dB Gain Calculator
Enter an input and output value to find the decibel gain or loss, or enter a known dB value to recover the underlying power or voltage ratio. Choose power gain (the 10 log formula used in electronics, RF and acoustics) or voltage gain (the 20 log formula standard in audio and signal chain analysis). Results update instantly with full step-by-step working.
Formula
Worked example
An amplifier takes a 10 mW input and delivers 10 W output. Power ratio = 10 W / 0.01 W = 1000. dB gain = 10 × log10(1000) = 10 × 3 = 30 dB. For voltage: if input is 0.1 V and output is 10 V, ratio = 100, dB = 20 × log10(100) = 20 × 2 = 40 dB.
What is dB gain?
Decibel (dB) gain is a logarithmic measure of how much a system amplifies or attenuates a signal. Instead of saying "the amplifier multiplies power by 100", engineers say "the amplifier has 20 dB of gain" - a far more convenient number to work with. The logarithmic scale compresses enormous ranges (a factor of 10,000,000 fits between +10 dB and +80 dB) and turns multiplicative chains of stages into simple addition. Gain is always a ratio, so dB is dimensionless: it says how many times bigger the output is than the input, not what the absolute levels are.
Power gain vs. voltage gain - why two formulas?
The factor of 10 vs. 20 comes from physics, not convention. Power is proportional to voltage squared (P = V² / R), so a voltage ratio of 2 corresponds to a power ratio of 4, and the logarithms of those two ratios differ by exactly a factor of 2. Using 20 log for voltage and 10 log for power keeps both scales consistent: 3 dB always means double the power, and it also means the voltage has increased by a factor of about 1.414 (the square root of 2). The rules of thumb: use the 10 log formula when you are comparing power levels in watts or milliwatts (RF, acoustics, electronics); use the 20 log formula when you are comparing voltages or other field quantities (audio signal chains, op-amp design).
Cascaded stages and why dB values add
When signals pass through multiple components in series - a preamplifier, a cable, an equaliser, a power amplifier - the overall power ratio is the product of the individual ratios. Multiplying ratios is the same as adding their logarithms, so the total dB gain is just the sum of each stage's dB gain. A preamp with 20 dB gain, followed by a cable with -3 dB loss, followed by a power amplifier with 30 dB gain gives 20 + (-3) + 30 = 47 dB net system gain. This additive property is the main reason engineers adopted the decibel scale for signal chains.
Practical benchmarks to memorise
+3 dB = double power = voltage up by root-2 (about 1.41). +6 dB = quadruple power = double voltage. +10 dB = 10x power = just over 3x voltage. +20 dB = 100x power = 10x voltage. -3 dB = half power (the half-power or -3 dB point defines filter bandwidth). -20 dB = power drops to 1% of input. Negative dB values always indicate attenuation or insertion loss. 0 dB means the output equals the input, called unity gain, which is the goal for buffers and impedance-matching networks.
Common dB gain values and their linear equivalents
| dB value | Power ratio | Voltage ratio | Typical application |
|---|---|---|---|
| -20 dB | 0.01 | 0.1 | Passive attenuator, cable loss at high frequency |
| -10 dB | 0.1 | 0.316 | Pad resistor, signal attenuation |
| -6 dB | 0.25 | 0.5 | Half-power point, half voltage |
| -3 dB | 0.5 | 0.707 | Half-power (-3 dB) filter cutoff frequency |
| 0 dB | 1 | 1 | Unity gain - buffer amplifier, matched network |
| +3 dB | 2 | 1.414 | Double power, half-power bandwidth marker |
| +6 dB | 4 | 2 | Double voltage, op-amp gain of 2 |
| +10 dB | 10 | 3.162 | One Bel of power gain |
| +20 dB | 100 | 10 | Typical preamp gain, one decade in voltage |
| +30 dB | 1,000 | 31.6 | High-gain amplifier stage |
| +40 dB | 10,000 | 100 | Strong RF amplifier, two decades voltage |
| +60 dB | 1,000,000 | 1,000 | Power amplifier (e.g. 1 mW to 1 W PA) |
Memorising a few key benchmarks makes dB intuitive to work with.
Frequently asked questions
What does a negative dB gain mean?
A negative dB value means the output is weaker than the input - the component is attenuating or losing signal rather than amplifying it. For example, -3 dB means the output power is half the input power. Passive components like cables, connectors, and filters always have negative dB gain (insertion loss) because they can only reduce signal, not add energy.
Why is 3 dB such an important threshold?
3 dB represents a doubling (or halving) of power, and in voltage terms a factor of root-2 (about 1.414). The "3 dB point" or "half-power frequency" is the standard way to define the bandwidth of a filter or amplifier: it is the frequency at which the output power drops to half the in-band level. This threshold is used universally because it corresponds to a factor of 2, the simplest meaningful ratio.
What is the difference between dB gain and dBm?
dB gain is a pure ratio with no units - it compares output to input. dBm is an absolute power level referenced to 1 milliwatt: 0 dBm = 1 mW, 10 dBm = 10 mW, 30 dBm = 1 W. If a signal at -10 dBm passes through a 20 dB amplifier, the output is -10 + 20 = 10 dBm. You can add dB gains to dBm absolute levels because both use the same logarithmic scale.
How do I convert dB gain back to a linear ratio?
For a power gain G in dB, the ratio is 10^(G/10). For a voltage gain G in dB, the ratio is 10^(G/20). So 20 dB of power gain = 10^(20/10) = 10^2 = 100x power ratio. 20 dB of voltage gain = 10^(20/20) = 10^1 = 10x voltage ratio. Use the "dB to power ratio" or "dB to voltage ratio" modes in this calculator to do the conversion instantly.
Can I add dB values for cascaded components?
Yes, and that is one of the main advantages of the decibel scale. Because dB is logarithmic, multiplying linear ratios is equivalent to adding dB values. A system with a 15 dB preamp, a -2 dB cable, and a 25 dB power amplifier has a total gain of 15 + (-2) + 25 = 38 dB. Use the cascaded stages mode in this calculator to add up to four stages at once.
What is 0 dB gain?
0 dB means the output equals the input - no gain and no loss. A linear ratio of exactly 1 (output/input = 1) gives log10(1) = 0, so multiplying by 10 or 20 still gives 0 dB. Buffer amplifiers and impedance transformers are designed for 0 dB gain: they change impedance without changing signal level.