Bit Depth Calculator
Calculate the dynamic range of any bit depth using DR = 6.02n + 1.76 dB. Output: dynamic range, quantization levels (2ⁿ), step size, data rate, and PCM file-size estimates. Supports 1 to 64-bit (1-bit DSD through 32-bit float).
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Result
Bit Depth Comparison
| Bit Depth | Dynamic Range | Levels (2ⁿ) | 1 min Stereo 44.1k | Typical Use |
|---|---|---|---|---|
| 1-bit | 7.78 dB | 2 | ~0.66 MB | DSD / Sigma-delta modulation |
| 4-bit | 25.84 dB | 16 | ~2.65 MB | Ancient sample-based games |
| 8-bit | 49.92 dB | 256 | ~5.29 MB | Lo-fi audio, telephone PCM (µ-law/A-law) |
| 12-bit | 74.00 dB | 4,096 | ~7.94 MB | AM radio, low-end ADPCM |
| 16-bit | 98.08 dB | 65,536 | ~10.58 MB | CD Audio, consumer download standard |
| 20-bit | 122.16 dB | 1,048,576 | ~13.23 MB | Pro audio, DAT, some older studio gear |
| 24-bit | 146.24 dB | 16,777,216 | ~15.87 MB | Pro audio, hi-res downloads, Blu-ray |
| 32-bit int | 194.40 dB | ~4.29 × 10⁹ | ~21.17 MB | Float-buffer intermediates, rare delivery |
| 32-bit float | ~1500 dB | 2³² values | ~21.17 MB | Production / mixing / mastering DAWs |
About Bit Depth & Dynamic Range
Bit depth (n) determines how many discrete amplitude levels each sample can take: levels = 2ⁿ. With more bits, you can represent quieter sounds without losing them to quantization noise. The theoretical signal-to-noise ratio of an ideal n-bit ADC is DR = 6.02n + 1.76 dB (Bennett's formula, assuming uniform quantization noise).
Why 6.02 per bit?
Each bit doubles the number of representable levels (2× factor in amplitude resolution). Amplitude doubling = 20 × log₁₀(2) = 6.0206 dB. The extra 1.76 dB comes from the assumption that quantization noise is uniformly distributed (mathematically: 10 × log₁₀(3/2)) — a refinement Walter Bennett published in 1948. The formula is the asymptotic best case; real ADCs are slightly noisier.
Why 16-bit for CDs?
16-bit gives 98 dB dynamic range — broadly matching the dynamic range of human hearing (about 120 dB total, but ~90 dB for usable music without pain). It also fits efficiently into computer memory (2 bytes per sample). The CD format committee in 1980 picked 16-bit as the sweet spot between fidelity, file size, and the cost of digital electronics at the time.
Why 24-bit for production?
24-bit gives 146 dB dynamic range — far more than any speaker, microphone, or human ear can use directly. The point isn't delivery; it's headroom during processing. When you cut/boost EQ, add compression, mix multiple tracks, etc., quantization errors can accumulate. The extra 48 dB headroom of 24-bit vs 16-bit (8 bits × 6.02) lets producers do many operations without audible degradation. The final master can then be dithered down to 16-bit for delivery.
32-bit float — the production format
32-bit float audio uses IEEE 754 floating-point representation: ~1500 dB effective dynamic range with virtually no clipping (a value of 2 = +6 dB above 0 dBFS — you can recover from "over" peaks). Most modern DAWs (Logic, Pro Tools, Reaper, Ableton) operate internally in 32-bit float. Delivery formats stay at 16-bit or 24-bit since the float advantages don't apply to passive listening.