Ratio to gain dB calculator

Select voltage or amplitude when the ratio compares like field quantities, and select power when it compares powers. The calculator applies 20 times the base-10 logarithm for voltage or amplitude and 10 times the logarithm for power. It returns the multiplier, formula, decibel result, and a plain classification as gain, attenuation, or unity. The computation is deterministic and needs no network connection. It is useful for electronics, audio, RF, measurement, and control work where an ambiguous ratio can otherwise produce a result that is wrong by a factor of two in decibels.

Choose the convention before calculating

Decibels express a ratio on a logarithmic scale, but the correct multiplier depends on what the ratio represents. For a power ratio, use gain in dB equals 10 times log base 10 of Pout divided by Pin. For a voltage ratio, use 20 times log base 10 of Vout divided by Vin when both voltages are measured across equal impedances, or when voltage is being treated as the relevant amplitude quantity. The same twenty-times convention applies to other amplitude or field quantities whose power is proportional to the square of amplitude. That square is why the multiplier doubles: 10 log10 of the squared amplitude ratio simplifies to 20 log10 of the amplitude ratio. Do not select voltage merely because a circuit contains voltages; first identify the ratio actually supplied. If the input is already Pout divided by Pin, choose power. If it is Vout divided by Vin, choose voltage. The calculator also accepts amplitude as an explicit label and treats it like voltage. A dimensionless ratio is required, so numerator and denominator should use matching units before division. For example, divide volts by volts or watts by watts, not volts by millivolts without first reconciling the scale. Making this choice deliberately prevents the common factor-of-two dB error.

Read positive, zero, and negative decibel results

Enter a finite linear ratio greater than zero. A ratio above one means the output quantity exceeds the input quantity, so the returned decibel value is positive and the interpretation is gain. A ratio exactly equal to one produces zero decibels and is classified as unity because output and input are equal. A ratio between zero and one produces a negative value and is classified as attenuation. Zero and negative linear ratios cannot be passed to a real base-10 logarithm, so they return an invalid input error instead of a misleading number. Familiar landmarks help with checking results. A power ratio of two is approximately 3.0103 dB, while an amplitude or voltage ratio of two is approximately 6.0206 dB. A power ratio of ten is 10 dB, and a voltage ratio of ten is 20 dB. In the other direction, a power ratio of one half is approximately negative 3.0103 dB, while a voltage ratio of one half is approximately negative 6.0206 dB. The response echoes the normalized ratio type, reports whether the multiplier was ten or twenty, and includes the applied formula. Results are rounded to a stable significant precision so fixtures and repeated calculations remain consistent while preserving useful engineering accuracy. Each successful API calculation costs $0.002.

Apply the result without mixing reference conditions

Use the calculated value only after confirming that numerator and denominator describe comparable conditions. Voltage gain expressed with 20 log10 is straightforward for the same circuit ports when their reference impedances are equal or when voltage gain itself is the intended specification. If input and output impedances differ and the real question concerns power transfer, a voltage ratio alone does not establish the power ratio. You must account for impedance and then apply 10 log10 to the resulting power ratio. This distinction matters in RF systems, transmission lines, audio interfaces, sensors, and amplifiers connected to different loads. Similarly, this calculator converts a pure ratio; it does not calculate absolute levels such as dBm, dBW, dBV, or sound pressure level, all of which require a defined reference quantity. It also does not infer whether a number came from peak, RMS, peak-to-peak, or another amplitude definition. Use the same definition on both sides of the ratio so common scaling factors cancel. For cascaded stages, decibel gains may be added after each stage has been computed with the correct convention, while linear ratios would be multiplied. Negative decibels describe attenuation rather than an invalid circuit, and zero decibels means unity rather than no signal. Treat the returned formula and multiplier as an audit trail: they make it easy to review spreadsheets, lab notes, design calculations, and test expectations for convention mistakes.