Decibel Guide: dB Addition, Subtraction & Conversion Explained

Master decibel calculations with clear formulas, worked examples, and practical applications for sound, RF, and electronics.

What Is a Decibel?

A decibel (dB) is a logarithmic unit that expresses the ratio between two power levels. One bel — named after Alexander Graham Bell — represents a 10:1 power ratio, and a decibel is one-tenth of a bel. The logarithmic scale compresses enormous ranges into manageable numbers: a ratio of 1,000,000:1 becomes simply 60 dB.

We use decibels because human perception of both sound loudness and signal strength is approximately logarithmic. A 10 dB increase sounds about "twice as loud" to the human ear, regardless of the starting level. This makes dB the natural unit for acoustics, RF engineering, audio systems, and telecommunications.

For voltage or amplitude ratios (where impedance is the same), the formula uses a factor of 20 instead of 10, because power is proportional to voltage squared:

Decibel Addition and Subtraction

Decibels cannot be added or subtracted directly because they represent logarithmic ratios. Two sound sources of 80 dB each do not produce 160 dB — they produce approximately 83 dB. To combine decibel values, you must first convert to linear power, add, then convert back.

Adding Decibels

Example: Two machines produce 80 dB and 83 dB respectively.

• Convert: 10^(80/10) = 10⁸ = 100,000,000 and 10^(83/10) ≈ 199,526,231
• Add: 100,000,000 + 199,526,231 = 299,526,231
• Convert back: 10 × log₁₀(299,526,231) ≈ 84.8 dB

Key dB Rules

Subtracting Decibels

To remove background noise from a total measurement:

Example: Total noise is 75 dB, background is 70 dB. The actual source level is 10 × log₁₀(10^(75/10) − 10^(70/10)) = 10 × log₁₀(31,622,776 − 10,000,000) ≈ 73.8 dB

dB vs dBm vs dBi

The "dB" alone is always a ratio — it has no absolute value without a reference. Different suffixes specify the reference:

Decibel Conversion Formulas

Practical Applications

Acoustics and Noise Control

Sound pressure levels are measured in dB SPL (sound pressure level), referenced to 20 μPa — the threshold of human hearing. Common reference points: a quiet library is approximately 40 dB SPL, normal conversation 60 dB SPL, a rock concert 110 dB SPL. Per IEC 61672-1, sound level meters use frequency weightings (A-weighting for environmental noise, C-weighting for peak measurements) to approximate human hearing sensitivity.

When combining noise sources, two identical machines produce 3 dB more than one machine. However, because human loudness perception is logarithmic, a 3 dB increase is only "just noticeable." A 10 dB increase is perceived as twice as loud, even though it represents 10× the acoustic power.

RF Engineering and Telecommunications

In RF systems, signal strength is measured in dBm and link budgets are calculated in dB. A typical Wi-Fi access point transmits at +20 dBm (100 mW). Free-space path loss at 2.4 GHz over 100 meters is approximately 80 dB. Receiver sensitivity might be −90 dBm. The link budget: +20 − 80 = −60 dBm received, which is 30 dB above sensitivity — a solid margin.

Fiber optic systems use dBm for optical power, with typical receiver sensitivities around −28 dBm for 10 Gbps links. Attenuation in single-mode fiber is approximately 0.4 dB/km at 1310 nm wavelength.

Audio Engineering

Audio signal levels use several dB references: dBu (referenced to 0.775 V, common in professional audio), dBV (referenced to 1 V, used in consumer equipment). Professional line level is +4 dBu (1.228 V), while consumer line level is −10 dBV (0.316 V) — a difference of about 12 dB. Understanding these references is essential for matching equipment and avoiding noise floor issues.

Loudness measurement per ITU-R BS.1770 uses LUFS (Loudness Units Full Scale), which is a dB-like unit with frequency weighting for broadcast loudness compliance. Streaming platforms typically target −14 LUFS integrated loudness.

Common Mistakes

• Adding dB values directly: Two 50 dB sources do not produce 100 dB. They produce 53 dB. Always convert to linear, add, then convert back.
• Confusing power dB and voltage dB: A 6 dB increase doubles voltage but quadruples power. The 10× vs 20× factor difference is the most common source of errors.
• Treating dBm as dB: dBm is an absolute power level; dB is a ratio. You can add a dB gain to a dBm level (e.g., 20 dBm + 6 dB gain = 26 dBm), but you cannot add two dBm values.
• Ignoring impedance in voltage dB calculations: The 20× factor (voltage dB) only applies when the impedance at both measurement points is the same. If impedances differ, you must account for the impedance ratio.

Use our Decibel Calculator for quick dB addition, subtraction, and conversion, the Unit Conversion Calculator for other engineering unit conversions, or the Power Calculator for electrical power calculations.

Frequently Asked Questions