dB Calculator — Decibel Gain & Ratio Converter
Convert between decibel gain and power or amplitude ratios. Enter either the gain in dB or the output-to-input ratio to compute the other — and switch between power (×10 log) and amplitude/voltage/pressure (×20 log) modes.
Quantity type
dB
Power gain: G = 10 × log₁₀(P_out / P_in)
- 1
Log multiplier k
10Power quantities use k = 10; amplitude, voltage and pressure quantities use k = 20. - 2
Output ÷ input ratio
100 - 3
Gain = k × log₁₀(ratio)
10 × log₁₀(100) = 20 dB
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dB gain = 10 × log₁₀(ratio) for power quantities, or 20 × log₁₀(ratio) for amplitude/voltage/pressure. Enter the ratio to get dB, or enter dB to get the ratio. Positive dB = amplification; negative dB = attenuation. 0 dB always means ratio = 1.
Foirmle
How this is calculated
The decibel is a logarithmic unit expressing a ratio between two quantities. Because power and amplitude (or voltage, pressure, current) scale differently, there are two related formulas. For power quantities — anything proportional to energy per unit time, such as radiated RF power or acoustic intensity — the gain is G = 10 × log₁₀(P_out / P_in). For amplitude quantities — voltage, sound pressure, current, or any field quantity — the gain is G = 20 × log₁₀(A_out / A_in). The factor-of-two difference reflects the fact that power is proportional to the square of amplitude.
The calculator works in both directions. Supply a dB value to get the corresponding ratio, or supply a positive ratio to get the dB gain. A positive dB indicates amplification; a negative dB indicates attenuation. Common reference points: 0 dB means ratio = 1 (no change), +3 dB means power is roughly doubled (ratio ≈ 2), +6 dB means amplitude doubled, and +20 dB means amplitude × 10 (power × 100).
Note that this calculator computes **gain or loss** between two signal levels — it is not the same as acoustic sound pressure level (SPL), which uses a fixed reference of 20 μPa. Use the Decibel Sound Level Calculator for SPL conversions.
Ceisteanna coitianta
Power is proportional to the square of amplitude (P ∝ A²). Squaring inside the log becomes multiplying the exponent by 2, so the amplitude formula uses 20 = 2 × 10 to keep dB values consistent between power and amplitude measurements.
A gain of 0 dB means output equals input — the ratio is exactly 1. Positive dB values indicate amplification (output exceeds input); negative dB values indicate attenuation (output is smaller than input).
This tool converts between a **gain or loss ratio** and decibels, useful in electronics, audio engineering, RF, and optics. The Sound Level Calculator converts physical acoustic intensity (W/m²) to SPL in dB using the fixed hearing-threshold reference of 20 μPa — a different use case.
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TG we-Calculate Editorial Team. (2026). dB Calculator — Decibel Gain & Ratio Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/ga/calculator/db-calculator
TG we-Calculate Editorial Team. "dB Calculator — Decibel Gain & Ratio Converter." TG we-Calculate. 2026. https://we-calculate.com/ga/calculator/db-calculator.
TG we-Calculate Editorial Team, "dB Calculator — Decibel Gain & Ratio Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/ga/calculator/db-calculator
@misc{wecalculate_db_calculator, title = {dB Calculator — Decibel Gain & Ratio Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/ga/calculator/db-calculator}}, year = {2026}, note = {TG we-Calculate} }
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