How to use the decibel calculator
- Choose a conversion: power ratio to dB, amplitude ratio to dB, dB to a ratio, sound pressure to dB, adding sound levels, or the level at another distance.
- Enter the values the mode needs. For ratios, use the same unit for both numbers.
- For adding sound levels, list each level on its own line.
- Read the answer and the steps. The formula used is shown with your numbers.
Formula
Power: dB = 10 x log10(P2 / P1)
Voltage, current or pressure: dB = 20 x log10(A2 / A1)
Sound pressure level: Lp = 20 x log10(p / 0.00002 Pa)
Adding levels: L = 10 x log10(sum of 10^(Li / 10))
Distance in open space: L2 = L1 - 20 x log10(r2 / r1)
Decibels compare two values on a logarithmic scale. The factor is 10 for power quantities and 20 for amplitude quantities, since power goes with the square of amplitude.
Worked example
A power ratio of 200 / 2 = 100 is 20 dB, and an amplitude ratio of 100 is 40 dB. A halving of power is -3.0103 dB. Going back, 20 dB is a power ratio of 100 and an amplitude ratio of 10.
A sound pressure of 0.2 Pa compared with 20 micropascals is 80 dB SPL. Sources of 80, 80 and 70 dB at one spot add up to 83.2222 dB, not 230. A source of 90 dB at 1 meter is 71.9382 dB at 8 meters, about 6 dB lower for each doubling of distance.
Why decibels use a logarithm
The range of sounds and signals people deal with is huge, so a log scale compresses it. Every 10 dB is a tenfold change in power, and every 20 dB is a tenfold change in amplitude. Three decibels is roughly a doubling of power. Because the scale is logarithmic, levels cannot be added directly. Two equal sources add 3.0103 dB to the level of one.
Sound levels in air
The usual reference for sound pressure in air is 20 micropascals, close to the quietest sound a young person can hear. A level in dB SPL says how many times larger the pressure is than that reference, on the 20 log scale. Weighted scales such as dBA, which adjust for the ear's sensitivity, are not applied here. Real rooms reflect sound, so the distance rule in this tool is for open space only.
Related tools
For general math use the scientific calculator, and for electrical ratios see the Ohm's law calculator. A change between two values can also be expressed with the percent change calculator.
Assumptions and limits
- Power ratios use 10 log10 and amplitude ratios use 20 log10. These are the standard definitions.
- Sound pressure level uses a reference of 20 micropascals, the standard reference for air.
- Adding levels assumes the sources are separate and do not interfere, and that all levels are measured at the same point.
- The distance rule assumes a point source in open space with no reflections.
Frequently asked questions
How do you calculate decibels?
Take 10 times the base 10 log of a power ratio, or 20 times the base 10 log of an amplitude ratio such as voltage.
How do you add decibels?
Convert each level to a power with 10 raised to the level over 10, add the powers, then take 10 times the log of the sum.
What does a 3 dB change mean?
A doubling or halving of power. For amplitude, a change of 6 dB is about a doubling.
How much does sound drop with distance?
In open space, about 6 dB each time the distance doubles. Indoors, reflections reduce the drop.