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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

Bit Depth (n)

bits

11632

Current: 16-bit (slider 1–32; type for wider)

Quick-Pick Bit Depths

Sample Rate (for file size)

Channels

Duration

Result

Dynamic Range

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dB (theoretical SNR)

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Quantization Levels (2ⁿ)

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Step Size (% of full scale)

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Smallest Step

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PCM Data Rate

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PCM File Size (uncompressed)

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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

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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

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 rounding error introduced when a continuous audio waveform is mapped onto a finite set of integer values during analog-to-digital conversion (ADC). 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). This same figure is also called the theoretical SNR or SQNR (signal-to-quantization-noise ratio) in digital signal processing texts. As a dynamic range calculator, this tool applies that formula instantly for any bit depth from 1 to 64, alongside quantization level counts and audio file size estimates.

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 in a process known as requantization noise. The extra 48 dB headroom of 24-bit vs 16-bit (8 bits × 6.02) lets producers perform many operations without audible degradation. The final master can then be dithered down to 16-bit for delivery. For the complementary question of how sample rate affects frequency bandwidth and file size, see the sample rate converter.

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. Some newer recording devices (like the Zoom F-series and Sound Devices MixPre) offer dual-converter 32-bit float recording, allowing you to capture extremely dynamic events — film explosions, live concerts — with guaranteed no-clip performance. You can verify how your bit depth choices translate to decibel headroom margins using the dB addition calculator alongside this tool.

Worked example: calculate 16-bit dynamic range and file size by hand

Given n = 16 bits, here is how to work out every output this tool produces:

Dynamic range: DR = 6.02 × 16 + 1.76 = 96.32 + 1.76 = 98.08 dB
Quantization levels: 2¹⁶ = 65,536 distinct amplitude values
Step size: 1 ÷ 65,536 ≈ 0.00153 % of full scale (≈ −96.3 dBFS per step)
PCM data rate (stereo, 44,100 Hz): 44,100 × (16 ÷ 8) × 2 = 44,100 × 2 × 2 = 176,400 bytes/s ≈ 1,411 kbps
Uncompressed file size for 60 seconds: 176,400 × 60 = 10,584,000 bytes ≈ 10.09 MiB (10.58 MB)

Common reference points: 16-bit / 44.1 kHz (CD) = 98.08 dB DR, 1,411 kbps; 24-bit / 48 kHz (broadcast/production standard) = 146.24 dB DR, 2,304 kbps. The same arithmetic applies at any bit depth — just substitute n. For the complementary sample-rate side of the equation (Nyquist bandwidth and aliasing), use the sample rate converter.

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%.

What bit depth should I record at — 16-bit or 24-bit?

Record at 24-bit whenever your audio interface and DAW support it, even if the final delivery is 16-bit. The extra 8 bits (48 dB of additional headroom) let you set conservative input gain levels without worrying that quiet passages will be buried in quantization noise. This is especially important for dynamic sources like acoustic instruments, orchestral recordings, or speech where peaks and troughs vary widely. Deliver the finished mix at 16-bit with proper dither applied. The storage cost of 24-bit vs 16-bit recording is modest given today's hard drive prices.

What is noise shaping, and how does it differ from dither?

Dither is random noise added before bit-depth reduction to decorrelate quantization errors from the signal. Noise shaping is a further refinement: instead of white (flat) dither, the error energy is spectrally shaped — pushed toward high frequencies (above ~16 kHz) where human hearing is least sensitive. This makes the audible noise floor even lower in the 1–10 kHz region the ear is most sensitive to. Popular noise-shaping curves include TPDF, POW-R, and Apogee UV22. Most mastering-grade dither plugins combine dither + noise shaping automatically. Without either, 24→16-bit truncation produces correlated distortion, which sounds far worse than the elevated noise floor you'd expect from simple dither.

Does choosing a higher bit depth increase DAW CPU or latency?

Very slightly. A 32-bit float session uses twice the RAM bandwidth of a 16-bit integer session, but modern CPUs handle floating-point arithmetic in dedicated FPUs with negligible overhead. DAW latency is set by the audio buffer size (typically 64–2048 samples), not by bit depth. In practice, switching from 16-bit to 24-bit or 32-bit float recording has no perceptible effect on real-time performance on any machine built after 2010. The dominant factors in DAW CPU load are plugin count, track count, sample rate, and buffer size — not bit depth.

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