Hong Life CalculatorsUnderstanding the bit depth and audio file size calculator — concept and principle
Digital audio stores sound as a stream of numbers: the sample rate says how many numbers per second, the bit depth says how finely each number can describe the signal's level, and the channel count says how many such streams run side by side. From those three values you can work out the theoretical dynamic range, the highest frequency that can be captured, the raw bit rate and the size of an uncompressed file such as WAV or AIFF. Engineers and editors use these figures to plan storage and choose session formats.
How it is calculated
- Dynamic range: DR ≈ 6.02 × N + 1.76 dB, where N is the bit depth.
- Nyquist frequency: f_N = f_s / 2 (sample rate in kHz gives kHz).
- Bit rate: bits × sample rate (kHz) × channels = kbps.
- File size: bits × sample rate (Hz) × channels × seconds ÷ 8 ÷ 10⁶ = MB (decimal megabytes).
The principle
Each extra bit doubles the number of available levels, and a doubling of amplitude is 20·log₁₀(2) ≈ 6.02 dB, so every bit adds about 6 dB of range. The extra 1.76 dB comes from comparing a full-scale sine wave with uniformly distributed quantisation noise; it is the textbook signal-to-quantisation-noise ratio for an ideal converter. The Nyquist–Shannon sampling theorem states that a band-limited signal can be reconstructed exactly if it is sampled at more than twice its highest frequency, so half the sample rate is the ceiling. File size is bookkeeping: each sample of each channel costs N bits.
Worked example
- Inputs: 24 bits, 48 kHz, 2 channels, 3 minutes.
- Dynamic range: 6.02 × 24 + 1.76 = 144.48 + 1.76 = 146.24 dB.
- Nyquist: 48 ÷ 2 = 24 kHz.
- Bit rate: 24 × 48 × 2 = 2,304 kbps.
- Size: 24 × 48,000 × 2 × 180 s ÷ 8 = 51,840,000 bytes = 51.84 MB.
| Bit depth | Dynamic range (dB) |
|---|---|
| 6 | 37.88 |
| 12 | 74 |
| 18 | 110.12 |
| 24 | 146.24 |
| 30 | 182.36 |
| 36 | 218.48 |
| 48 | 290.72 |
How to read the result
16-bit audio gives about 98 dB, already more than most listening rooms allow; 24-bit gives about 146 dB, which exceeds what real converters achieve (good ones reach roughly 115–125 dB) but leaves headroom for recording at modest levels. 44.1 kHz (CD) and 48 kHz (video) both place Nyquist above the roughly 20 kHz limit of human hearing. CD-quality stereo runs at 1,411.2 kbps.
Common mistakes
- Mixing kHz and Hz: the bit-rate output expects kHz, the size formula converts to Hz internally.
- Confusing MB (10⁶ bytes) with MiB (1,048,576 bytes); operating systems may show the smaller-looking MiB figure.
- Assuming 24-bit sounds "50% better"; it mainly lowers the noise floor.
Frequently asked questions
Why is 32-bit float popular for recording?
Floating-point samples carry an exponent, so levels above 0 dBFS are not clipped inside the file, which gives huge headroom while editing. The converter itself is still limited by its analog stage.
Is 96 kHz worth it?
It raises Nyquist to 48 kHz and can ease filter design or extreme time-stretching, but it doubles file size compared with 48 kHz and the extra band is inaudible for most listeners.
Sources: C. E. Shannon, "Communication in the Presence of Noise," Proceedings of the IRE, 1949 · K. C. Pohlmann, Principles of Digital Audio, McGraw-Hill