Decibel (dB) calculator
A decibel expresses a ratio between two values on a logarithmic scale. This calculator converts a power or amplitude ratio into decibels — useful in audio, electronics, RF and acoustics, where gains, losses and signal levels are quoted in dB.
How it works
The formula depends on the type of quantity:
- Power (watts): dB = 10 · log₁₀(P / P₀)
- Amplitude (voltage, current, sound pressure): dB = 20 · log₁₀(A / A₀)
The amplitude form uses 20 instead of 10 because power is proportional to amplitude squared, and log of a square doubles the coefficient. Both values must be greater than zero. A positive result is a gain; a negative result is a loss (attenuation); zero means the values are equal.
Key ratios to know
These reference points come up constantly across audio, electronics, and RF work:
| Ratio | Power (10·log) | Amplitude (20·log) | Common meaning |
|---|---|---|---|
| 2 : 1 | +3.01 dB | +6.02 dB | Double the power / double the voltage |
| 10 : 1 | +10 dB | +20 dB | Ten times the power / ten times the voltage |
| 100 : 1 | +20 dB | +40 dB | One hundred times power |
| 1 : 2 | −3.01 dB | −6.02 dB | Half the power (3 dB loss) |
| 1 : 1 | 0 dB | 0 dB | No gain, no loss |
Why use a logarithmic scale?
The range of signal values in electronics and acoustics is enormous. Audible sound ranges from the threshold of hearing at 20 micropascals to painful levels over a million times larger. A linear scale for this range would require unwieldy numbers. The decibel compresses the entire useful range into tens of numbers, and each doubling of power is always +3 dB regardless of the starting level. This makes comparisons and mental arithmetic much easier once you internalise a few key milestones.
Worked examples
Audio amplifier gain. An amplifier takes a 10 mV input and produces a 2 V output. In amplitude mode: dB = 20 · log₁₀(2000 mV / 10 mV) = 20 · log₁₀(200) = 20 · 2.301 = 46 dB. This is a typical figure for a preamplifier stage.
Transmission line loss. A coaxial cable delivers 50 mW of signal when 100 mW is input. In power mode: dB = 10 · log₁₀(50 / 100) = 10 · log₁₀(0.5) = 10 · (−0.301) = −3.01 dB. The cable has about 3 dB of insertion loss — it passes roughly half the power.
Sound pressure level. For SPL, the reference value is 20 micropascals (the threshold of hearing). A sound pressure of 200 micropascals gives: 20 · log₁₀(200/20) = 20 · log₁₀(10) = 20 · 1 = 20 dB SPL. Conversational speech is around 60 dB SPL and a lawn mower around 90 dB SPL.
Useful identities
- Every time power doubles, add +3 dB.
- Every time power increases by 10×, add +10 dB.
- Every time voltage (or current) doubles, add +6 dB.
- A “0 dB” reading means the measured value equals the reference — not that there is no signal.
- The human ear perceives a +10 dB increase as roughly “twice as loud” in subjective loudness terms, even though it represents ten times the acoustic power.
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