Decibel (dB) Converter
Convert between gain in decibels and voltage or power ratio, and find an output voltage from an input and a gain.
Decibels, voltage and power
Gain (dB) = 20 · log₁₀(Vout / Vin) = 10 · log₁₀(Pout / Pin)
Voltage ratio = 10^(dB / 20) · Power ratio = 10^(dB / 10)
A decibel is a logarithmic ratio. Because power is proportional to voltage squared, the same gain in dB corresponds to a voltage ratio and a power ratio that is its square. Handy landmarks: +6 dB ≈ ×2 voltage(×4 power), +20 dB = ×10 voltage (×100 power), and−3 dB ≈ ×0.707 voltage (half power — the filter cutoff point).
A negative dB value is attenuation (ratio below 1); zero dB means the output equals the input.
Why use decibels at all
Decibels compress huge ranges into manageable numbers and turn multiplication into addition. A chain of stages that multiply a signal by 100, then 0.5, then 20 is a headache in ratios, but in dB it's just +20, −3, +13 = +30 dB added up. That's why gains and losses through an amplifier, cable, and filter are all quoted in dB — you sum them along the signal path instead of multiplying, which is exactly how thelink budget works.
Worked example
An amplifier turns 0.1 V into 1 V. The voltage ratio is 10, so the gain is 20·log₁₀(10) = 20 dB. Follow it with a cable that halves the voltage (−6 dB) and the net is 14 dB — a voltage ratio of 10^(14/20) ≈ 5.0, i.e. 0.1 V out at 0.5 V. The calculator converts in either direction, so you can enter a dB figure to get the ratio or a pair of values to get the dB.
Voltage dB vs power dB
The single most common mistake is using the wrong factor. Use 20·log₁₀ for voltage (or current) ratios and 10·log₁₀ for power ratios — they differ because power goes as voltage squared. Mixing them up throws the answer off by a factor of two in dB. Absolute units likedBm reference the ratio to a fixed power (1 mW), which is why they use the power form.
Common questions
- Why is it 20·log for voltage but 10·log for power?
- Because power goes with the square of voltage. Doubling a voltage into the same load quadruples the power, and since log(x²) is 2·log(x), the factor of 2 comes out front and 10·log becomes 20·log. Both formulas describe the same physical change in decibels — they just start from different quantities. Use 20·log for voltage, current and pressure; 10·log for power and intensity.
- What does 3 dB actually mean?
- A factor of two in power, near enough — 3.0103 dB is exactly double, and 3 dB is the universally used approximation. It is why a filter's cutoff is quoted at the −3 dB point: that is where the circuit passes half the power it does in the passband. In voltage terms the same −3 dB is a factor of 1/√2, or about 0.707, which is why that number appears everywhere in filter design.
- Is a decibel always a ratio?
- Yes. A bare dB figure only ever describes the relationship between two quantities, which is why it has no units. To express an absolute level you need a suffix naming the reference: dBm against 1 milliwatt, dBW against 1 watt, dBV against 1 volt, dBu against 0.7746 V, dBSPL against the threshold of hearing. Seeing "dB" alone where an absolute level is meant is a sign the reference has been left out.
- Why use a logarithmic scale at all?
- Two reasons, both practical. Real signal chains span enormous ranges — a receiver might handle powers a trillion times apart — and logarithms compress that into a couple of hundred manageable numbers. And because gains multiply, working in logarithms turns multiplication into addition: a chain of stages becomes a sum you can do in your head rather than a product you need a calculator for.