Calculator
Formula used
This calculator converts a linear ratio into decibels using a base‑10 logarithm. Choose the scaling that matches your quantity.
- Amplitude ratio (voltage, current, field): dB = 20 · log10(value / reference)
- Power ratio (watts, mW): dB = 10 · log10(value / reference)
- Inverse conversion: value = reference · 10^(dB / factor) where factor is 20 or 10.
How to use this calculator
- Select a conversion mode: relative, dBm, or dBW.
- Enter the linear value you want to convert.
- If using relative mode, enter a positive reference value.
- Choose amplitude or power scaling for relative calculations.
- Optionally enter a dB value to compute the inverse.
- Press Calculate, then export CSV or PDF if needed.
Example data table
| Linear ratio | Amplitude dB (20·log10) | Power dB (10·log10) | Meaning |
|---|---|---|---|
| 1.000 | 0.0000 | 0.0000 | Unity (no change) |
| 2.000 | 6.0206 | 3.0103 | Doubling |
| 0.500 | -6.0206 | -3.0103 | Halving |
| 10.00 | 20.0000 | 10.0000 | Ten times |
| 0.100 | -20.0000 | -10.0000 | One tenth |
Values shown assume a reference of 1.00. Real cases use your chosen baseline.
Article: Understanding Linear to dB Conversion
1) Why decibels exist
Decibels compress huge ranges into small numbers, making comparisons easy. A radio link budget, an audio gain stage, and a filter attenuation curve all become readable when ratios are shown on a logarithmic scale.
2) Linear ratio vs absolute level
A linear ratio compares a value to a reference, such as output/input. That ratio becomes dB. Absolute modes use a fixed reference: dBm is referenced to 1 mW, while dBW is referenced to 1 W. This calculator supports both styles for quick checks.
3) The 10 or 20 rule
Power ratios use 10·log10 because power is proportional to the square of many field quantities. Amplitude ratios (voltage, current, pressure) use 20·log10. If you are unsure, pick power for watts and amplitude for volts.
4) Common data points you should remember
Some ratios appear constantly in engineering work. Doubling an amplitude is about +6.02 dB, while doubling power is about +3.01 dB. A tenfold increase is +20 dB (amplitude) or +10 dB (power). The example table includes these references.
5) Negative dB and what it means
Negative dB simply means the value is below the reference. For example, 0.5 of a reference equals about -6.02 dB (amplitude) or -3.01 dB (power). In audio, negative dB is attenuation. In RF, it may indicate path loss or insertion loss.
6) Reference selection affects the answer
In relative mode, the reference sets the baseline. Using a reference of 2 instead of 1 shifts the computed dB because the ratio changes. In dBm and dBW modes, the reference is fixed, so your linear input is treated as power in mW or W, respectively.
7) Precision, rounding, and reporting
Real instruments have tolerance, so excessive decimals can be misleading. Use 2–4 decimals for typical reporting, and increase precision only when you are comparing close values. The calculator also reports percent change versus the reference to help interpret small differences.
8) Verification and exports
Always sanity-check with known points: unity should yield 0 dB, and a tenfold change should yield 10 dB (power) or 20 dB (amplitude). When you need documentation, export to CSV for spreadsheets and to PDF for quick sharing with teammates, lab notes, or project reports.
FAQs
1) What does “linear” mean in this calculator?
It is a positive numeric value used in a ratio with a reference. The ratio is converted to dB using a base-10 logarithm for compact comparison.
2) When should I use 20·log10 instead of 10·log10?
Use 20·log10 for amplitude quantities like voltage, current, sound pressure, or field strength. Use 10·log10 for power quantities like watts or milliwatts.
3) Why must the linear value be greater than zero?
Logarithms are undefined for zero and negative numbers. A linear value of 0 would imply an infinite loss in dB, which cannot be computed directly.
4) What is the difference between dB, dBm, and dBW?
dB is a ratio. dBm is an absolute power level referenced to 1 mW. dBW is an absolute power level referenced to 1 W.
5) Can I convert back from dB to a linear value?
Yes. Enter a dB value in the inverse field. The calculator uses the same reference and scaling factor to compute value = reference · 10^(dB/factor).
6) Why is doubling sometimes 3 dB and sometimes 6 dB?
Doubling power gives about +3.01 dB using 10·log10. Doubling amplitude gives about +6.02 dB using 20·log10 because amplitude relates to power squared.
7) What decimal setting should I choose?
Use 2–4 decimals for most practical work. Increase decimals when comparing close values or when exporting data for further analysis in a spreadsheet.