20·log10 Calculator (Amplitude to dB)
Use this calculator when converting an amplitude ratio (like voltage, pressure, or field strength) to decibels.
Inverse Calculator (dB to Amplitude Ratio)
Convert decibels back to an amplitude ratio using 10^(dB/20).
- +6.0206 dB ≈ 2× amplitude
- -6.0206 dB ≈ 0.5× amplitude
- +20 dB = 10× amplitude
- +40 dB = 100× amplitude
What is a 20 log dB calculation?
A 20 log dB calculation converts an amplitude ratio into decibels. The formula is:
dB = 20 × log10(A2 / A1)
This is used when your values are amplitude-like quantities, such as voltage, current (in equal impedance systems), sound pressure, or electric field strength. Decibels make large ratios easier to compare and communicate.
Why 20 log and not 10 log?
This is one of the most common sources of confusion. The short answer:
- 20 log10(...) for amplitude ratios (voltage, pressure, field, etc.)
- 10 log10(...) for power ratios
Because power is proportional to amplitude squared in many systems, squaring introduces a factor of 2, which turns 10 log into 20 log when you work in amplitude terms.
How to use this calculator
Method 1: Ratio to dB
- Enter a positive amplitude ratio (A2/A1).
- Click Calculate dB.
- Read your result in decibels.
Example: If A2/A1 = 2, then dB = 20 × log10(2) ≈ 6.02 dB.
Method 2: dB to ratio
- Enter a dB value.
- Click Calculate Ratio.
- The calculator returns 10^(dB/20).
Example: 40 dB gives a ratio of 100, meaning the amplitude is 100 times larger than the reference.
Practical engineering examples
Audio voltage gain
If an amplifier outputs 5 V from a 0.5 V input, the amplitude ratio is 10. So gain = 20 log10(10) = 20 dB. This is the standard way to express voltage gain in audio and instrumentation.
Acoustics and sound pressure
Sound pressure level comparisons use amplitude-style equations. When pressure doubles, the increase is about +6 dB. This helps explain why small dB changes can sound significant.
RF and communications
In antenna and field measurements, amplitude ratios are often converted using 20 log10. Power quantities still use 10 log10, so it is important to identify which quantity you are handling.
Common mistakes to avoid
- Using 10 log for voltage or pressure ratios when 20 log is required.
- Entering zero or negative ratios. Logarithms require a positive input.
- Confusing dB (ratio) with absolute units like dBV, dBu, or dBm.
- Ignoring impedance context when converting voltage and power.
Frequently asked questions
Can decibels be negative?
Yes. A negative dB value means the amplitude ratio is less than 1 (attenuation).
Is 0 dB equal to zero signal?
No. 0 dB means ratio equals 1, so the signal equals the reference level.
What ratio equals 3 dB in amplitude terms?
About 1.4125× amplitude. (Note: +3 dB is often discussed as nearly double power, not double amplitude.)
Bottom line
The 20 log dB calculator is the right tool whenever you compare amplitude quantities. Use it to move quickly between intuitive ratios and compact decibel values, and always verify whether your problem is amplitude-based or power-based.