Decibel Calculator (add dB levels, ratio ⇄ dB)

Understanding the decibel calculator — concept and principle

The decibel (dB) expresses a ratio of two powers on a logarithmic scale. Because sound levels are already logarithmic, you cannot add them like ordinary numbers: two 80 dB machines do not make 160 dB. Use it to combine noise sources or to convert a ratio into decibels.

Convert each level to power, add, and convert back: 80, 80 and 75 dB make 83.65 dB.

How it is calculated

Combined level: L = 10 · log₁₀( Σ 10^(Lᵢ/10) ). Each level Lᵢ (dB) is converted back to a relative power 10^(Lᵢ/10), the powers are added, and the sum is converted back to dB.
Power ratio in dB: 10 · log₁₀(ratio). Use this for power, intensity or energy.
Amplitude ratio in dB: 20 · log₁₀(ratio). Use this when the ratio entered is between field quantities such as sound pressure, voltage or current.

The principle

A sound pressure level is defined as Lp = 20 log₁₀(p/p₀), with p₀ = 20 µPa in air, which equals 10 log₁₀(p²/p₀²). Sound power is proportional to p², so the decibel is really a logarithm of power. When sources are independent (uncorrelated), their powers add, not their pressures or their dB values. That is why the calculator goes back to the linear power domain, adds, and returns to dB. The factor 20 for amplitudes comes from the square: doubling a pressure or voltage quadruples the power, which is 10 log₁₀4 ≈ 6.02 dB.

Worked example

Default inputs: levels 80, 80 and 75 dB; ratio 2.
Relative powers: 10^8.0 = 100,000,000, again 100,000,000, and 10^7.5 ≈ 31,622,777.
Sum ≈ 231,622,777. Combined level = 10 · log₁₀(231,622,777) ≈ 83.65 dB (83.64781263).
Power ratio 2: 10 · log₁₀2 ≈ 3.01 dB.
Amplitude ratio 2: 20 · log₁₀2 ≈ 6.02 dB.

How to read the result

Two equal sources add 3 dB. A source 10 dB quieter than another adds only about 0.4 dB, so the loudest sources dominate and removing a quiet one barely helps. As rough benchmarks, +3 dB is double the power, +10 dB is ten times the power and is perceived as roughly "twice as loud", and +20 dB is a hundredfold power. For occupational noise, NIOSH recommends limiting exposure to 85 dBA averaged over 8 hours, with the allowed time halved for every 3 dB increase.

Common mistakes

Adding dB values arithmetically (80 + 80 = 160) instead of adding powers.
Using 10 log for a voltage or pressure ratio, or 20 log for a power ratio.
Mixing weightings or references, such as dBA with dBC, or dB SPL with dB re 1 mW (dBm).

Keep in mind: The summing formula assumes independent, incoherent sources measured at the same point with the same weighting; identical in-phase signals can add up to 6 dB. It is an estimate, not a substitute for a calibrated sound level meter, and it is not a hearing assessment.

Frequently asked questions

How do I subtract background noise from a measurement?

Convert both to powers and subtract: L = 10 log₁₀(10^(Ltotal/10) − 10^(Lbg/10)). The correction is reliable only when the total is at least about 3 dB above the background.

How many dB is a tenfold voltage gain?

20 · log₁₀10 = 20 dB. A tenfold power gain is 10 dB.

Sources: IEC 60027-3, Letter symbols to be used in electrical technology — Logarithmic and related quantities, and their units · ISO 80000-8, Quantities and units — Acoustics · NIOSH, Criteria for a Recommended Standard: Occupational Noise Exposure (Publication 98-126)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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