What this calculator does
Decibels are logarithmic, which is the single fact that explains everything odd about them. Human hearing spans a range of intensities so vast, around a trillion to one, that a linear scale would be unusable, so the decibel compresses it into a range of about 0 to 120.
The consequence is that decibels do not add the way ordinary numbers do. Doubling the sound intensity adds only 3 dB, and two identical sources together are 3 dB louder than one, not twice as loud.
The formula
Take the ratio of the sound intensity to the reference intensity of 1 × 10⁻¹² watts per square metre, which is roughly the quietest sound a healthy ear can detect, then take ten times its base-ten logarithm.
| Term | Meaning |
|---|---|
| Decibel (dB) | A logarithmic unit comparing a quantity against a reference. For sound intensity the reference is the threshold of hearing. |
| Threshold of hearing | The reference intensity of 1 × 10⁻¹² W/m², defined as 0 dB. |
| Intensity | Sound power passing through a unit area, in watts per square metre. |
The inputs explained
| Field | What to enter |
|---|---|
| Sound intensity (W/m²) | The sound intensity in watts per square metre. Ordinary conversation is around a millionth of a watt per square metre. |
When to use it
Interpreting a noise measurement
A meter reading in decibels corresponds to an intensity that is far more extreme than the number suggests, and converting back shows by how much.
Understanding why quietening is hard
Removing half the sound energy only reduces the level by 3 dB, which is barely perceptible, which is why noise control is so difficult.
Comparing two sound sources
The difference in decibels translates into a multiplying factor in intensity, and the factor is much larger than the difference implies.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What decibel levels do different intensities give?
A range of sound intensities across the audible scale.
| Intensity (W/m²) | Sound level | Level if intensity doubled |
|---|---|---|
| 1e-12 | 0.0 dB | 3.0 dB |
| 1e-9 | 30.0 dB | 33.0 dB |
| 1e-6 | 60.0 dB | 63.0 dB |
| 1e-3 | 90.0 dB | 93.0 dB |
| 1e+0 | 120.0 dB | 123.0 dB |
Questions
Why does doubling the sound only add 3 dB?
Because the scale is logarithmic and ten times the logarithm of two is about 3. The energy genuinely doubled; the decibel scale simply reports changes as ratios rather than as differences.
Is 10 dB louder twice as loud?
Roughly, as perceived. Ten decibels is a tenfold increase in intensity, and human hearing happens to judge that as approximately a doubling in loudness. Perceived loudness and measured intensity are not the same thing.
Why can decibel values be negative?
Because the scale is referenced to the threshold of hearing rather than to zero sound. Anything quieter than that threshold gives a negative value, which is perfectly valid and simply means inaudible to a typical ear.
How do I add two sound sources?
Not by adding the decibel figures. Convert each back to intensity, add the intensities, then convert the total back to decibels. Two equal sources come out 3 dB above one, not double the figure.
For the pitch of a sound rather than its loudness, see the Doppler effect calculator. For the same logarithmic idea applied to acidity, see the pH calculator.