ADC and bit-depth calculator
Four converter questions in one place: how big is one step, what signal-to-noise can the bits deliver, how many bits does a measured SINAD really give, and what does oversampling or a higher bit depth cost.
Converter
Convention: LSB = full-scale range ÷ 2N. Some datasheets divide by 2N − 1; the difference matters only at very low resolutions. Real converters fall short of the ideal SQNR because of thermal noise, jitter and nonlinearity — use ENOB for those.
Measured performance
Requirement
Example: a converter marketed as 16-bit that measures 84 dB SINAD behaves like an ideal 13.7-bit converter.
Sampling
Plain oversampling adds about 3 dB (half a bit) per doubling of the sample rate. Noise shaping pushes quantization noise above the band of interest, which is how a 1-bit delta-sigma converter reaches high resolution. These are ideal-model figures; real modulators are limited by stability and analog noise.
Recording
Where these formulas come from
An ideal N-bit converter divides its full-scale range into 2N steps. Rounding each sample to the nearest step leaves an error between −½ and +½ LSB. For busy signals that error behaves like uniformly distributed noise with variance LSB²/12, so its rms value is LSB ÷ √12 ≈ 0.29 LSB. Dividing the power of a full-scale sine wave by that noise power gives the familiar SQNR ≈ 6.02N + 1.76 dB. Our ADC quantization guide walks through the derivation step by step.
Worked example: 12-bit, 3.3 V
LSB = 3.3 ÷ 4096 ≈ 0.806 mV. Noise rms ≈ 0.806 ÷ 3.464 ≈ 0.233 mV. Ideal SQNR = 6.02 × 12 + 1.76 = 74.0 dB.
Frequently asked questions
Why does my 24-bit audio interface not reach 146 dB?
Analog noise in the input stage and the converter itself sets the real floor. The best converters measure somewhere around 120–125 dB, so the lowest bits of a 24-bit word are noise. The extra word length still matters: it keeps quantization noise far below that analog floor.
Does SQNR depend on the signal?
Yes. The 6.02N + 1.76 dB figure assumes a full-scale sine. A signal 20 dB below full scale gets 20 dB less SQNR, and very quiet or simple signals produce error that is correlated with the signal rather than noise-like, which is where dither helps.
What is the difference between SNR, SINAD and SQNR?
SQNR counts only quantization noise. SNR counts all noise but excludes harmonic distortion. SINAD counts noise and distortion together, which is why ENOB is computed from SINAD.