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Inverting Op-Amp Gain Calculator

Enter the feedback and input resistors to find the inverting amplifier gain.

How it is calculated

The tool takes the feedback resistor Rf, the input resistor Rin and the input voltage Vin (in volts), then computes gain = −Rf / Rin and Vout = gain × Vin. It also reports the gain magnitude |gain|, which drops the minus sign. Only the ratio matters, so Rf and Rin just need to be in the same unit (ohms, kilo-ohms and so on). Rin must be greater than zero; with Rin of 0 no result is produced. Results are rounded to two decimals. The formula assumes an ideal op-amp: it does not clip the output at the supply rails and ignores bandwidth, so check the real limits against your part's datasheet.

Worked example

Take Rf = 47000, Rin = 10000 and Vin = 0.5 V. Divide the resistors: 47000 / 10000 = 4.7, so the gain is −4.7 and the tool shows -4.70. The output is −4.7 × 0.5 = −2.35, shown as -2.35 V. The gain magnitude is 4.70. The negative sign means the output is the inverse of the input, so a +0.5 V input gives −2.35 V. A −0.5 V input would give +2.35 V.

Try this example →

Common mistakes

  • Dividing Rin by Rf instead of Rf by Rin, which gives the reciprocal of the gain.
  • Entering Rf in kilo-ohms and Rin in ohms. The ratio is wrong by a factor of 1000 unless both use the same unit.
  • Forgetting the minus sign and expecting Vout to have the same polarity as Vin. In this circuit it is always flipped (for positive resistors).
  • Trusting the output voltage beyond the supply. With a ±5 V supply, a calculated −12 V output is not reachable; the real op-amp saturates.
  • Using this for a non-inverting stage, whose gain is 1 + Rf/Rin, not −Rf/Rin.

About this calculator

An inverting op-amp circuit feeds the output back to the inverting (−) input through a resistor Rf, while the signal enters through another resistor Rin and the non-inverting input is grounded. Because the op-amp’s open-loop gain is enormous, negative feedback forces the inverting input to sit at a “virtual ground” — the same 0 V as the non-inverting pin — even though no current actually flows into that pin. All the input current through Rin is forced through Rf instead, which gives the closed-loop gain Av = −Rf/Rin, with the minus sign meaning the output is 180° out of phase with the input.

This topology is one of the most common building blocks in analog electronics: audio mixers, active filters, current-to-voltage converters, and signal-conditioning front ends all use it because the gain depends only on a resistor ratio, not on the op-amp’s own (variable) open-loop gain. The output voltage is simply Vout = −(Rf/Rin) · Vin, clamped in practice by the supply rails — this calculator applies that formula directly from the resistor values and input voltage you enter.

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