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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).

Input

bits
11632
Current: 16-bit (slider 1–32; type for wider)
Quick-Pick Bit Depths

Result

Dynamic Range
dB (theoretical SNR)
Quantization Levels (2ⁿ)
Step Size (% of full scale)
Smallest Step
PCM Data Rate
PCM File Size (uncompressed)
Formulas
Dynamic Range = 6.02 × n + 1.76 dB   (Bennett's formula)
Quantization levels = 2ⁿ
Step size = 1/2ⁿ of full scale
PCM bytes/sec = SR × (n/8) × channels

Bit Depth Comparison

Bit DepthDynamic RangeLevels (2ⁿ)1 min Stereo 44.1kTypical Use
1-bit7.78 dB2~0.66 MBDSD / Sigma-delta modulation
4-bit25.84 dB16~2.65 MBAncient sample-based games
8-bit49.92 dB256~5.29 MBLo-fi audio, telephone PCM (µ-law/A-law)
12-bit74.00 dB4,096~7.94 MBAM radio, low-end ADPCM
16-bit98.08 dB65,536~10.58 MBCD Audio, consumer download standard
20-bit122.16 dB1,048,576~13.23 MBPro audio, DAT, some older studio gear
24-bit146.24 dB16,777,216~15.87 MBPro audio, hi-res downloads, Blu-ray
32-bit int194.40 dB~4.29 × 10⁹~21.17 MBFloat-buffer intermediates, rare delivery
32-bit float~1500 dB2³² values~21.17 MBProduction / mixing / mastering DAWs
Note: this calculator uses Bennett's formula assuming linear PCM. 32-bit float achieves its ~1500 dB DR through IEEE 754 floating-point exponent representation, not integer quantization — typing 32 in the tool returns 194.4 dB (the integer-PCM case).

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.

Frequently Asked Questions

How do I calculate dynamic range from bit depth?
Use DR = 6.02 × n + 1.76 dB. For 16-bit: 6.02 × 16 + 1.76 = 98.08 dB. For 24-bit: 6.02 × 24 + 1.76 = 146.24 dB. The formula gives the theoretical best case (assuming a full-scale sine input and perfect uniform-noise quantization); real-world performance is 1-3 dB worse due to other noise sources.
Is 16-bit "good enough" for music listening?
For passive listening: yes, almost always. 16-bit gives 98 dB DR, more than any consumer playback system can reproduce. Audiophile listening tests consistently fail to distinguish 16-bit from 24-bit when the bit-reduction includes proper dither. The case for 24-bit/96 kHz is mostly for PRODUCTION headroom or audiophile preference, not measurable advantage in delivery.
What's a "quantization level"?
An n-bit sample can hold one of 2ⁿ distinct values. 8-bit = 256 levels (each step is 1/256 of full scale, ~0.4% precision). 16-bit = 65,536 levels (each ~0.0015% of full scale). 24-bit = 16.7 million levels (~0.0000060% per step). More levels = smaller step = less noise from rounding.
What is dither?
Dither is intentional low-level random noise added before bit-depth reduction (e.g., 24-bit → 16-bit). It prevents quantization "harmonic distortion" by randomizing the rounding errors. Properly dithered 16-bit audio can faithfully represent signals well below the theoretical -96 dB noise floor. Without dither, very quiet signals become distorted rather than just noisy.
Why is 32-bit float "almost limitless" DR?
Float representation has a 23-bit mantissa + 8-bit exponent. The exponent gives ~10⁷⁵ range; the mantissa gives ~150 dB local precision. Effective total DR is about 1500 dB — far beyond physical reality. The practical benefit isn't more loudness range, it's that you can't "clip" 32-bit float during processing — signals can briefly exceed 0 dBFS and be brought back without distortion.
How does bit depth affect file size?
Linearly. Going from 16-bit to 24-bit multiplies file size by 24/16 = 1.5×. From 16-bit to 32-bit: 2×. A 1-minute stereo CD-quality file is 10.58 MB; the same recording at 24-bit/44.1k is 15.87 MB; at 32-bit/96k stereo it's 46.08 MB. Compression formats (FLAC, ALAC) cut these by ~40%; lossy (AAC, MP3, Opus) cut by ~90%.