Decibel (dB) Calculator
Convert between dB and a ratio, as a power ratio (10 × log10) or a voltage ratio (20 × log10). You can also find the power ratio when the two points have different resistances.
Power ratio vs. voltage (amplitude) ratio
A decibel is a logarithm of the ratio of two quantities. The factor depends on whether the quantities compared are power or voltage (and other amplitudes such as current or sound pressure).
- Power ratio: dB = 10 × log10(P2 ÷ P1)
- Voltage ratio: dB = 20 × log10(V2 ÷ V1). The amplitude ratio of a current, or of a quantity whose power is proportional to its square, uses the same factor of 20.
The same dB gives different ratios. 6 dB, for example, is about a 2 times ratio for voltage and about 4 times for power. Power is proportional to the square of the voltage (P = V² ÷ R), so doubling the voltage quadruples the power.
When the resistances are different
"Voltage dB = power dB" holds only when the resistance is the same at the two points where V1 and V2 are measured. With different resistances, P = V² ÷ R gives:
- Power ratio = (V2 ÷ V1)² × Z1 ÷ Z2 (Z1: the resistance where V1 is measured, Z2: the resistance where V2 is measured)
- Power dB = voltage dB + 10 × log10(Z1 ÷ Z2)
Choose the voltage ratio and enter both Z1 and Z2 to get the power ratio and the power dB from this formula. If you leave them empty, the resistances are assumed to be equal.
This applies to pure resistances. AC circuits with complex impedance (circuits with a phase shift, such as capacitors and inductors) are outside the scope of this calculator.
Boundary values
- A ratio of 1 is 0 dB. A ratio below 1 (attenuation) is a negative dB (a power ratio of 0.5 is about −3.0103 dB). A ratio above 1 (gain) is a positive dB.
- A ratio of 0: the dB is not defined (it would be −∞). An error is shown.
- A negative ratio (for example, a voltage ratio of −2): the sign of a voltage means a phase inversion, and dB expresses only the size. An error is shown, and you are asked to enter the absolute value.
- 0 dB is a ratio of 1. dB can be entered from −300 to 300. A ratio can have up to 12 digits before the decimal point and 6 decimal places. Text such as "infinity" is not a number and is rejected.
How it is calculated, and the precision
Logarithms and powers are calculated with ordinary floating-point numbers, and the result is aligned to 10 decimal places (12 significant digits for a ratio) before being rounded to the number of digits shown, so that floating-point error does not show. When the ratio is an integer power of 10, or the dB is a multiple of 10 (or 20), the result is exact and no floating point is used (a ratio of 10 is exactly 10 dB). Ratios that do not come out evenly are labeled "rounded value".
Examples
- Power × 2 → about 3.0103 dB. Voltage × 2 → about 6.0206 dB
- Power × 10 → 10 dB. Voltage × 10 → 20 dB
- Power × 0.5 → about −3.0103 dB
- −6 dB (voltage) → about 0.5012×. −6 dB (power) → about 0.2512×
- 3 dB (power) → about 1.9953×
- 40 dB (voltage) → 100× (10,000× in power)
- Different resistances: a voltage ratio of 2 with Z1 = 600 Ω and Z2 = 50 Ω → a power ratio of 4 × 12 = 48 (about 16.81 dB). The voltage dB is about 6.02 dB
Notes
- This calculator handles relative dB only, with no reference value. Decibels that have a reference (dBu, dBV, dBm, dB SPL, dBFS and so on) are not covered.
- Use a period as the decimal separator; commas are accepted only as thousands separators (1,234.5).
- For the relation between voltage, current, resistance and power, use the Ohm's Law Calculator. For powers and logarithms, use the Exponent & Logarithm Calculator.
Frequently asked questions
How many times is a 3 dB increase?
About 2 times in power and about 1.41 times in voltage.
How many times is a 6 dB increase in voltage?
About 2 times (and about 4 times in power).
What is −20 dB in voltage?
0.1 times (0.01 times in power).
Why is the factor 20 for voltage?
Because power is proportional to the square of the voltage. Since log10(V²) = 2 × log10(V), 10 × log10 of the power ratio becomes 20 × log10 of the voltage ratio.