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Decibel Calculator
Use this free decibel calculator to turn ratios into decibels and back again. It covers the three jobs people actually need: power ratios to dB, amplitude and voltage ratios to dB, and adding two sound levels together. It also converts dBm to watts, so you can see what a transmitter or amplifier figure means in real power. Decibels are logarithmic, which is why doubling a sound adds only 3 dB, and this calculator does the log work for you.
Power ratio 10 means the second power is 10 times the first: 10 × log10(10) = 10 dB.
How it works
A decibel is not a unit like a metre or a second; it is a way of comparing two values on a logarithmic scale. The formula for power is dB = 10 × log10(P2 ÷ P1), where P2 is the power you are measuring and P1 is the reference power. A ratio of 10 gives 10 × log10(10) = 10 dB, because log10(10) is 1. A ratio of 100 gives 20 dB, a ratio of 1,000 gives 30 dB, and a ratio of 2 gives 3.01 dB. Each tenfold step in power adds exactly 10 dB, and each doubling adds 3.01 dB, which is why the scale can describe everything from a whisper to a jet engine in numbers from 0 to about 140.
Amplitude and voltage use a different multiplier: dB = 20 × log10(A2 ÷ A1). The reason is that power is proportional to amplitude squared, so taking the log of a squared quantity brings down a factor of 2, turning the 10 into a 20. A 20 times amplitude ratio is 20 × log10(20) = 26.02 dB, which is the same as a 400 times power ratio, because 20 squared is 400 and 10 × log10(400) is also 26.02 dB. Use the 20 log form for voltage, current, sound pressure, and any other amplitude-like quantity, and the 10 log form for power, intensity, and energy. Mixing them up is the most common decibel mistake, and it doubles or halves the answer.
Adding decibels is the part that surprises everyone. You cannot add the numbers directly, because they are logarithms. Two 100 dB sources together are not 200 dB; they are 103.01 dB. The rule is to convert each level back to power, add the powers, and convert back: total = 10 × log10(10^(L1/10) + 10^(L2/10)). Two equal sources double the power, and doubling adds 3.01 dB, so any equal pair is the single level plus 3.01 dB. Ten equal sources add 10 dB, and a hundred add 20 dB. If one source is 10 dB louder than the other, the quieter one adds less than half a decibel to the total, which is why the loudest source dominates what you hear.
The reference matters. A plain dB is only a ratio, but dBm fixes the reference at 1 milliwatt, so 0 dBm is 1 mW, 10 dBm is 10 mW, 20 dBm is 100 mW, and 30 dBm is 1 W. Radio and Wi-Fi equipment is usually rated in dBm, and this calculator converts dBm to watts and milliwatts so you can compare it with a charger or a light bulb. dBV is the same idea for voltage, with a 1 volt reference, and dB SPL, the sound level you see on a meter, is referenced to 20 micropascals, the quietest sound an average ear can hear. The calculator’s dB-to-ratio mode reverses the process: 10 dB is a power ratio of 10, 20 dB is a ratio of 100, and 3 dB is a ratio of about 2.
Human hearing is logarithmic too, which is why the decibel fits it so well. A change of about 1 dB is the smallest most people can notice, a change of 3 dB is clearly noticeable, and a change of 10 dB sounds about twice as loud, even though it is ten times the power. That gap between power and perception is worth remembering when you buy speakers: an amplifier with twice the watts is only 3 dB louder, barely noticeable, while a speaker that is 3 dB more efficient gives the same gain for free. For hearing safety, 85 dB over an 8-hour working day is the usual exposure limit, and every 3 dB above that halves the safe time.
Amplitude / voltage: dB = 20 × log10(A2 ÷ A1)
Add levels: L = 10 × log10(10^(L1/10) + 10^(L2/10))
dBm to watts: P (W) = 10^((dBm − 30) ÷ 10)
Common sound levels
| Sound | Level (dB) |
|---|---|
| Quiet room, breathing | 20–30 |
| Normal conversation | 60 |
| Busy traffic | 80–85 |
| Motorcycle, lawn mower | 90–95 |
| Concert, chainsaw | 110–115 |
| Jet take-off (nearby) | 130–140 |
Worked example
An amplifier’s output power is 10 times its input power, a microphone’s voltage is 20 times its reference, and two 100 dB speakers play together. What is each result in decibels?
Step 1: Power — 10 × log10(10) = 10 × 1 = +10 dB.
Step 2: Amplitude — 20 × log10(20) = 20 × 1.3010 = +26.02 dB.
Step 3: Adding levels — 10 × log10(10^(100/10) + 10^(100/10)) = 10 × log10(2 × 10^10) = 103.01 dB.
Enter a power ratio of 10 in the calculator and it gives +10.00 dB. Switch to amplitude mode with a ratio of 20 and it gives +26.02 dB. Switch to add mode with 100 dB and 100 dB and it gives 103.01 dB. All three answers match the worked steps exactly.
FAQ
How do you calculate decibels from a power ratio?
Use 10 times the base-10 logarithm of the power ratio: dB = 10 × log10(P2 ÷ P1). A power ratio of 10 gives 10 × log10(10) = 10 dB, and a ratio of 100 gives 20 dB. Every tenfold increase in power adds exactly 10 dB.
Why is amplitude 20 log and power 10 log?
Because power is proportional to amplitude squared. Taking the log of a square brings down a factor of 2, so 10 × log10(amplitude squared) becomes 20 × log10(amplitude). A 20 times amplitude ratio is therefore 20 × log10(20) = 26.02 dB, the same as a 400 times power ratio.
What happens when you add 100 dB and 100 dB?
You get 103.01 dB, not 200 dB. Decibels add by power, not by number: two equal sources double the power, and doubling power adds 10 × log10(2) = 3.01 dB. So 100 dB plus 100 dB is 103.01 dB, and 90 dB plus 90 dB is 93.01 dB.
How many decibels is twice as loud?
Twice the power is 3.01 dB more, but twice as loud to human hearing is roughly 10 dB more, which is ten times the power. That is why a 3 dB change is just noticeable, a 10 dB change sounds about twice as loud, and a 20 dB change sounds about four times as loud.
What is the difference between dB, dBm and dBV?
A plain dB is a ratio between two values with no fixed reference. dBm is power measured against 1 milliwatt, so 0 dBm is 1 mW and 30 dBm is 1 W. dBV is voltage measured against 1 volt, so 0 dBV is 1 V. This calculator works with plain dB ratios and also converts dBm to watts.