Bit Depth to Dynamic Range
Enter the bit depth N of a PCM audio file and get the theoretical dynamic range in decibels from DR = 6.02·N + 1.76, the quantization noise ceiling.
DR (dB)
—
SNR and dynamic range by bit depth
With ideal PCM quantization, every extra bit buys you a fixed amount of signal-to-noise ratio. The relationship is linear: SNR ≈ 6.02 · n + 1.76 dB, where n is the number of bits per sample. So 16-bit audio lands around ~98.1 dB, which is the CD standard and plenty for most rooms you'll ever listen in. Push to 24-bit and you get roughly ~146.3 dB, well past anything an analog noise floor can produce; that extra room is what lets you mix and edit without hearing quantization creep in. 32-bit float sits in a different category altogether. Because it stores values as an exponent plus a mantissa, there's no real SNR ceiling, and a signal that clips past 0 dBFS can still be pulled back down intact. Dither is the last piece: a sliver of low-level noise added before you quantize, which breaks up the correlation between the quantization error and the signal and effectively buys you another 1–2 bits of perceived depth down at the quiet end.
Applications: recording, mastering and broadcast
Studios track at 24-bit for two reasons: it leaves room when someone sets a level wrong, and it keeps quantization out of long signal chains. When the project is done, CD masters get dithered back down to 16-bit, and video broadcast (TV, streaming) usually goes out as 16-bit AAC. Inside the box, modern DAWs like Pro Tools and Reaper do their summing in 32-bit float, so a track clipping on its own never destroys data. The one place you still have to watch your gain is the master bus.
FAQ
Is 24-bit audibly better than 16-bit? On playback, most people won't hear a difference. Dithered 16-bit already covers more dynamic range than a normal room can use. Where 24-bit actually earns its keep is during recording and processing.
Why use dither? Skip it and the quantization error tracks the signal, which shows up as audible distortion when things get quiet. Dither trades that distortion for harmless white noise instead.
Does 32-bit float really have no limit? Functionally, no. The exponent range spans something like ~1500 dB, which is so far past what any analog source can deliver that clipping a float recording just doesn't happen.
Related Tools
Second-Leg Flaw Depth (Angle-Beam Ultrasonics)
Computes the true depth of a discontinuity found on the second leg of the beam in angle-beam ultrasonics, d = 2 × t − S × cos(θ), where S is the sound path read on the instrument and θ is the probe refracted angle. After bouncing off the back wall the beam travels back upwards, so depth stops growing with sound path and starts shrinking: depth is now counted from the back wall, not from the scanning surface, which is the classic mistake of applying the first-leg formula out of range. The tool only accepts sound paths whose projection falls between one and two thicknesses, which is exactly the second-leg band — below that the reflector is on the first leg and d = S × cos(θ) applies. Enter the part thickness, the sound path and the refracted angle.
Weld Cooling Time t8/5
Computes how long the heat affected zone takes to cool from 800 °C to 500 °C, the t8/5 parameter of EN 1011-2, from the heat input, the preheat temperature and the joint shape factor. The formula multiplies the term (6700 − 5 × preheat temperature) by the heat input, by the difference between the reciprocals of (500 − T₀) and (800 − T₀), and by the shape factor tabulated in the standard, which is 1.0 for a bead deposited on a plate and drops to about 0.9 for a butt weld and 0.67 for a fillet weld on a T-joint. Austenite decomposes in that range, so t8/5 decides the microstructure of the joint: cooling too fast forms martensite and opens the door to cold cracking, cooling too slowly coarsens the grain and destroys impact toughness, and most structural steels call for something between 5 and 25 seconds. The three-dimensional heat flow equation was adopted, valid when the plate is thick relative to the weld bead; in thin plate the flow is two-dimensional and t8/5 grows with the square of the heat input rather than in proportion to it. Enter the heat input, the preheat temperature and the joint shape factor.
Bachelier Model Call
Computes the price of a call option with the Bachelier model, which assumes the price follows normal (arithmetic) motion instead of lognormal. Because it allows negative prices, it came back into fashion for pricing options on assets that can go negative, as happened with oil in 2020 and with some spreads. The volatility here is absolute, in price units, not a percentage. The premium is e^(−rT)·[(F−K)·N(d) + σ√T·φ(d)]. Enter the forward price, the strike, the interest rate, the normal volatility and the term.
Retirement Goal Monthly Contribution
Calculates monthly contribution to reach a retirement goal with compound interest.
Elephant Lifespan
Shows elephant lifespan by species.
Lightning Frequency per km2
Computes lightning density per km2 per year from the total observed strikes, the area in km2 and the time interval.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.