About the Decibel Calculator
This decibel calculator handles the four jobs people most often need dB for: converting a power ratio to decibels, converting a voltage (or current, or sound-pressure) ratio to decibels, turning a dB figure back into power and voltage ratios, and combining several sound levels into one total. In power mode it also expresses the measured power in dBm.
It is built for audio and RF engineers, electronics students checking amplifier gain or cable loss, and anyone working with noise measurements who needs to know what two machines at 85 dB add up to. Decibels are logarithmic, so they cannot simply be added or averaged like ordinary numbers — the calculator does the conversion for you.
The voltage formula (20·log) assumes both voltages are measured across the same impedance, which is the usual convention for gain in a matched system. Sound levels are combined as incoherent (uncorrelated) sources, which is correct for separate machines, vehicles or loudspeakers playing different signals.
How to use the decibel calculator
- 1Choose what you want to calculate.
- 2Enter the measured and reference powers or voltages, a dB value, or a list of sound levels.
- 3Read the decibel result and the equivalent power and voltage ratios.
- 4Use the reference table to sanity-check common values like 3 dB and 6 dB.
Formula and method
A decibel is one tenth of a bel, the base-10 logarithm of a power ratio, so power ratios use 10·log₁₀. Voltage, current and sound pressure are amplitude quantities whose power goes with their square, so their ratio uses 20·log₁₀ — which is why +6 dB doubles voltage but +3 dB doubles power. Going backwards, the power ratio is 10^(dB/10) and the voltage ratio is 10^(dB/20).
To combine sound levels, each level is converted back to relative intensity (10^(L/10)), the intensities are added, and the sum is converted back to dB. Two equal sources therefore add 3.01 dB, and ten equal sources add 10 dB. The energy average divides the summed intensity by the number of levels before converting back. dBm expresses power relative to 1 milliwatt, so 1 W = 30 dBm.
- P₁, P₀
- Measured and reference power
- V₁, V₀
- Measured and reference voltage (same impedance)
- Lᵢ
- Individual sound level in dB
- L
- Combined sound level in dB
Worked examples
100 W relative to 1 W
A power ratio of 100 is 10 × log₁₀(100) = 20 dB. 100 W is 100,000 mW, which is 10 × log₁₀(100,000) = 50 dBm. The same 20 dB corresponds to a 10× voltage ratio.
Amplifier: 50 mV in, 2 V out
The voltage gain is 2 ÷ 0.05 = 40, and 20 × log₁₀(40) ≈ 32.04 dB. Into equal impedances that is a power gain of 40² = 1,600.
What does −3 dB mean?
10^(−3/10) ≈ 0.501, so −3 dB is half the power, and 10^(−3/20) ≈ 0.708 of the voltage. That is why a filter’s −3 dB cutoff is also called the half-power point.
Three machines at 85, 88 and 90 dB
Converting to intensities gives 10^8.5 + 10^8.8 + 10^9.0 ≈ 1.947 × 10⁹; 10 × log₁₀ of that is about 92.9 dB, not 263 dB. The energy-average level is 10 × log₁₀(1.947 × 10⁹ ÷ 3) ≈ 88.1 dB.
Frequently asked questions
How do you add decibels?+
Convert each level to intensity with 10^(L/10), add the intensities, and convert back with 10·log₁₀(sum). Two equal sources give +3 dB, so 85 dB plus 85 dB is about 88 dB, not 170 dB.
Why is it 10 log for power and 20 log for voltage?+
Power is proportional to voltage squared, and log(V²) = 2·log(V). Using 20·log for voltage makes a given dB value mean the same change whether you measure power or voltage across the same impedance.
How much louder is 10 dB?+
A 10 dB increase is ten times the sound intensity, and most listeners perceive it as roughly twice as loud. A 3 dB increase doubles the acoustic power but is only a just-noticeable change for many people.
What is dBm?+
dBm is power in decibels relative to 1 milliwatt. 0 dBm is 1 mW, 30 dBm is 1 W and −30 dBm is 1 µW. It is widely used for radio, fibre and audio signal levels.
What does −3 dB mean on a filter?+
It is the frequency where output power has fallen to half, or voltage to about 70.7%, of the passband level. That point defines the cutoff frequency of simple RC and LC filters.