Bit Depth Dynamic Range Calculator
Bit depth determines the number of amplitude levels available for each audio sample, which directly sets the theoretical dynamic range of a digital audio system. The standard formula from the AES and IEEE is: dynamic range (dB) = 6.02 * n + 1.76, where n is the bit depth. Each additional bit adds approximately 6 dB of dynamic range (it doubles the number of quantization levels). This calculator converts any bit depth to its theoretical maximum dynamic range and the number of quantization levels.
Bit depth dynamic range formula
Dynamic range (dB) = 6.02 * n + 1.76
Quantization levels = 2^n
SNR for full-scale sine = 6.02n + 1.76 dB
6.02 = 20 * log10(2) (dB per bit)
Each bit of depth doubles the number of quantization levels (2^n total). Doubling levels adds 20 * log10(2) = 6.0206 dB to the dynamic range. The 1.76 dB term accounts for the RMS amplitude of a full-scale sine wave versus a DC signal of the same peak amplitude.
Standard bit depths and dynamic ranges
- 8-bit: 49.93 dB, 256 levels. Used in some early digital audio and game consoles.
- 16-bit: 98.09 dB, 65,536 levels. CD standard, adequate for consumer listening.
- 20-bit: 122.17 dB, 1,048,576 levels. Some high-end DACs.
- 24-bit: 146.25 dB, 16,777,216 levels. Professional recording standard.
- 32-bit integer: 194.49 dB, 4,294,967,296 levels. Theoretical, exceeds hardware ADC/DAC capability.
Bit depth dynamic range: frequently asked questions
What is the formula for dynamic range from bit depth?
Dynamic range (dB) = 6.02 * n + 1.76, where n is the bit depth. For 16-bit: 6.02 * 16 + 1.76 = 98.09 dB. For 24-bit: 6.02 * 24 + 1.76 = 144.49 dB. The 6.02 factor comes from 20 * log10(2) = 6.0206 dB per bit.
Why is the formula 6.02n + 1.76?
Each bit doubles the number of quantization levels, adding 6.02 dB per bit (20 * log10(2)). The 1.76 dB offset comes from the theoretical signal-to-quantization-noise ratio for a full-scale sine wave: SQNR = 6.02n + 1.76 dB. This is derived from the AES and IEEE audio standards.
What bit depth do professional recordings use?
CD audio: 16-bit (98 dB dynamic range). Professional recording: 24-bit (144 dB). Consumer streaming uses 16-bit or 24-bit depending on the service. 32-bit floating point (used internally in DAWs) provides virtually unlimited dynamic range for processing.
Is 24-bit dynamic range audible?
Human hearing spans roughly 120 dB (threshold of hearing to pain). 16-bit provides about 98 dB, which is adequate for most listening. 24-bit provides 144 dB, which exceeds human hearing range. The extra headroom in 24-bit is valuable during recording and mixing to avoid clipping during processing.
What is the dynamic range of 32-bit float audio?
32-bit float has a mantissa of 23 bits plus a sign bit, giving approximately 6.02 * 24 + 1.76 = 144.5 dB within each exponent range. However, the floating-point exponent allows a total dynamic range of over 1,500 dB, making clipping essentially impossible in a DAW.
Official sources
- Audio Engineering Society (AES): aes.org - AES17 digital audio measurement standards including dynamic range.
- NIST (nist.gov): nist.gov - signal-to-noise ratio and digital measurement standards.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.