Decibel Calculator

Results

At 85.0 dB (if A-weighted), NIOSH's 3 dB rule limits exposure to about 8 h a day; its recommended limit is 85 dBA for 8 hours.

How to Use the Decibel Calculator

1. 1. Pick the job. Sound level converts between dB, intensity and pressure. Add or subtract levels combines noise sources. Distance applies the inverse-square law. Ratios and absolute levels handle power and voltage in electronics and audio.
2. 2. Enter what you know. Intensity runs from pW/m² to W/m², pressure from µPa to kPa, distances in cm, m, km or feet, and powers and voltages in watts, dBm, volts or dBV.
3. 3. Choose decimal places. Sound levels are normally quoted to one decimal place; choose 0 to 3.
4. 4. Read the result and the working. Each result is written out as a formula with your numbers, so you can copy the method into a lab report.

What a Decibel Is

A decibel (dB) is ten times the logarithm (base 10) of a ratio of two powers: dB = 10 log₁₀(P₂ ÷ P₁). The scale is logarithmic because the ear and many instruments respond to ratios, not differences, so a huge range of powers — a trillion to one for sound — fits into a few hundred units. Every factor of 10 in power is 10 dB, and doubling the power adds about 3 dB (10 log₁₀ 2 = 3.01).

Quantities whose square is proportional to power — voltage, current, sound pressure — use 20 log₁₀ instead, so doubling the voltage adds about 6 dB. A decibel on its own describes a ratio; it becomes an absolute level once a reference is fixed. For sound that is the threshold of hearing: I₀ = 10⁻¹² W/m² for intensity, or 20 µPa for pressure in air, which give the same level (dB SPL).

Worked Examples

• Level to intensity and pressure. 85 dB is I = 10⁻¹² × 10^8.5 = 3.162 × 10⁻⁴ W/m² and p = 20 µPa × 10^(85/20) = 0.3557 Pa. NIOSH recommends no more than 8 hours a day at 85 dBA, and it halves the allowed time for every 3 dBA more.
• Adding sources. Machines of 85, 82 and 79 dB run together: 10 log₁₀(10^8.5 + 10^8.2 + 10^7.9) = 87.4 dB. Levels add by energy: two equal 60 dB sources make 63 dB, not 120.
• Subtracting the background. A reading of 70 dB with the machine on and 60 dB with it off means the machine alone is 10 log₁₀(10⁷ − 10⁶) = 69.5 dB.
• Distance. A source measuring 90 dB at 1 m is 90 − 20 log₁₀(10) = 70 dB at 10 m. Each doubling of distance costs 6.02 dB.
• Electronics. 20 dBm is 100 mW, 30 dBm is 1 W and 0 dBm is 1 mW. +4 dBu, the professional audio line level, is 1.228 V RMS; −10 dBV, the consumer level, is 0.316 V.

Limits and Conventions

• Adding assumes uncorrelated sources. Two coherent tones in phase can add more (up to +6 dB), and out of phase they can cancel.
• The distance rule is for free field. Outdoors with no reflections, a point source follows the inverse-square law. Indoors, reverberation slows the decline; a long line source such as a busy road loses only 3 dB per doubling.
• A-weighting is not applied. dBA adjusts levels toward the ear's sensitivity. This calculator treats every dB as an unweighted level, so use it on a number you have already weighted if you need dBA.
• Reference pairs. I₀ = 10⁻¹² W/m² and p₀ = 20 µPa match for air at a characteristic impedance of about 400 Pa·s/m, which is close enough that the two levels are treated as equal.

Frequently Asked Questions

How do you add decibels?

Not by simple addition. Convert each level to a power with 10^(L/10), add them, and convert back with 10 log₁₀. Two equal sources add 3 dB, ten equal sources add 10 dB, and a source 10 dB quieter than another adds only 0.4 dB to it.

What is the formula for the decibel level of sound?

L = 10 log₁₀(I ÷ I₀), with I₀ = 10⁻¹² W/m². In terms of pressure it is L = 20 log₁₀(p ÷ p₀), with p₀ = 20 µPa. A sound ten times as intense is 10 dB louder; one a hundred times as intense is 20 dB louder.

How much does sound drop with distance?

For a point source in open air, 6 dB for each doubling of distance, since the intensity falls with the square of the distance (20 log₁₀ 2 = 6.02). From 1 m to 10 m the drop is 20 dB; from 1 m to 100 m it is 40 dB.

What is the difference between 10 log and 20 log?

Use 10 log for power and intensity, and 20 log for quantities whose square is proportional to power, such as voltage, current and sound pressure. Both give the same decibels for the same physical change, since power goes as the square of amplitude.

What do dBm, dBW, dBV and dBu mean?

They are decibels relative to a fixed reference: dBm to 1 milliwatt, dBW to 1 watt, dBV to 1 volt RMS and dBu to 0.7746 volt RMS. So 0 dBm is 1 mW, 30 dBm is 1 W, and dBW = dBm − 30.

What decibel level is harmful to hearing?

NIOSH recommends limiting exposure to 85 dBA averaged over an 8-hour day, and halving the time for every 3 dBA more, so 100 dBA is limited to about 15 minutes. Levels of about 120 dB and above can cause pain and immediate damage.