Calculate decibels - how it works
In audio technology, levels are given in decibels (dB). You can calculate decibel values using a simple formula. How to convert a linear sound pressure, voltage or intensity scale into a logarithmic dB scale, which has a much smaller scope. Unfortunately, this conversion is often misunderstood and incorrect application leads to incorrect results. We show you how to calculate in decibels and use a number of numerical examples to explain how the conversion to decibels works.
Calculate decibels
With a simple formula, you can convert the ratio of two values to decibel:
- 10 * lg (x / x0)
- Here "lg" is the logarithm to base 10.
- The numerator "x" describes a control value, the denominator "x0" serves as a reference value. X and x0 must be the same physical quantity. Both must have the same unit.
- If the physical quantity is an energy quantity, such as electrical power (P) or sound intensity (I), x and x0 are simply replaced by P and P0 or I and I0 in the formula.
- In the case of so-called “field sizes” or “power root sizes”, such as electrical voltage (U) or sound pressure (p), x and x0 are replaced by the square of U and U0 or I and I0.
- For example 10 * lg (U² / U0²).
- The difference lies in the fact that energy sizes are proportional to the square of the field sizes, i.e. I ~ p².
- The formula 10 * lg (U² / U0²) can also be converted to 20 * lg (U / U0).
Decibel Examples
It is worth having a few ratios and corresponding decibel values as well as other basic facts in mind:
- The doubling of an energy quantity always corresponds to 10 * lg (2 * x0 / x0) = 3 dB.
- On the other hand, doubling a field size corresponds to 10 * lg ((2 * x0) ² / x0²) = 6 dB.
- A tenfold increase in power corresponds to 10 dB. A tenfold increase in AC voltage, on the other hand, is 20 dB.
- 60 dB means a thousandfold sound pressure and a millionfold sound energy (1000² = 1000 * 1000-fold).
- If a dB value is referred to as a "level", the reference value is fixed, for example 0.00002 Pa at absolute volume levels. Often the reference value corresponds to the maximum possible value, i.e. the scale ranges from undefined to negative values up to a maximum of 0 dB.
- Incidentally, decibel information does not have a physical unit. Finally, decibels indicate a ratio. The equivalent in colloquial language is "double". No matter whether twice as far, twice as fast or twice as difficult; double is always "times two" and not two meters, Herzt or Newton.
- For certain data, for example in dB (A) or dB (C), frequencies are weighted individually first before the above formula is applied.
- Ears are alternating pressure receivers and the radiated sound pressure of a loudspeaker is roughly proportional to its alternating voltage.
The next practical tips will help you to better understand the level values in Audacity and Wavelab.