Why do some bit-depth calculations use 6.02N instead of 6.02N + 1.76?

6.02N dB describes the amplitude ratio between the full-scale span and one LSB. The extra 1.76 dB belongs to the RMS signal-to-quantization-noise ratio for a full-scale sine wave under the ideal uniform-noise model.

Is the quantization noise floor the same as an audio interface's measured noise floor?

No. The calculator shows an ideal integrated quantization-noise result. A real interface also has analog thermal noise, clock jitter, power-supply noise, nonlinear distortion, filtering, and other limitations.

Does 32-bit float audio have a 194 dB fixed dynamic range?

No. The simple 2-to-the-N integer quantizer model does not describe IEEE floating-point audio across its full exponent range. A 32-bit float sample normally has 24 bits of significand precision, while its exponent provides a much wider representable range.

Does dither change the number of quantization levels?

No. Dither does not add code values. It decorrelates quantization error from the signal and changes the error's spectral character, usually by adding a small amount of noise.

Are my values uploaded or saved?

No. Calculations, copying, and CSV creation happen locally in the browser. The page does not upload, save, or place input values in the URL.

Audio Bit Depth Calculator — Dynamic Range, Quantization Levels & Noise Floor

Calculate the exact number of integer PCM code values, LSB size, ideal full-scale-sine SQNR, integrated quantization noise, and the effect of recording below 0 dBFS.

Audio quantizer settings

Integer bit depth

Whole-number PCM resolution from 1 to 64 bits. See the 32-bit float note below.

Sine-wave peak level (dBFS)

0 dBFS is full-scale peak. Use a negative value for normal recording level.

Common integer PCM depths

Your values stay in this browser. They are not uploaded, saved, or added to the URL.

Bit-depth result

Ideal full-scale sine SQNR 146.26 dB 24-bit ideal uniform quantizer; integrated over the Nyquist band

Quantization levels16,777,216

One-LSB range144.49 dB

Ideal noise floor−146.26 dBFS

SQNR at entered level128.26 dB

One LSB of full-scale span0.00000596046%

RMS quantization error0.288675 LSB

Signed PCM code range−8,388,608 to 8,388,607

Approx. precision used at signal level21.01 bits

Theoretical result: This is an ideal integer quantizer model, not a measured converter or complete recording-chain noise specification.

How to use this audio bit depth calculator

Enter the stored integer precision. Choose 16 or 24 bits for common PCM recording, or enter another whole-number depth.
Set the sine-wave peak level. Use 0 dBFS to see the formula's full-scale limit. A value such as −18 dBFS shows how lower signal level reduces SQNR relative to the same fixed quantization noise.
Read levels and LSB size. Every extra bit doubles the available code count and halves the ideal step size.
Treat the dB result as a ceiling. Real A/D and D/A converters add analog noise, distortion, jitter, and implementation limits. Consult measured dynamic range, SNR, SINAD, or ENOB for hardware comparisons.

The entered level changes only the signal-to-quantization-noise ratio. It does not change the format's code count or the model's integrated quantization-noise power.

Bit depth, dynamic range, and quantization noise formulas

For an ideal, uniform, linear N-bit integer quantizer with a sufficiently varying signal, step size q, and error distributed from −½ LSB to +½ LSB:

Quantization levels = 2ᴺ
One LSB as a fraction of full-scale span = 1 ÷ 2ᴺ
One-LSB range = 20 log₁₀(2ᴺ) = 6.0206N dB
RMS quantization error = q ÷ √12 = 0.288675 LSB
Ideal full-scale sine SQNR = 6.0206N + 1.7609 dB
SQNR at signal level L dBFS = 6.0206N + 1.7609 + L

The 1.7609 dB term is not an extra bit of resolution. It comes from comparing the RMS value of a full-scale sine wave with the RMS value of the ideal uniform quantization error. This is why a one-LSB span calculation gives 6.02N dB while full-scale-sine SQNR gives 6.02N + 1.76 dB.

On this page, “ideal noise floor” is the negative of the full-scale-sine SQNR and refers to total integrated quantization noise across the Nyquist band. It is not a per-Hz noise-density value or the height of one FFT bin. FFT noise-floor appearance changes with sample rate, transform length, window, and bandwidth.

Important: 32-bit float is not a 32-bit integer quantizer

Choose 32 bits here only for 32-bit integer PCM. IEEE 754 single-precision floating point uses a sign, an 8-bit exponent, and 23 stored fraction bits with an implicit leading bit for normal values. That gives about 24 bits of significand precision while the exponent supplies a far wider representable level range. Therefore, applying 6.02 × 32 + 1.76 to a complete 32-bit float format is not a meaningful fixed dynamic-range specification.

Floating-point DAW files can preserve values above 0 dBFS internally, but the analog input converter's real capture range is still limited by its hardware. Bit depth also does not determine file loudness or prevent analog clipping.

Common integer PCM bit depths compared

Bit depth	Exact levels	One-LSB range	Ideal full-scale sine SQNR	Typical context
8-bit	256	48.16 dB	49.93 dB	Legacy or deliberately lo-fi integer PCM.
16-bit	65,536	96.33 dB	98.09 dB	Audio CD and many delivery files.
20-bit	1,048,576	120.41 dB	122.17 dB	Some legacy professional converters and formats.
24-bit	16,777,216	144.49 dB	146.26 dB	Common production recording and interchange depth.
32-bit integer	4,294,967,296	192.66 dB	194.42 dB	Integer processing or storage; distinct from 32-bit float.

These are mathematical limits for the stated model. They are not claims about the acoustic noise, analog electronics, or effective performance of a product.

What bit depth changes in real audio work

More capture margin: a lower quantization step lets engineers leave sensible headroom without bringing the ideal quantization floor close to ordinary recording levels.
More storage: uncompressed PCM data rate grows linearly with bit depth. Use the Audio File Size Calculator to calculate the storage impact.
Dither behavior: properly chosen dither decorrelates quantization error and makes very low-level distortion noise-like, but it does not create more PCM code values.
Hardware reality: nominal bits and effective number of bits are different. Analog noise and distortion usually make a converter's measured performance lower than the ideal N-bit limit.

Audio bit depth FAQ

How many quantization levels does an N-bit audio format have?

It has 2^N code values. For example, 16-bit PCM has 65,536 possible values per sample and 24-bit PCM has 16,777,216.

What is the theoretical dynamic range of 16-bit and 24-bit audio?

Using ideal full-scale-sine SQNR, 16-bit audio is about 98.09 dB and 24-bit audio is about 146.26 dB. The simpler one-LSB span is about 96.33 dB and 144.49 dB respectively. Neither is a measured hardware specification.

Why do some calculators use 6.02N and others use 6.02N + 1.76?

They use different references. The first is the amplitude ratio from full-scale span to one LSB. The second is RMS SQNR for a full-scale sine wave against ideal uniform quantization error.

Is quantization noise floor the same as measured interface noise?

No. This result includes ideal quantization error only. An audio interface also contains analog circuit noise, distortion, jitter, filtering, power-supply effects, and other implementation limits.

Does recording at −18 dBFS waste three bits?

It uses roughly three fewer bits' worth of instantaneous amplitude resolution because about 6.02 dB corresponds to one bit. With 24-bit storage, the ideal mathematical margin remains very large; actual analog-system noise is usually the more relevant limit.

Does 32-bit float audio have a fixed 194 dB dynamic range?

No. That figure comes from treating 32 bits as a linear integer code. Single-precision float has about 24 bits of significand precision plus an exponent, so it behaves differently and has no single fixed LSB across its full range.

Does dither increase bit depth?

No. Dither does not increase the code count. It trades correlated quantization distortion for a controlled noise characteristic and can make signals below one LSB statistically recoverable over time.

Are my settings uploaded or saved?

No. The calculation, clipboard report, and CSV file are created locally by JavaScript in your browser.

Method and references

Formula and assumptions checked 2 August 2026. Analog Devices derives the RMS quantization error and the classical ideal full-scale-sine result. Texas Instruments documents the same ideal ADC equation, distinguishes effective bits from nominal resolution, and explains that thermal noise and jitter also contribute to real converter noise.