Find the voltage gain of an inverting or non-inverting op-amp amplifier circuit from its feedback and input resistor values.
Calculator verified • Last updated: August 2026
Inverting mode: the output is flipped in polarity relative to the input — a positive input produces a negative-going output swing, scaled by the resistor ratio.
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An operational amplifier (op-amp) is almost never used "open loop" — a feedback resistor is added between the output and one of the inputs to set a precise, predictable gain. The two most common configurations are the inverting amplifier and the non-inverting amplifier, and each has its own simple gain formula based only on the ratio of two resistors.
$$\text{Inverting: } A_v = -\frac{R_f}{R_{in}} \qquad \text{Non-Inverting: } A_v = 1 + \frac{R_f}{R_{in}}$$
Av: voltage gain, the ratio of output voltage to input voltage (unitless).
Rf: the feedback resistor, connecting the output back to the inverting input.
Rin: the input resistor the signal passes through before reaching the amplifier.
Gain is also commonly quoted in decibels, on a logarithmic scale:
$$A_{v,dB} = 20 \log_{10}(|A_v|)$$
In the inverting configuration, the op-amp's inverting input is held at a "virtual ground" by negative feedback — it sits at essentially zero volts even though it isn't physically connected to ground. The input signal pushes current through the input resistor toward that virtual ground, and the feedback resistor has to push an equal and opposite current from the output to balance it. The result is an output that always swings opposite to the input, which is exactly what the negative sign in the formula captures. The non-inverting configuration doesn't have this virtual-ground behavior at the input, so its output tracks the input's polarity directly, and its gain — 1 plus the resistor ratio — can never fall below 1.
Using the calculator's own defaults in Inverting mode — a 100 kΩ feedback resistor and a 10 kΩ input resistor — the gain is negative 100 divided by 10, or negative 10. A 1-volt input signal produces a negative 10-volt output, an amplitude increase of 10 times with the polarity flipped. In decibels, that's 20 times the base-10 logarithm of 10, or 20 dB. Switching to Non-Inverting mode with the same resistor values instead gives a gain of 1 plus 100 divided by 10, or 11 — positive, and always at least 1.
The operational amplifier traces back to analog computing in the 1940s, where circuits built from vacuum tubes performed mathematical operations — addition, integration, differentiation — hence the name "operational." The modern integrated-circuit op-amp arrived with devices like the Fairchild uA709 in the mid-1960s and, soon after, the enormously popular uA741 in 1968, which remained a standard teaching and hobbyist part for decades. The key insight that makes today's op-amp circuits so predictable — using external feedback resistors to set a precise gain, rather than relying on the amplifier's own inconsistent internal gain — dates back to Harold Black's negative-feedback amplifier work at Bell Labs in the late 1920s, developed originally to reduce distortion in long-distance telephone repeaters.
Forgetting the negative sign on inverting gain is the most frequent error — the magnitude of the ratio is correct, but the output polarity is backwards from what was assumed, which matters a great deal in an AC signal chain. Mixing up the two formulas is the second-most common: a non-inverting circuit's gain always includes the "plus 1" term (from the resistor divider seeing the full input at both amplifier inputs), while an inverting circuit's does not. Assuming a real op-amp is a perfect, ideal device is a subtler mistake — these formulas assume infinite open-loop gain and infinite input impedance, which real devices only approximate; at very high gains or high frequencies, a real op-amp's own limitations start to matter.
Virtual Ground — the near-zero-volt condition at the inverting input of an inverting-configuration op-amp, maintained by negative feedback rather than a physical ground connection.
Open-Loop Gain — an op-amp's raw, uncontrolled gain with no feedback resistor connected — extremely large and imprecise, which is exactly why feedback resistors are used to tame it into a known value.
Negative Feedback — routing a portion of the output signal back to the inverting input, which is what stabilizes gain and reduces distortion in a real op-amp circuit.
Decibel (dB) — a logarithmic unit used to express gain or signal ratios, calculated here as 20 times the base-10 logarithm of the absolute voltage gain.
This calculator assumes an ideal op-amp with infinite open-loop gain and input impedance. Real circuits should be verified against the specific op-amp's datasheet, especially at high gains or high frequencies.
An inverting amplifier flips the signal's polarity and its gain is always negative or zero in magnitude terms — Rf divided by Rin, with a minus sign. A non-inverting amplifier keeps the same polarity as the input and its gain is always 1 or greater, since it's 1 plus Rf divided by Rin — it can never amplify by less than unity.
In the inverting configuration, the input signal drives current through the input resistor into the op-amp's virtual-ground summing junction, and the feedback resistor forces the output to swing the opposite direction to keep that junction at zero volts. The output is therefore always the mirror image of the input, scaled by the resistor ratio — hence the negative sign in the gain formula.
Decibel gain expresses the same voltage gain on a logarithmic scale: 20 times the base-10 logarithm of the absolute value of the gain. It's the standard way gain is quoted in audio and RF engineering because it compresses a huge range of ratios into manageable numbers and makes cascaded stages easy to combine by simple addition.