About

In electronics and physics, Decibels express the ratio between two values. However, the calculation depends entirely on the physical quantity being measured. A common error in circuit design is applying the wrong logarithmic formula; a 6 dB increase doubles Voltage but quadruples Power. This distinction is critical when designing amplifiers, antennas, or analyzing signal integrity.

This tool separates the physics into two clear domains: Power Ratios (Watts, Joules) and Field/Amplitude Ratios (Volts, Amperes, Pressure). By displaying both resulting multipliers side-by-side for a given dB input, engineers and students can immediately distinguish the magnitude of change for energy versus field strength, preventing cascading errors in system link budgets.

Formulas

The definitions of the decibel differ based on the nature of the quantity Q.

For Power (Energy):

R_P = 10^L_dB10

For Amplitude (Voltage/Current):

R_V = 10^L_dB20

Note the divisor is 20 for voltage because power is proportional to voltage squared (P ∝ V²), and logarithmic rules move the exponent 2 to the multiplier.

Reference Data

dB Value	Power Ratio (x)	Voltage Ratio (x)	Effect
20	100	10	Large Gain
10	10	3.16	Standard Decade
6	3.98 (~4)	2.0	Voltage Doubles
3	1.99 (~2)	1.41 (√2)	Power Doubles
0	1	1	Unity / No Change
-3	0.5	0.707	Half Power
-6	0.25	0.5	Half Voltage
-20	0.01	0.1	Attenuation

Frequently Asked Questions

Decibels define power ratios. Since Power = Voltage^2 / Resistance, the squared term in the power equation becomes a multiplier of 2 in the logarithmic domain. Therefore, 10 * log(V^2) becomes 20 * log(V).

Sound pressure is an amplitude (field) quantity, similar to voltage. You should use the Amplitude/Voltage ratio column (20 log rule). A 6 dB increase in SPL corresponds to a doubling of sound pressure.

Negative dB indicates attenuation or loss. The resulting ratio will be a fraction between 0 and 1. For example, -20 dB means the signal is reduced to 1/10th of its original voltage.

Yes. Current is an amplitude quantity like Voltage. Use the Voltage Ratio section.