Op-Amp Gain Calculator
Gain of an inverting or non-inverting op-amp stage from its two resistors, with the output voltage and the input level at which it starts clipping.
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The formula
non-inverting: A = 1 + R_f ÷ R_in inverting: A = −R_f ÷ R_in A(dB) = 20 × log₁₀|A|
Both come from assuming the op-amp does whatever it takes to hold its two inputs at the same voltage. Once you accept that, the gain is set entirely by the two resistors — the op-amp’s own gain, which is enormous and badly specified, drops out of the answer completely.
What to watch out for
The two configurations differ in more than the sign:
- Non-inverting has very high input impedance — the signal goes straight into the op-amp’s input pin. Its minimum gain is 1.
- Inverting has an input impedance equal to R_in, because the signal drives that resistor into a virtual earth. It can have a gain below 1, and it inverts the phase.
Both formulas assume an ideal op-amp. Real ones run out of gain at high frequency — the gain-bandwidth product means a stage with a gain of 100 has a hundredth of the bandwidth of a unity-gain buffer built from the same part.
Frequently Asked Questions
What is the gain of a non-inverting amplifier?
1 + R_f ÷ R_in. With 100 kΩ of feedback and 10 kΩ to ground the gain is 11×, or about 20.8 dB. It can never be less than 1.
Why is the inverting gain negative?
The minus sign means a 180° phase shift, not attenuation. The output is the same magnitude as a non-inverting stage of the same ratio would give, just upside down.
Why does the op-amp’s own gain not appear?
Because negative feedback swamps it. The open-loop gain is typically 100,000 or more and varies wildly between parts, so the feedback loop is designed to make the result depend only on the two resistors, which are precise and stable.