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Decibel Calculator

dB to Ratio, Adding Levels and Distance Drop

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How the Decibel Calculator works

This decibel calculator does the four everyday decibel jobs. It converts a power or voltage ratio to dB, converts a dB change back to a ratio, adds the levels of several sound sources the correct logarithmic way, and works out how much quieter a sound gets as you move away from it. Choose the calculation, enter the numbers and the answer updates as you type.

Decibels compare two quantities on a logarithmic scale, which is why 3 dB is a doubling of power and why two 80 dB machines together make 83 dB, not 160.

How the decibel calculator works

There are two versions of the formula. For power-like quantities (watts, intensity) the level change is 10 × log10(ratio). For field quantities (voltage, sound pressure) it is 20 × log10(ratio), because power goes with the square of voltage. Going back, the power ratio is 10^(dB ÷ 10) and the voltage ratio is 10^(dB ÷ 20).

First example. Doubling amplifier power from 50 W to 100 W is a ratio of 2, so 10 × log10(2) = +3.01 dB. Doubling the voltage is +6.02 dB. To sound roughly twice as loud a sound needs about +10 dB, which is ten times the power.

Second example. Adding sources: incoherent sounds add by power, so convert each level to 10^(L ÷ 10), sum, and take 10 × log10 of the total. Two 80 dB sources give 83.01 dB; 85, 82 and 80 dB give about 87.6 dB. A source 10 dB quieter than the loudest adds less than half a decibel.

Distance. From a small source in open air, sound pressure falls with the inverse square law: the change is −20 × log10(d2 ÷ d1), about −6 dB for every doubling of distance. A speaker measuring 100 dB at 1 metre gives about 88 dB at 4 metres. Rooms reflect sound, so indoors the drop is smaller.

How many decibels is double? For power, 3 dB; for voltage or pressure, 6 dB; for perceived loudness, about 10 dB. Knowing which one a spec sheet means avoids most decibel confusion.

Decibels to power and voltage ratios

Level change Power ratio Voltage ratio
-40 dB 0.0001× 0.01×
-30 dB 0.001× 0.03162×
-20 dB 0.01× 0.1×
-12 dB 0.0631× 0.2512×
-10 dB 0.1× 0.3162×
-6 dB 0.2512× 0.5012×
-3 dB 0.5012× 0.7079×
-1 dB 0.7943× 0.8913×
0 dB 1× 1×
+1 dB 1.259× 1.122×
+2 dB 1.585× 1.259×
+3 dB 1.995× 1.413×
+4 dB 2.512× 1.585×
+5 dB 3.162× 1.778×
+6 dB 3.981× 1.995×
+9 dB 7.943× 2.818×
+10 dB 10× 3.162×
+12 dB 15.85× 3.981×
+15 dB 31.62× 5.623×
+20 dB 100× 10×
+30 dB 1,000× 31.62×
+40 dB 10,000× 100×
+60 dB 1,000,000× 1,000×

FAQ

What does adding 3 dB mean?

It means doubling the power. Two identical incoherent sources together are 3 dB louder than one, and a 200 W amplifier is 3 dB louder than a 100 W one at the same settings. Most listeners hear 3 dB as a small but clear increase, not as twice as loud.

Why is voltage 20 log and power 10 log?

Power is proportional to the square of voltage or sound pressure, and squaring inside a logarithm doubles the result. So a voltage ratio of 2 is a power ratio of 4, which is 6.02 dB either way you calculate it, keeping the two scales consistent.

How much does sound drop with distance?

From a small source outdoors, about 6 dB each time the distance doubles, following the inverse square law. A line source such as a busy road drops about 3 dB per doubling instead. Indoors, reflections reduce the drop once you are beyond a few metres.

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