Inverting Amplifier Calculator
The inverting amplifier is one of the most common operational amplifier circuits. It sets a precise voltage gain using just two resistors and produces an output that is the inverse of the input. The gain depends only on the ratio of the feedback resistor to the input resistor, which makes the circuit predictable and stable. Enter the input resistor, the feedback resistor, and an input voltage; this calculator returns the closed-loop voltage gain, the gain magnitude in decibels, and the resulting output voltage for the ideal op-amp model.
Inverting amplifier formula
Voltage gain = -Rf / Rin
Output voltage = gain * input voltage
Gain magnitude (dB) = 20 * log10(Rf / Rin)
Rin is the input resistor and Rf the feedback resistor, both in ohms. The negative sign shows that the output is inverted. The decibel figure is the magnitude of the voltage gain.
Op-amp circuit context
- The gain depends only on the resistor ratio, not on the op-amp's open-loop gain, provided that gain is very large.
- The inverting input sits at virtual ground, so the input impedance equals Rin.
- Choosing larger resistors reduces current draw but makes the circuit more sensitive to bias current and noise.
- For a unity inverter, set Rf equal to Rin so the gain is exactly minus one.
- Real output voltage is limited by the supply rails; the ideal result assumes the op-amp does not saturate.
Inverting amplifier: frequently asked questions
What is the gain of an inverting amplifier?
For an ideal inverting op-amp the closed-loop voltage gain equals the negative of the feedback resistor divided by the input resistor: gain = -Rf / Rin. The minus sign means the output is inverted relative to the input.
Why is the gain negative?
The input signal is applied to the inverting (minus) input through Rin while the non-inverting input is grounded. A rising input voltage drives the output down to keep the inverting input near virtual ground, so the output is the inverse of the input.
What is virtual ground?
In an ideal inverting amplifier the op-amp adjusts its output so the inverting input stays at almost the same voltage as the grounded non-inverting input, about zero volts. This point is called virtual ground because it acts like ground without being directly connected to it.
What is the input impedance of an inverting amplifier?
Because of the virtual ground at the inverting input, the input impedance of the basic inverting amplifier equals the input resistor Rin. This is lower than the non-inverting configuration, which presents a very high input impedance.
Can the inverting amplifier have a gain less than one?
Yes. If the feedback resistor is smaller than the input resistor, the magnitude of the gain is below one, attenuating the signal while still inverting it. Setting Rf equal to Rin gives a gain of exactly minus one, a unity inverter.
Official sources
- NIST: SI electrical units, the volt and ohm (SP 811).
- NIST: Physical Measurement Laboratory (electrical metrology).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.