Decibel Calculator
Convert between decibels and ratios, add sound levels or find the level at a distance.
What this tool does
A power ratio in decibels is 10 × log10(P2 ÷ P1), and a voltage or sound-pressure ratio is 20 × log10(V2 ÷ V1). Doubling power is +3.01 dB, doubling amplitude is +6.02 dB, and two 60 dB sounds together make 63 dB, not 120. Pick a mode above and enter your values.
Converts between ratios and decibels, using the right multiplier for power and for amplitude.
Adds levels logarithmically and applies the inverse-square rule for distance.
How to use it
- Choose what to calculate.
- Enter the values the mode needs (the field labels say which).
- For adding levels, list the dB values separated by commas.
- Read the result and the note.
Why use this calculator
Handles the five decibel jobs in one tool: ratio to dB for power or amplitude, dB back to a ratio, adding several sound levels together, and the level at a different distance. Decibels are logarithmic, so everyday arithmetic does not work: two 60 dB sources are not 120 dB. A calculator avoids the common mistakes in audio, acoustics and electronics.
Why we built it
We built the decibel calculator to cover ratio to dB, dB to ratio, adding levels and distance in one place, with the right 10 log or 20 log. Check logs with the logarithm calculator and generate tones with the tone generator.
Handy alongside this: the Sound Level Meter.
Who this tool is for
- Audio engineers and musicians
- Students of sound and electronics
- People estimating noise from several sources
When to use it
- Adding the noise from several machines.
- Working out gain or loss in an audio or radio chain.
- Estimating how quiet a sound is at a greater distance.
- Checking homework on logarithms and sound.
How it works
Power: dB = 10 log10(P2 ÷ P1). Amplitude (voltage, current, sound pressure): dB = 20 log10(A2 ÷ A1), because power goes with the square of the amplitude. To add levels, convert each to power (10^(L/10)), sum, and convert back. For a small point source in open space, the level falls by 20 log10(r2 ÷ r1) with distance, about 6 dB each time the distance doubles.
Example: doubling power is 10 log10(2) = 3.01 dB, and doubling amplitude is 6.02 dB. Two 60 dB sources give 10 log10(2 × 10⁶) = 63.01 dB. A sound of 80 dB at 1 m is 73.98 dB at 2 m.
The distance rule assumes a small source in open space. Rooms, walls and large sources behave differently.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Calculate | Decibels from a power ratio (10 log) |
| First value (power or amplitude), or the dB value, or the level in dB | 1 |
| Second value, or the first distance | 2 |
| Second distance | 2 |
| Levels in dB to add together, separated by commas | 60, 60 |
With those inputs, the calculator returns:
- Level difference: 3.01 dB
- Ratio (second ÷ first): 2
What you give it, and what you get back
| Item | Details |
|---|---|
| Mode | Power ratio, amplitude ratio, dB to ratio, add levels or level at distance. |
| Values | The two values, a dB level, a list of levels or a level and two distances. |
| Output | The result in dB or as a ratio, with the supporting figure. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Two sources only add 3 dB | Decibels are logarithmic. | This is correct: doubling sound power adds about 3 dB. |
| A value must be above zero | A ratio needs positive values. | Check both values. |
| Level at distance is too low | Rooms reflect sound. | Use it as an open-space estimate only. |
Assumptions and limitations
- Ideal free-field distance model.
- No frequency weighting such as dBA.
Frequently asked questions
How do I add decibels?
Convert each to power with 10^(dB ÷ 10), add them, and convert the total back with 10 × log10.
Why is 3 dB a doubling?
Because 10 × log10(2) is about 3.01, and dB is a logarithm of the power ratio.
What is the difference between 10 log and 20 log?
Use 10 log for power and 20 log for voltage, current or sound pressure.
How does sound fall with distance?
By about 6 dB each time the distance doubles, in open space.
What is 0 dB?
A ratio of 1: no change.
Is my information sent anywhere?
No. The calculation runs in your browser and nothing leaves the page.