Example 1
I = 1e-12 W/m² -> L = 0 dB.
Sound level calculator
Enter intensity I in W/m². You get the level L = 10 log10(I/I0). I = 10⁻⁶ at the 10⁻¹² threshold is 60 dB, a typical conversation. I itself is power over area, I = P/A.
Inverse, I from a dB label: I from L. Frequency shift in motion: Doppler f′. Wavelength: λ = v/f.
Result
Intensity I (W/m²) and Reference I0 (W/m², blank = 1e-12). The result shows up here.
How it works
The ear does not hear watts on a linear scale. Level L = 10 log10(I/I0) compresses a huge intensity range into decibels. I is wave power per unit area, I = P/A, in watts per square meter. Lab-quiet I0 is 10⁻¹² W/m², the conventional hearing threshold at 1 kHz. A blank second field takes that value.
Table talk: I = 10⁻⁶ W/m² and default I0 give L = 60 dB. A whisper at 10⁻¹⁰ is 20 dB. A street at 10⁻⁵ is 70 dB. A concert at 0.1 W/m² is 110 dB. I = 1 W/m² is 120 dB, the school-book pain threshold. Each ×10 in I is +10 dB.
I must be greater than zero. Typed I0 must be too. Zero and a negative value do not give a real logarithm. The calculator computes the raw ratio I/I0, with no A-weighting and no sones. A city sound meter often shows dBA, a different number.
If you know power and area, first I = P/A. A 0.01 W speaker spread evenly over 10 m² is I = 0.001 W/m² and L = 90 dB at I0 = 10⁻¹². Doubling I at the same I0 is +3 dB: 2e-6 and I0 = 1e-6 give L ≈ 3.0 dB.
Type I, for example 1e-6 or 0.000001, leave I0 blank, click Calculate. The result is 60 dB. To return to watts, open I from L and type 60. A comma and scientific 1e-6 both work.
Doppler changes frequency, not this L. Wavelength λ = v/f is about meters of wave, not decibels. Those cards sit nearby when a problem mixes a siren, λ, and level.
How to use
- Type intensity I in W/m². That is power over area, I = P/A. Conversation is about 1e-6, a whisper 1e-10, threshold 1e-12.
- You can leave I0 blank: the calculator uses 10⁻¹² W/m². Type your own I0 when you compare two intensities with each other.
- Click Calculate. 1e-6 and blank I0 give 60 dB. 1 W/m² is 120 dB. 0.1 W/m² is 110 dB.
- I must be positive. 1e-6, 0.000001 and 10⁻⁶ are the same value. +10 dB means ten times the intensity.
- When you only have a dB label, open I from L. Doppler and λ = v/f are about frequency and wavelength, not this L.
Formula
L = 10 log10(I / I0)
I > 0. Blank I0 = 10−12 W/m². Unit of L: dB.
Letters in L = 10 log10(I/I0)
Level squeezes watts into decibels: L = 10 log10(I/I0). I = 10⁻⁶ W/m² at the 10⁻¹² threshold is 60 dB, talk at a table.
- L
- Level in dB. 10⁻⁶ / 10⁻¹² is 60 dB; 10⁻¹⁰ is 20 dB; 1 W/m² is 120 dB.
- I
- Intensity in W/m², power over area. 1e-6 with blank I0 is that 60 dB conversation.
- I0
- Reference threshold. A blank field is 10⁻¹² W/m²; then I = 1e-6 builds exactly 60 dB.
Real-life examples
Example 2
I = 1e-10 W/m² -> L = 20 dB.
Example 3
I = 1e-6 W/m² -> L = 60 dB.
Example 4
I = 1e-5 W/m² -> L = 70 dB.
Example 5
I = 0.1 W/m² -> L = 110 dB.
Example 6
I = 1 W/m² -> L = 120 dB.
Example 7
I = 1e-8 W/m² -> L = 40 dB.
Example 8
I = 2e-6, I0 = 1e-6 -> L ≈ 3.0 dB.
Ways to use this calculator
- You type 1e-6 and leave I0 blank: 60 dB of conversation.
- You compare 1e-5 (street) with 0.1 (concert): +40 dB, ten thousand times in I, not “four times as loud”.
- You set I0 = I and see 0 dB: that is the same reference level.
Frequently asked questions
How many dB at I = 10⁻⁶ W/m² and blank I0?
L = 60 dB. I = 10⁻¹⁰ is 20 dB. I = 1 W/m² is 120 dB.
What is I, if I = P/A?
Wave power divided by area, in W/m². 0.01 W over 10 m² is I = 0.001 and L = 90 dB at I0 = 10⁻¹².
Is +10 dB twice as loud?
Intensity rises 10 times, not 2. 60 dB is 10⁻⁶ W/m²; 70 dB is 10⁻⁵. The ear often feels closer to a doubling; the formula counts I.
What is blank I0?
10⁻¹² W/m², the conventional 1 kHz threshold. A typed I0 must be positive.
Where is A-weighting (dBA)?
It is not here. L is the raw I/I0 ratio with no frequency filter. A city meter usually shows dBA.
How does this relate to I from L?
There you compute I from L. Here you compute L from I. Same constants, two directions.
What L at I = 2e-6 and I0 = 1e-6?
L = 10 log10(2) ≈ 3.0 dB. Doubling I is always about +3 dB.
Can I type 1e-6?
Yes. 1e-6, 0.000001 and 10⁻⁶ are the same I and 60 dB at blank I0.
What L at I = 0.1 W/m²?
110 dB at I0 = 10⁻¹². I = 1e-8 is 40 dB, I = 1e-5 is 70 dB.
Does Doppler change this result?
Doppler changes f, not I in this calculator. L comes from the I you type.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.