Decibel CalculatordB = 10 log₁₀(P₁ ÷ P₀)
Decibels compare two levels on a logarithmic scale: dB = 10 log₁₀(power ratio), or 20 log₁₀ for voltage and sound-pressure ratios. Every +3 dB doubles power, +10 dB is ten times the power, and two equal 80 dB sources make 83 dB, not 160. Convert ratios to decibels, add up to four sound sources, estimate how a level falls with distance and see the NIOSH safe exposure time.
Formula verified against CDC / NIOSH — Noise and Occupational Hearing Loss · OpenStax — University Physics, Volume 1
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Levels & ratios
Sound levels in dB SPL (sound pressure level).
Step-by-step working
What is decibel?
A decibel (dB) is a logarithmic unit that expresses how much bigger or smaller one power level is than another. In sound, decibels compare a pressure with the faintest sound a healthy ear can hear.
Because the scale is logarithmic, a 10 dB rise is ten times the power. Decibels are used for sound, amplifier gain, radio signal strength and fibre-optic loss.
Quick answers
How do you add decibels?
Convert to intensities, add, and convert back: L = 10 log₁₀(10L₁/10 + 10L₂/10). Two 90 dB sources give 93 dB.
How many decibels is twice as loud?
About +10 dB sounds twice as loud to most listeners, even though it is 10× the power. +3 dB is double the power but only just noticeable.
How much does sound decrease with distance?
Outdoors, about 6 dB per doubling of distance from a point source. Going from 2 m to 20 m cuts 20 dB.
How many dB is safe for hearing?
NIOSH recommends 85 dBA for 8 hours at most, halving the time for each extra 3 dB. Above 100 dB the safe daily dose is under 15 minutes.
Decibel formulas
Reference for dB SPL: p₀ = 20 µPa, the threshold of hearing.
| Symbol | Meaning | SI unit |
|---|---|---|
| L | Level | dB |
| P, P₀ | Power and reference power | W |
| V, p | Voltage or sound pressure | V, Pa |
| r | Distance from the source | m |
How to add decibels
- Convert each level to relative intensity: 10L/10.
- Add the intensities together.
- Convert back: 10 × log₁₀(sum).
- Shortcut: two equal sources add 3 dB; a source 10 dB quieter adds only 0.4 dB.
Worked example: two 80 dB machines
Two machines each produce 80 dB at your position. What is the combined level?
A 100 dB source measured at 1 m falls to 100 − 20 log₁₀(10) = 80 dB at 10 m. Under the NIOSH rule, 94 dB is safe for only 1 hour a day, and 100 dB for 15 minutes.
NIOSH recommended exposure limits
85 dBA for 8 hours, halving for every 3 dB increase.
| Level (dBA) | Max daily exposure | Example |
|---|---|---|
| 85 | 8 hours | Heavy city traffic |
| 88 | 4 hours | Food blender |
| 91 | 2 hours | Lawnmower |
| 94 | 1 hour | Motorcycle |
| 100 | 15 minutes | Nightclub |
| 110 | ≈ 1.5 minutes | Rock concert |
| 120 | ≈ 9 seconds | Thunder, sirens |
Common mistakes to avoid
- Adding decibels arithmetically. 80 dB + 80 dB = 83 dB, not 160 dB.
- Using 10 log for voltages. Amplitude ratios use 20 log because power goes with amplitude squared.
- Expecting −6 dB per doubling indoors. Reflections reduce the drop-off in rooms.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Decibel Calculator: frequently asked questions
A logarithmic unit expressing the ratio of two power-like quantities: 10 log₁₀(P₁ ÷ P₀). In acoustics, dB SPL is referenced to 20 µPa.
Human hearing spans a 10-trillion-fold range of intensity. A log scale compresses that into roughly 0 to 130 dB.
dBA applies an A-weighting filter that matches how the ear responds at moderate levels, de-emphasising low and very high frequencies.
A doubling (or halving) of power. For voltage or sound pressure, doubling is +6 dB.
Long exposure above 85 dBA can cause permanent damage; levels above about 120 dB can cause immediate harm.
References & sources
- CDC / NIOSH — Noise and Occupational Hearing Loss — 85 dBA REL and 3 dB exchange rate
- OpenStax — University Physics, Volume 1 — Ch. 17.4, Sound Intensity
- HyperPhysics, Georgia State University — decibels and the inverse-square law
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.