keepcalculator

06 Numbers and Powers

AC Voltage Amplifier Calculator and Gain Formula

Card No. 06·13582 · Updated · Standard formula, shown below

Output voltage 10.00 V RMS
Voltage gain
20.00 dB
Result
Input voltage
1 V RMS
You entered
Output voltage
10 V RMS
You entered
You enter
Input voltage, Output voltage, Voltage gain
You get
Output voltage, Voltage gain
Rounding
2 dp

An AC voltage amplifier calculator works out the output voltage or voltage gain of an amplifier from its input and gain. Enter the input voltage and either the voltage gain or output voltage; the calculator returns the missing quantity, with voltage gain expressed as a ratio and in decibels.

Formula

The headline result is calculated with the voltage-gain relation:

Vout = Vin × Av

  • Vout is the output AC voltage in volts RMS (V RMS).
  • Vin is the input AC voltage in volts RMS (V RMS).
  • Av is the linear voltage gain, a dimensionless ratio.

The second result gives the same voltage gain in decibels: GdB = 20 log10(Av). The factor is 20 because this expression describes an amplitude or voltage ratio. The calculator uses positive voltage magnitudes; its gain input must be greater than zero for the decibel result to be defined.

Worked Example

Using the default inputs, Vin = 1 V RMS and Av = 10:

  1. Multiply input voltage by gain: 1 V RMS × 10 = 10 V RMS.
  2. Convert the gain to decibels: 20 × log10(10) = 20 dB.

The calculator therefore returns an output voltage of 10.00 V RMS and a gain of 20.00 dB. The separate output-voltage field is included as a reference value; the headline calculation uses the input voltage and gain.

What AC Voltage Gain Means

An amplifier increases the size of an alternating signal while ideally preserving its waveform. Voltage gain compares the output voltage amplitude with the input amplitude. A gain of 10 means the output voltage is ten times the input voltage under the specified measurement conditions. A gain below 1 means attenuation rather than amplification; this calculator’s decibel output requires a positive gain, so gains between zero and one produce negative decibels.

AC voltage varies with time, so a voltage needs a measurement convention. RMS (root mean square) voltage is commonly used for AC signals because it corresponds to the heating effect of an equivalent DC voltage in a resistive load. Peak voltage and peak-to-peak voltage are other valid descriptions, but they cannot be mixed casually in the same ratio. If both input and output are measured using the same convention and waveform conditions, their ratio is consistent.

How to Use the Calculator

  • Enter the input voltage as a positive RMS value in volts. For example, enter 0.2 for 200 mV RMS.
  • Enter the amplifier’s linear voltage gain as a ratio, not as a percentage or a decibel number.
  • Read the calculated output voltage and the equivalent gain in dB. The result is an ideal arithmetic estimate, not a promise that a physical amplifier can deliver that voltage.

If a specification gives gain in decibels instead, convert it to a linear ratio before using the calculator: Av = 10(GdB/20). For example, 20 dB corresponds to a gain of 10. A gain of 6 dB is approximately 2, while 0 dB corresponds to a ratio of 1. Small differences can arise from rounding.

What the Result Does—and Does Not—Tell You

The computed output is the voltage predicted by multiplying input voltage by the stated gain. It does not determine output power, current, distortion, noise, bandwidth, or whether an amplifier can sustain the result into a particular load. Those depend on the amplifier circuit, its supply voltage, load impedance, frequency, and operating limits. A real output may clip or distort before reaching the calculated value.

For example, a 1 V RMS input and gain of 10 give an ideal 10 V RMS output. For a sine wave, 10 V RMS is about 14.14 V peak, because peak voltage equals RMS voltage multiplied by √2. That conversion applies to a sine wave, not automatically to every waveform. The amplifier needs enough voltage headroom to reproduce the signal peaks; the simple gain calculation does not check that condition.

Common Mistakes and Limits

  • Entering dB as linear gain: A value of 20 in the gain box means a ratio of 20, or about 26.02 dB—not 20 dB. Convert decibels using the formula above.
  • Mixing units: Convert millivolts to volts before comparing or calculating. For example, 250 mV is 0.250 V.
  • Mixing peak and RMS: Use matching measurement conventions for input and output. Converting between RMS and peak requires knowing the waveform shape.
  • Confusing voltage gain with power gain: The voltage ratio alone does not reveal power gain unless the relevant input and output impedances are known. The 20 log formula is for voltage or amplitude ratios; power ratios use 10 log.
  • Ignoring frequency: Amplifier gain can vary across frequency. A single stated gain may apply only over a specified frequency range and under stated load conditions.

The calculator rounds displayed results to two decimal places. Keep additional precision in intermediate calculations when checking results. Also note that the input fields are independent: the output-voltage input is not used to infer gain. To find gain from known input and output measurements, use Av = Vout/Vin and then, if needed, calculate 20 log10(Av).

Frequently Asked Questions

How do I calculate AC amplifier output voltage?
Multiply the input voltage by the linear voltage gain: Vout = Vin × Av. Make sure the voltage and gain refer to the same signal conditions.

How do I convert amplifier voltage gain to dB?
Use 20 log10(Av). For instance, a voltage ratio of 10 is 20 dB. To convert dB back to a ratio, use 10(dB/20).

Is AC voltage gain the same as power gain?
No. Voltage gain compares voltages; power gain compares powers. Different input and output impedances mean a voltage ratio alone is not enough to determine power gain.

Should I enter RMS or peak voltage?
This calculator labels voltage as RMS. You can use another convention only if input and output are treated consistently, but compare the result with equipment specifications using the convention those specifications state.

Why is the real output lower than the calculated value?
The ideal result may exceed the amplifier’s available voltage swing or its gain at the signal frequency and load. Supply voltage, load, bandwidth, and distortion limits can all affect actual output.

Related

Formula used
in vin | Input voltage | V RMS | 1 | 0
in vout | Output voltage | V RMS | 10 | 0
in gain | Voltage gain | ratio | 10 | 0
out voutcalc | Output voltage | V RMS | vin * gain | 2
out gaindb | Voltage gain | dB | 20 * log10(gain) | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

More cards in this drawer

The whole Numbers and Powers drawer →