Decibel calculator
Add sound levels, adjust for distance, or check safe exposure time.
How do you add decibels?
Not arithmetically — convert each level to intensity, add, and convert back: L = 10 log₁₀(Σ 10^(Lᵢ/10)). Two 90 dB sources together make 93 dB, not 180 dB.
How does sound drop with distance?
From a point source in open air, the level falls by 20 log₁₀(r₂ ÷ r₁) — about 6 dB each time the distance doubles. Rooms and walls change this.
How long can I be exposed to a noise level?
NIOSH recommends no more than 85 dBA averaged over 8 hours, halving the time for every 3 dB more: 88 dBA for 4 hours, 94 dBA for 1 hour, 100 dBA for 15 minutes.
What is the OSHA limit?
OSHA’s legal limit is 90 dBA for 8 hours, halving the time for every 5 dB: 95 dBA for 4 hours, 100 dBA for 2 hours, 115 dBA for 15 minutes or less. Employers need a hearing conservation program from 85 dBA averaged over 8 hours.
What is a decibel?
A logarithmic measure of sound intensity: β = 10 log₁₀(I ÷ I₀), with I₀ = 10⁻¹² W/m², about the quietest sound people can hear at 1,000 Hz. Every 10 dB is ten times the intensity.
Why do two equal sounds add only 3 dB?
Because doubling the intensity is a factor of 2, and 10 log₁₀(2) is about 3.01. Two 85 dB sources together give 88.0 dB, and three 70 dB sources give 74.8 dB. A 90 dB source plus an 80 dB source gives only 90.4 dB: the quieter one adds about 0.4 dB, which is why removing the lesser source rarely helps.
What does the A in dBA mean?
It means the sound level was measured with A-weighting, a filter that follows the ear's lower sensitivity to low and very high frequencies. Hearing-protection limits such as those from OSHA and NIOSH are stated in dBA. A plain dB value with no weighting does not tell you how loud a sound seems to the ear.
The formulas
The sound intensity level is β = 10 log₁₀(I ÷ I₀) with I₀ = 10⁻¹² W/m², so a ratio of 10 in intensity is 10 dB and a ratio of 100 is 20 dB. To combine levels, convert each to a relative intensity, 10^(L ÷ 10), add them and convert back. In open air a point source's level changes by 20 log₁₀(r₂ ÷ r₁) with distance, about 6 dB per doubling, because intensity falls with the square of the distance. The permissible exposure time halves for each 3 dB (NIOSH) or 5 dB (OSHA) above the base level.
Worked example: a 94 dB source and the exposure limits
Suppose a machine measures 94 dB at 1 m. At 4 m the level is 82.0 dB, at 10 m 74.0 dB. Two identical machines together read 97.0 dB at the same spot. At a steady 95 dBA a worker may be exposed for 0.79 hours by the NIOSH recommended limit (85 dBA over 8 hours, 3 dB exchange rate) but 4.0 hours by the OSHA permissible limit (90 dBA over 8 hours, 5 dB exchange rate). At 100 dBA the two limits are 15 minutes and 120 minutes.
Common mistakes
Adding decibels like ordinary numbers is the classic error: 90 dB plus 90 dB is 93 dB, not 180 dB. The 6 dB per doubling rule holds only for a point source in the open; inside a room, reflections keep the level from falling as fast. Another is mixing dB SPL with dBA, or applying a limit to a level that fluctuates: the exposure limits use a time-weighted average, not the loudest reading.
Sources: NIOSH, Criteria for a Recommended Standard: Occupational Noise Exposure (DHHS/NIOSH 98-126); OSHA 29 CFR 1910.95 (occupational noise exposure, Table G-16a); OpenStax University Physics, Volume 1, chapter 17 (sound intensity level). Related: speed of sound calculator, Doppler effect calculator, standing wave calculator and radiation dose calculator.