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Inverting Op-Amp Gain

G=−RfRinG = -\frac{R_{f}}{R_{in}}
sig figs

Worked example: 100 kΩ over 10 kΩ → gain −10. Press Try an example to run it live, then adjust anything.

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See also

Non-Inverting Op-Amp Gain: Both use voltage gain and feedback resistance.
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Inverting Op-Amp Gain explained

RinRfG

Negative feedback drives the inverting input to the same potential as the grounded non-inverting input: the "virtual earth". The source current Vin/Rin therefore has nowhere to go but through Rf, and the output must sit at −(Rf/Rin)Vin. A 100 kΩ feedback resistor with a 10 kΩ input resistor gives a gain of −10: ten times bigger, upside down. The op-amp's own gain, a million or more, barely enters the result, which is the whole point of feedback.

Note that the input impedance of this stage is just Rin, so it loads the source; where that matters, the non-inverting configuration is the better choice. Two more practicalities: gain-bandwidth product is fixed, so a ×100 stage on a 1 MHz op-amp runs out of steam at 10 kHz, and the virtual earth makes this the natural summing point for mixers. Several inputs, each with its own resistor, add at that node.

Inverting Op-Amp Gain formula

G=−RfRinG = -\frac{R_{f}}{R_{in}}
Where
  • GG= Voltage gain
  • RfR_{f}= Feedback resistance (Ω)
  • RinR_{in}= Input resistance (Ω)
Revised 31 October 2026
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formula.expert. (2026, October 31). Inverting Op-Amp Gain Formula & Calculator. https://formula.expert/solvers/inverting-op-amp-gain

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