double the reading by doubling the voltage, it is an amplitude. If doubling the voltage quadruples the reading, it is a power.
A related trap sits in the middle: quantities that look like powers but are stored as amplitudes. The magnitude of an FFT bin is an amplitude. The squared magnitude is a power. Software that plots a power spectral density has already squared, and applying 20 log to it doubles the error rather than fixing it. When in doubt, put a known two-to-one change into the system and see whether the displayed decibel figure moves by 6 dB or by 3 dB. Six means you are looking at an amplitude scale.
Why Bandwidth Belongs in Every Quoted SNR
Noise is spread over frequency; a signal usually is not. Widening the measurement bandwidth admits more noise power without admitting more signal, so the SNR falls. This means an SNR quoted with no bandwidth attached is not a reproducible measurement, and two laboratories can honestly report figures ten decibels apart for the same hardware.
For noise that is flat across the band of interest, the power scales in direct proportion to bandwidth, so halving the bandwidth improves SNR by 3 dB. In amplitude terms the noise falls with the square root of bandwidth, which is why noise densities are quoted in volts per root hertz. The tool reports the density implied by your noise reading and your stated bandwidth, which is the figure that lets someone else reproduce your result at a different bandwidth.
This is also why matched filtering and integration work. Averaging many repetitions of the same waveform narrows the effective bandwidth around the signal, and the ratio improves with the square root of the number of averages in amplitude terms. Nothing about the hardware changed; only the bandwidth over which the noise was allowed to accumulate.
SNR, SINAD and What Each One Hides
Plain SNR treats only random noise as the enemy. That is the right model when the impairment is thermal, shot or quantisation noise, all of which are broadband and uncorrelated with the signal. It is the wrong model when the dominant impairment is distortion, because distortion products sit at specific frequencies related to the signal and behave nothing like noise.
SINAD is the honest single number for a system that has both. It answers a question a listener or a demodulator actually cares about: how much of what comes out is the thing you wanted. A converter with excellent SNR and poor linearity can have a SINAD ten decibels below its SNR, and quoting only the SNR would be misleading. Where harmonics specifically are the concern rather than everything non-signal, the total harmonic distortion calculator isolates that term on its own.
The effective-number-of-bits figure is SINAD restated in the language of converter resolution. It is useful because it is unforgiving: a nominally sixteen-bit converter with a real analogue front end often delivers eleven or twelve effective bits, which a specification sheet's resolution figure hides. Treat it as a comparison between measurements taken the same way, not a claim about the silicon.
Reading SNR in Sound, Radio and Images
The definition is universal but the conventions around it are not. In audio, the signal reference is usually a stated level such as the nominal operating level rather than the loudest possible one, so an audio SNR and a dynamic range figure are different numbers for the same equipment. Converting between the sound pressure and sound level worlds is what the sound level converter is for.
In radio links, the ratio that matters at the demodulator is often expressed per bit rather than per hertz, and the link budget that produces it involves path loss, antenna gains and receiver noise. The free space path loss calculator handles the propagation term of that budget; this page handles the ratio once you have measured what actually arrived.
In imaging, the noise is frequently shot noise, whose amplitude grows with the square root of the signal itself, so the ratio improves with exposure for reasons unrelated to the sensor's electronics.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Applying 20 log to a power measurement — this doubles the decibel figure. A genuine 30 dB power ratio becomes a reported 60 dB, which is a thousand-fold overstatement in power terms.
- Comparing a peak signal with an RMS noise — noise has no useful peak value, so the mismatch inflates the ratio by the crest factor of the signal and makes results incomparable between waveforms.
- Quoting SNR without a bandwidth — the same hardware can honestly produce very different figures at different measurement bandwidths, so the number cannot be reproduced or compared.
- Adding noise and distortion arithmetically — uncorrelated contributions combine in power, so they add as the square root of the sum of squares. Adding the amplitudes directly overstates the impairment.
- Treating ENOB as a hardware property — it depends on sample rate, input frequency, filtering and layout, so an ENOB figure is only meaningful next to the conditions it was measured under.
Related Free Tools From Arb Digital
For the electrical basics behind a measurement, the Ohm's law calculator converts between the voltage, current and power forms of the same reading, which is often what settles whether you are holding an amplitude or a power. The RLC impedance calculator covers the filtering that sets your measurement bandwidth, and the wavelength calculator is useful when the noise floor question is really a propagation question. Everything Arb Digital publishes sits on the free online tools hub.
Frequently Asked Questions
Use ten times the logarithm when the two quantities are powers, energies or intensities. Use twenty times it when they are amplitudes such as volts, amps, sound pressures or converter counts. The factor of two exists because power is proportional to the square of amplitude, and the square becomes a multiplication by two once it is inside a logarithm.
It depends entirely on what the signal is for, and there is no universal threshold. A digital link may decode reliably at a ratio that would sound unacceptable in audio, while a scientific measurement may need a ratio hundreds of times larger than either. The useful question is what ratio your demodulator, listener or estimator requires, and whether the measured figure clears it with margin.
SNR compares the signal only with random noise. SINAD compares it with noise and distortion together, including harmonics and spurious tones. A system can have a high SNR and a much lower SINAD if it is quiet but non-linear, and in that case SINAD is the figure that describes what a listener or a demodulator actually experiences.
Yes. A negative figure simply means the noise is larger than the signal, which is normal in spread-spectrum links, deep-space telemetry and many scientific measurements where processing gain recovers the signal afterwards. A ratio of minus three decibels means the noise power is about twice the signal power.
Noise occupies the whole band while the signal usually occupies part of it, so widening the bandwidth admits more noise without more signal. For flat noise the power scales directly with bandwidth, so halving the bandwidth improves the ratio by about three decibels. This is why an SNR quoted without its bandwidth is not reproducible.
Effective number of bits restates SINAD as the resolution an ideal quantiser would need to be equally clean, using the relation that each extra bit is worth about 6.02 decibels plus a 1.76 decibel offset from the statistics of quantisation error. It is a comparison figure that depends on sample rate, input frequency and the analogue front end, not a fixed property of a converter.
The noise figure calculator predicts how much a chain of amplifiers and mixers degrades a ratio, using the Friis cascade relation and stage gains and noise figures, and reports an output ratio as a by-product of that prediction. This page starts from two measured numbers and expresses the ratio they imply. One is a design tool for a receiver chain, the other a measurement conversion.
This tool is provided for educational and preliminary engineering use. It performs the standard decibel and SINAD conversions on figures you supply, and the quality of the result depends entirely on how those figures were measured. Use calibrated instrumentation and a documented measurement bandwidth for work that will be published or relied upon.
