Enter your input power and output power (or input voltage and output voltage) to calculate dB gain. The dB Gain Calculator applies the standard logarithmic formulas — 10·log₁₀(P₂/P₁) for power and 20·log₁₀(V₂/V₁) for voltage — and returns your decibel gain value along with the gain ratio. Positive results indicate amplification; negative values indicate attenuation.
dB Gain
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Gain describes the amount of amplification applied to a signal — it's the ratio of the output signal to the input signal. In audio, gain controls how loud or strong a signal becomes after passing through an amplifier or other processing device. A gain greater than 1 (or positive dB) means the signal was amplified; less than 1 (or negative dB) means it was attenuated.
For power quantities, the formula is dB = 10 × log₁₀(P₂ / P₁), where P₁ is input power and P₂ is output power. For voltage (or amplitude) quantities, the formula is dB = 20 × log₁₀(V₂ / V₁). The factor of 20 for voltage arises because power is proportional to the square of voltage.
Yes — a negative dB value means the output signal is weaker than the input, indicating attenuation or damping (loss). For example, a gain of -10 dB means the output power is one-tenth of the input power. This is common in attenuators, lossy cables, or signal splitters.
A gain of 0 dB means the output signal equals the input signal — no amplification and no attenuation has occurred. The ratio of output to input is exactly 1. This is sometimes called unity gain.
Using the formula dB = 10 × log₁₀(P₂ / P₁), rearranging gives P₁ = P₂ / 10^(dB/10). So P₁ = 150 / 10^(20/10) = 150 / 100 = 1.5 W. The input power would be 1.5 watts.
Using dB = 20 × log₁₀(V₂ / V₁), rearranging gives V₂ = V₁ × 10^(dB/20). So V₂ = 12 × 10^(-10/20) = 12 × 10^(-0.5) ≈ 12 × 0.3162 ≈ 3.79 V.
Power is proportional to the square of voltage (P ∝ V²). When you take the logarithm of a squared ratio, the exponent comes out as a factor of 2, turning the coefficient 10 into 20. So both formulas are mathematically consistent — they describe the same physical gain on a decibel scale.
dB gain is used extensively in audio engineering, radio communications, electronics, and acoustics. Engineers use it to characterize amplifiers, attenuators, antennas, and cables. Because dB is a logarithmic scale, the total gain of a chain of devices is simply the sum of each device's individual dB values, making complex signal path calculations much simpler.