Audio Quantization Noise & SNR Calculator | Bit Depth to SNR, One Panel

Turn bit depth, dither type and signal level into full-scale SNR, noise floor, dynamic range, signal SNR and quantization levels at once. A working calculator for mastering and ADC/DAC design when you need to know how much quieter 24-bit really is than 16-bit.

💡 About this tool

The theoretical SNR of a PCM converter comes straight from the textbook formula 6.02·n + 1.76 dB, where n is the bit depth. It assumes a full-scale sine wave and quantization error modelled as uniformly distributed white noise. That single line is why "16-bit ≈ 98 dB" and "24-bit ≈ 146 dB" get quoted everywhere — they fall out of the equation, not out of any measurement.

The part that actually trips people up is dither. Adding dither removes the correlated, non-linear distortion on low-level signals, but you pay for it with a higher noise floor: about 3.01 dB for RPDF (rectangular PDF) and about 4.77 dB for TPDF (triangular PDF). And if your real signal is sitting at −20 dBFS rather than full scale, the number that matters is the gap from that level down to the noise floor — not the headline full-scale figure.

This calculator shows four things side by side: full-scale SNR, noise floor in dBFS, dynamic range, signal SNR at any level you pick, and the number of quantization steps (2 to the power of n). Move a slider and every figure updates, so you can watch each extra bit buy roughly 6 dB and see exactly what TPDF costs you.

🧐 Frequently Asked Questions

Q. Where does the +1.76 dB come from? A. A full-scale sine has an RMS value of peak/√2, and comparing its power to uniformly distributed quantization noise leaves a factor of 1.5, i.e. 10·log10(1.5) ≈ 1.76 dB. Use a square wave or noise as the reference signal and that constant changes.

Q. Should I read the undithered or the TPDF figure? A. For the theoretical best-case dynamic range in the table, read undithered. If you're about to render a real master, switch to TPDF — the dither that replaces quantization distortion with white noise — and treat the value about 4.77 dB lower as your realistic number.

Q. Why is signal SNR smaller than full-scale SNR? A. Signal SNR is the distance from the level you entered (say −20 dBFS) down to the noise floor. Anything below full scale loses exactly that much SNR, which makes this a quick way to sanity-check how much recording headroom you can afford.

Q. Does this apply to 32-bit float recording? A. No — these are integer (fixed-point) PCM figures, including the 32-bit row. 32-bit float uses a 24-bit mantissa plus an exponent, so its effective dynamic range behaves differently; read the 194 dB integer number as a separate thing from float headroom.

Q. Does more bit depth always sound better? A. SNR and dynamic range always widen, but in the audible band 16-bit already buries the noise floor in most material. The real payoff of 24-bit is headroom during tracking and editing, and avoiding error build-up across many processing stages.

📚 Fun Facts

The rigorous case for dither was made by Lipshitz and Vanderkooy: with TPDF (a triangular probability density), the quantization error becomes statistically independent of the input, and both its mean and variance stay constant regardless of signal. That independence is the whole trick — for a tiny rise in noise floor you completely eliminate the ugly, signal-correlated distortion that plagues low-level audio. Engineers sometimes point out that analog tape hiss quietly did the same job for decades, acting as a kind of accidental dither.