Inverting vs Non-Inverting Op-Amp Gain Explained
How Rin and Rf set closed-loop gain, why the two topologies differ by one, and how to read gain in decibels, with worked resistor examples.
Two topologies, two formulas
A single op-amp stage almost always uses one of two feedback arrangements. In the inverting configuration the signal enters through Rin into the inverting input, and the gain is minus Rf over Rin. In the non-inverting configuration the signal drives the non-inverting input directly, and the gain is 1 plus Rf over Rin. The extra 1 is the key difference: with Rin = 1k and Rf = 10k, the inverting stage gives -10 while the non-inverting stage gives 11. The ratio Rf over Rin is 10 in both cases, but the topology decides whether you add the unity term and whether the sign flips.
Why the ratio is what counts
Only the ratio of Rf to Rin sets the gain, not the absolute resistor values. That means 1k and 10k give the same gain as 2k and 20k or 10k and 100k. Designers usually pick values in the low kilohm to hundreds of kilohm range: too low and the op-amp output has to source excess current into the feedback network, too high and resistor thermal noise and stray capacitance start to matter. A common starting point is Rin around 1k to 10k, then choose Rf to hit the target ratio.
Reading gain in decibels
Decibels compress a wide gain range into an easy-to-compare number and use the magnitude, so an inverting -10 and a gain of +10 both read 20 dB. The formula is 20 times the base-10 log of the absolute gain. A gain of 1 is 0 dB, 10 is 20 dB, 100 is 40 dB, and the non-inverting 11 in the example above works out to about 20.83 dB. Because dB ignores the sign, always keep the raw gain value handy when phase matters, such as when several stages cascade.
Where the ideal model stops
These formulas assume an ideal op-amp with infinite open-loop gain and bandwidth. Real parts have a finite gain-bandwidth product, so the usable closed-loop bandwidth shrinks as you demand more gain: a part with 1 MHz gain-bandwidth gives only about 100 kHz at a gain of 10. Slew rate limits large fast signals, and input offset voltage and bias current add small DC errors that the higher-gain stages amplify. For audio, sensor front-ends and most control loops the ideal result is close enough; for high-speed or precision work, check the datasheet limits too.