Decibel calculator (dB, dBm and sound levels)
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Result
Convert between ratios and decibels. Power ratios use 10·log₁₀, voltage and current ratios use 20·log₁₀, and dBm measures power relative to 1 mW. You can also add sound levels: decibels do not add directly, so the calculator converts each level to an intensity, adds those and converts back.
Step-by-step solution
Voltage ratio to decibels
How to work with decibels
- Power ratio to dB: L = 10·log₁₀(P₂/P₁). A factor 2 in power is +3 dB, a factor 10 is +10 dB.
- Voltage or current ratio to dB: L = 20·log₁₀(V₂/V₁). A factor 10 in voltage is +20 dB.
- Back from dB: P₂/P₁ = 10^(L/10) and V₂/V₁ = 10^(L/20).
- dBm: L = 10·log₁₀(P/1 mW). 1 W is 30 dBm and 1 mW is 0 dBm.
- Adding sound levels: L = 10·log₁₀(Σ 10^(Lᵢ/10)).
Questions and answers
Why 20·log for voltage but 10·log for power?
Power is proportional to the voltage squared, P = V²/R, so 10·log₁₀(P₂/P₁) = 10·log₁₀((V₂/V₁)²) = 20·log₁₀(V₂/V₁), as long as both voltages are across the same resistance.
How loud are two 80 dB sources together?
83 dB, not 160 dB. Each doubling of the sound intensity adds 10·log₁₀ 2 ≈ 3 dB.
What is the difference between dB, dBm and dBW?
dB is a ratio without a reference. dBm and dBW are absolute power levels relative to 1 mW and 1 W, so dBW = dBm − 30.
What does −3 dB mean in a filter?
The output power has dropped to half, and the voltage to 1/√2 ≈ 0.707 of its maximum. That point defines the cut-off frequency and the bandwidth.
Practise it yourself
Practise Bode plots & margins
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.