MusicReasonProduction, Synthesis, and Audio Math
How much dynamic range does this bit depth give me?
Choose a bit depth and one or more depths to compare it against. This tool reports the theoretical ideal signal-to-noise ratio for a full-scale sine test signal at each depth. It does not claim this figure predicts a real recording's actual noise floor or perceived loudness.
Answer
Want to learn more? Frequency, Sampling, Nyquist, and Spectra
Understand
Every added bit of PCM quantization doubles the number of discrete amplitude steps available, which raises the theoretical signal-to-noise ceiling by a fixed amount. This figure describes the format's own quantization noise floor under an idealized full-scale sine signal, not the noise floor of any specific recording chain, converter, or microphone, all of which add their own noise on top of this theoretical ceiling.
Worked examples
16-bit PCM has an ideal signal-to-noise ratio of about 98.08 dB. Moving to 24-bit adds eight more bits, each contributing about 6.02 dB, for a theoretical ceiling around 146 dB, far beyond what any real analog signal chain actually achieves in practice. Each single added bit, at any starting depth, always adds about 6.02 dB.
Method and limitations
The formula is SNR ≈ 6.02N + 1.76 dB, where N is the bit depth, derived from the ratio of a full-scale sine wave's RMS level to the RMS level of rectangular quantization noise. It assumes no dither is applied and that the signal fully uses the format's available range; a quieter signal, real dithering noise shaping, or an analog stage's own noise floor all change the practical result in ways this idealized formula does not account for. This tool states the formula's assumptions rather than presenting the number as a guarantee of audible quality.
The 1.76 dB constant in the formula comes from the specific statistics of a full-scale sine wave's RMS level relative to its peak; a different test signal, such as full-scale white noise, would replace that constant with a different value even though the 6.02 dB per bit relationship stays the same regardless of signal shape, since that part of the formula depends only on the number of quantization steps available, not on what kind of signal fills them.