About this calculator
The decibel (dB) is a logarithmic way of comparing two quantities, used for sound, radio signals, audio gear and electronics. Because it is logarithmic, you cannot add or subtract levels the usual way.
Choose what you need: turn a ratio into dB, turn dB into a ratio, add several sound levels together, or find how a level changes as you move closer or further from the source.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Power ratio of 2 is how many dB?
- Decibels (power, 10 × log)
- 3.0103 dB
- Decibels (voltage or sound pressure, 20 × log)
- 6.0206 dB
A power ratio of 2 is 3.0103 dB. A voltage or sound-pressure ratio of 2 is 6.0206 dB.
Show the working
- Power: dB = 10 × log₁₀(ratio) = 10 × log₁₀(2) = 3.0103.
- Voltage, current or sound pressure: dB = 20 × log₁₀(ratio) = 6.0206, because power goes with the square of amplitude.
What ratio is +3 dB?
- Power ratio
- 1.995262
- Voltage or pressure ratio
- 1.412538
3 dB is a power ratio of 1.995262, or a voltage or sound-pressure ratio of 1.412538.
Show the working
- Power ratio = 10^(dB ÷ 10) = 10^(0.3) = 1.995262.
- Voltage or pressure ratio = 10^(dB ÷ 20) = 1.412538.
Two 60 dB sources together
- Combined level
- 63.0103 dB
- Louder than the loudest alone by
- 3.0103 dB
2 sources (60, 60 dB) combine to 63.0103 dB.
Show the working
- Decibels are logarithmic, so you can't add them directly. Convert each to power: 10^(L ÷ 10), add the powers, then convert back: 10 × log₁₀(total).
- Total = 10 × log₁₀(10^6 + 10^6) = 63.0103 dB.
- Two equal sources always add 3 dB; ten equal sources add 10 dB.
80 dB at 1 m, how loud at 2 m?
- Level at distance 2
- 73.9794 dB
- Change
- -6.0206 dB
Moving from 1 to 2 from a point source changes the level by -6.0206 dB, from 80 dB to 73.9794 dB.
Show the working
- For a small source in open space the level falls by 6 dB each time the distance doubles (the inverse square law).
- Change = −20 × log₁₀(2 ÷ 1) = -6.0206 dB.
- Indoors, reflections make real levels fall more slowly.
The formulas
- Power: dB = 10 × log₁₀(P₂ ÷ P₁)
- Voltage, current or sound pressure: dB = 20 × log₁₀(V₂ ÷ V₁)
- Adding levels: 10 × log₁₀(10^(L₁÷10) + 10^(L₂÷10) + …)
- Distance: level falls by 20 × log₁₀(d₂ ÷ d₁)
Handy rules of thumb
- +3 dB is double the power (and only about 1.41 times the voltage)
- +6 dB is double the voltage or sound pressure
- +10 dB is ten times the power and sounds roughly twice as loud
- Two equal sources add 3 dB; ten equal sources add 10 dB
- Each doubling of distance from a small source costs 6 dB
Why there are two formulas
Power depends on the square of voltage or pressure, and a square becomes a factor of two in a logarithm. That is why amplitude ratios use 20 and power ratios use 10. Use the first row for power and the second for voltage, current or sound pressure.
Frequently asked questions
How do I convert a ratio to decibels?
For power, 10 × log₁₀(ratio). For voltage or sound pressure, 20 × log₁₀(ratio).
How do I add decibels?
Convert each to power, add the powers and convert back. Two equal levels add 3 dB.
Why does distance reduce sound by 6 dB per doubling?
Sound spreads over the surface of a sphere, whose area grows with the square of the distance. That gives 6 dB per doubling in open space.
What does 0 dB mean?
A ratio of exactly 1: no change. It does not mean silence.
Are negative decibels possible?
Yes. They mean the second quantity is smaller than the first.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.