Decibels Calculator
Use this tool to convert between ratios and decibels (dB), or find the dB difference between two levels.
What is a decibel?
A decibel (dB) is a logarithmic way to describe a ratio between two quantities. It is commonly used in acoustics, audio engineering, electronics, telecommunications, and control systems. The big advantage of dB is that it compresses very large ranges into manageable numbers.
Decibels are not absolute by themselves. A dB value always compares one quantity to another reference quantity. For example, +3 dB means an increase relative to the reference; -3 dB means a decrease.
The core formulas
1) Power ratio to decibels
dB = 10 × log10(P2 / P1)
Use this when comparing power quantities such as electrical power or acoustic intensity.
2) Amplitude ratio to decibels
dB = 20 × log10(A2 / A1)
Use this for amplitude-like quantities such as voltage, current, or sound pressure, assuming equal impedance conditions.
3) Decibels back to ratios
- Power ratio = 10^(dB/10)
- Amplitude ratio = 10^(dB/20)
How to use this calculator
- Select the calculation type from the dropdown.
- Enter either one ratio input or two level values, depending on mode.
- Click Calculate to get the result instantly.
- Use Clear to reset all fields.
Common quick-reference values
- +3 dB ≈ 2× power
- +10 dB = 10× power
- +20 dB = 10× amplitude
- -3 dB ≈ half power
- -6 dB ≈ half amplitude
Examples
Example A: Power increase
If an amplifier goes from 25 W to 100 W, then the power ratio is 100/25 = 4. So the gain is dB = 10 × log10(4) ≈ 6.02 dB.
Example B: Voltage gain
If output voltage doubles from 1 V to 2 V, then A2/A1 = 2. dB = 20 × log10(2) ≈ 6.02 dB. This is why people often remember “doubling amplitude is about +6 dB.”
Example C: Converting dB to ratio
For +12 dB: power ratio = 10^(12/10) ≈ 15.85. That means the output power is about 15.85 times the reference power.
10 vs 20: why two multipliers?
The multiplier depends on what quantity you are measuring. Power is proportional to amplitude squared. Because of that squared relationship, the logarithmic multiplier becomes 20 for amplitude ratios and 10 for power ratios. Choosing the wrong formula is one of the most common mistakes in decibel work.
Practical applications
- Audio engineering: mixer gain staging, speaker sensitivity, dynamic range.
- Electronics: amplifier gain in voltage and power terms.
- Wireless systems: link budgets, antenna gains, path loss.
- Acoustics: comparing sound levels and pressure changes.
Common mistakes to avoid
- Entering zero or negative values for ratios and levels (logarithms need positive values).
- Mixing power and amplitude formulas.
- Assuming dB is an absolute unit without a reference.
- Rounding too early when precision matters in engineering calculations.
Final thought
Decibels may look intimidating at first, but they become intuitive quickly once you practice with ratios. Use this calculator to check your intuition and speed up day-to-day engineering or audio calculations.