Inverting Op-Amp Gain Calculator

How it is calculated

For an ideal inverting amplifier the voltage gain is Av = −Rf ÷ Rin, where Rf is the feedback resistor from output to the inverting input and Rin is the series input resistor. The minus sign means the output is inverted. The tool also gives the magnitude |Av| and the gain in decibels, dB = 20 × log10(|Av|). The two resistors can be in any unit (ohms, kΩ) as long as both use the same one, because only the ratio matters. Rin must be above zero, otherwise there is no result. A feedback resistor of 0 gives a gain of 0 and -∞ dB, and a gain magnitude below 1 gives a negative dB value (attenuation). Results are rounded to two decimals. Real op-amps add limits from finite open-loop gain, bandwidth and supply voltage that this ideal formula ignores.

Common mistakes

• Dropping the minus sign. The gain of this stage is negative, and the 180° phase inversion matters when cascading stages or summing signals.
• Swapping Rf and Rin. Rf is the feedback resistor, so swapping them gives the reciprocal gain, for example 0.10 instead of 10.
• Mixing units, such as Rf in kΩ and Rin in Ω. The ratio is then off by a factor of 1000.
• Computing dB from the signed gain. A negative value has no logarithm; dB uses the magnitude, so −10 and +10 both give 20 dB.
• Expecting this formula to hold at any frequency or amplitude. A gain of 100 or more can run into the op-amp's gain-bandwidth limit and the supply rails, which the formula does not check.