Decibel Calculator
Add sound levels in decibels, convert dB to power and amplitude ratios, find the level at another distance, and convert dBm to watts.
Result…
How it's calculated
Adding: L = 10 log₁₀ Σ 10^(Lᵢ ÷ 10) Power: dB = 10 log₁₀(P₂ ÷ P₁); amplitude: dB = 20 log₁₀(A₂ ÷ A₁) Distance: L₂ = L₁ − 20 log₁₀(r₂ ÷ r₁) dBm = 10 log₁₀(P ÷ 1 mW), P = 10^((dBm − 30) ÷ 10) W
The decibel is a logarithmic way to write a ratio: ten times the base-10 logarithm of a power ratio, or twenty times that of an amplitude ratio such as sound pressure or voltage. Because it is logarithmic, levels from separate sources cannot be added directly: they are turned back into energies, summed and converted again, so two 90 dB machines make about 93 dB. The same idea gives the drop with distance from a small source in open air, about 6 dB each time the distance doubles, and the absolute power scales dBm (relative to 1 milliwatt) and dBW used in radio and audio.
Your numbers, step by step
About the Decibel calculator
This decibel calculator covers four everyday decibel jobs. It adds the levels of separate sound sources, such as machines in a workshop or speakers playing different material, by turning each level back into energy, summing and converting again. It converts between decibels and power ratios (10 log₁₀) or amplitude ratios such as voltage and sound pressure (20 log₁₀). It estimates the level at another distance from a small source in open space with the inverse-square law, about 6 dB lower for each doubling of distance. It also converts dBm to watts and milliwatts and back, as used for radio transmitters, receivers and audio gear. Distances can be in metres, feet or any other unit, as long as both use the same one. The steps show every logarithm with your numbers, so the result is easy to check.
How to use it
- Choose what to “Find”: “Add levels”, “dB ↔ ratio”, “Level at a distance” or “dBm ↔ watts”.
- To add, type the “Levels to add (dB)” separated by commas.
- For a ratio, pick what “I know” (decibels, a power ratio or an amplitude ratio) and enter the “Value”.
- For distance, enter the “Level at the first distance”, the “First distance” and the “Second distance” in the same unit.
- For radio power, pick dBm or watts and enter the “Power level” or the “Power”.
Worked example
Three machines measure 90, 90 and 85 dB. Combined: 90 + 10 × log₁₀(1 + 1 + 10^(−0.5)) = 93.65 dB, only 3.65 dB above the loudest. A source measuring 100 dB at 1 m gives 100 − 20 × log₁₀(8 ÷ 1) = 81.94 dB at 8 m, three doublings of about 6 dB each. An amplitude ratio of 2 is 20 × log₁₀(2) = 6.02 dB, which is a power ratio of 4, and 20 dBm is 0.1 W (100 mW, or −10 dBW).
Updated
Questions people ask
How do you add decibels together?
Convert each level to an energy with 10^(L ÷ 10), add those, and convert back with 10 × log₁₀ of the total. Two equal sources give 3 dB more than one, not double the number; the Wikipedia decibel article gives the same rule.
When do I use 10 log and when 20 log?
Use 10 log₁₀ for power-like quantities such as watts and sound intensity, and 20 log₁₀ for amplitude-like quantities such as voltage, current and sound pressure, because power goes with the square of amplitude.
How much does sound drop when the distance doubles?
From a small source in open space, about 6 dB per doubling of distance, since sound pressure falls in proportion to distance and intensity with its square, as the inverse-square law describes. Indoors, reflections keep levels higher, and a long line source such as a busy road drops about 3 dB per doubling.
How do I convert dBm to watts?
P in watts = 10^((dBm − 30) ÷ 10), so 0 dBm is 1 mW, 30 dBm is 1 W and every 10 dB is a factor of 10. To go back, dBm = 10 × log₁₀(P ÷ 1 mW).
Can I add levels of identical signals this way?
Not if they are in phase, such as one signal fed to two speakers next to each other: they can add up to 6 dB at some points and cancel at others. The energy sum assumes unrelated sources. To work with the frequency of a sound, use the frequency calculator.
What are the limits of these sound level estimates?
They are idealised: real rooms, barriers, wind, air absorption and the weighting of your meter (dBA or dBC) all change the result. For hearing protection or legal noise limits, rely on a calibrated measurement and the rules where you live.