What is the decibel formula for sound intensity?

Sound intensity level in decibels is L = 10 times log base 10 of (I divided by I0), where I is the measured intensity in watts per square metre and I0 is the reference intensity of 1 times 10 to the power of negative 12 watts per square metre, which corresponds to the threshold of human hearing.

How do you add decibels from two sources?

You cannot add decibels directly. To combine two incoherent sources, convert each dB level to its intensity using I = I0 times 10 to the power (L/10), add the two intensities, then convert the total back to decibels. Two identical sources each at 60 dB produce a combined level of about 63 dB, not 120 dB.

What is 60 dB in watts per square metre?

60 dB corresponds to an intensity of 1 times 10 to the power of negative 6 watts per square metre, which is 1 microwatt per square metre. This is a moderate sound level similar to normal conversation at about one metre distance.

Decibel Calculator

The decibel scale is a logarithmic measure of sound intensity that compresses the enormous range of intensities audible to humans into a manageable set of numbers. The threshold of hearing is defined as the reference intensity I0, equal to 1 times 10 to the power of negative 12 watts per square metre. The sound level in decibels is then L = 10 times log base 10 of (I divided by I0). Because the scale is logarithmic, a tenfold increase in intensity adds 10 dB; a doubling of intensity adds about 3 dB. This calculator has three modes. The first converts intensity in watts per square metre to decibels. The second reverses the calculation, converting a dB level back to the corresponding intensity. The third mode combines two incoherent sound sources by converting each level to intensity, adding the intensities, and converting the sum back to decibels. You cannot add dB values arithmetically: two identical 60 dB sources together produce about 63 dB, not 120 dB. Enter the intensity in scientific notation or decimal form. The calculator is used by physics and engineering students, acoustic consultants, audio engineers and anyone working with noise measurement. The reference intensity used throughout is 1e-12 W/m squared, which is the standard for airborne sound.

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Mode

Intensity I (W/m²)

Sound level L (dB) - fordB to intensity mode

Source 1 level (dB) - foradd mode

Source 2 level (dB) - foradd mode

60.00 dB

sound intensity level

Intensity I1.00e-6 W/m²

Ratio I/I₀1,000,000

Reference intensity I₀ = 1 x 10⁻¹² W/m² (threshold of hearing). Sources are treated as incoherent (intensities add, phases do not).

How it works

The decibel formula for sound intensity is L = 10 log₁₀(I / I₀) where I₀ = 1 x 10⁻¹² W/m². To convert dB back to intensity: I = I₀ x 10^(L/10). To combine two incoherent sources at levels L1 and L2: convert each to intensity, add them (I_total = I1 + I2), then convert back: L_total = 10 log₁₀(I_total / I₀). An increase of 3 dB approximately doubles the perceived intensity; an increase of 10 dB is perceived as roughly twice as loud by most listeners.

Worked example

A sound has intensity I = 1 x 10⁻⁶ W/m². The intensity level is L = 10 x log₁₀(1e-6 divided by 1e-12) = 10 x log₁₀(1,000,000) = 10 x 6 = 60.00 dB. The ratio I/I₀ is 1,000,000. These match the defaults pre-filled above.

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