Inverting Op-Amp Gain Calculator

This inverting op-amp gain calculator works out the closed-loop voltage gain of an operational amplifier wired in the standard inverting configuration, one of the most common building blocks in analogue electronics, from audio preamps to sensor signal conditioning. You enter the feedback resistor (Rf), the input resistor (Rin), and an input voltage (Vin) you want to test. The calculator returns the gain, worked out as minus Rf divided by Rin, alongside the gain magnitude and the resulting output voltage for the input you specified. The minus sign matters: it shows the output is inverted, swinging in the opposite direction to the input, so a positive input voltage produces a negative output and vice versa. Because the gain depends purely on the ratio of the two resistors, you can quickly see how changing either value alters the amplification, whether you are designing a circuit from scratch or checking an existing one. Use it to size resistors for a target gain, to predict the output voltage a given input will produce, or to understand why a circuit behaves the way it does on the bench. The calculation assumes an ideal operational amplifier with enough open-loop gain that only the resistors set the closed-loop gain, so treat the result as a design estimate rather than an exact prediction, since real components, supply rails and bandwidth limits will affect the actual output.

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Gain = -10
Gain magnitude10
Output voltage-5 V

The formula

The gain of an inverting amplifier is Av = minus Rf / Rin, where Rf is the feedback resistor and Rin the input resistor. The output is Vout = Av times Vin, inverted relative to the input.

Worked example

With a 10 k feedback resistor and a 1 k input resistor, the gain is minus 10000/1000 = minus 10, so a 0.5 V input gives a minus 5 V output. Enter 10000, 1000, 0.5 to confirm.

Frequently asked questions

What sets the gain of an inverting amplifier?

The ratio of the feedback resistor to the input resistor, with a minus sign: Av = minus Rf / Rin.

Why is the gain negative?

The configuration inverts the signal, so the output swings opposite to the input. The magnitude is Rf over Rin.

Does the op-amp itself affect the gain?

For an ideal op-amp with enough open-loop gain, only the resistors set the closed-loop gain.

Who this calculator is for

This calculator is for electronics students, hobbyists and engineers.

What this calculator assumes

  • You enter values in the units shown.
  • Ideal components are assumed.
  • Results are rounded for display.

Formula and sources

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