Op Amp Gain Calculator — Inverting, Non-Inverting, Buffer and Difference

Background.

Put a 9 kΩ resistor from an op-amp's output back to its inverting input, a 1 kΩ resistor from that input to ground, feed the signal into the other input, and the stage amplifies by ten. Replace the chip with a different part from another manufacturer and it still amplifies by ten. That indifference to the device is why operational amplifiers run so much of analogue electronics. An op-amp's own open-loop gain is enormous — often more than 100,000 — but it drifts with temperature and varies from one unit to the next. Negative feedback throws nearly all of it away and replaces it with a ratio of two resistors you can buy to one percent or better.

A resistor ratio is only the start of a working stage, though. Before anything is soldered, four things need answering: what the gain is for the way the parts are wired, how far the output will travel for the signal you feed in, how much of the op-amp's bandwidth survives at that gain, and whether the result fits between the supply rails. All four come out of one calculation here, for the four resistive configurations that cover most practical circuits: non-inverting, inverting, the voltage follower and the single-op-amp difference amplifier.

Those four are less interchangeable than their formulas suggest. Wire the same 1 kΩ and 9 kΩ pair as an inverting stage and the gain becomes −9, one unit smaller and opposite in sign, yet the bandwidth stays exactly where it was. Bandwidth follows the noise gain, which is 1 + Rf/Ri in both layouts, rather than the gain the signal sees. Push that to unity gain and an inverter made from two equal resistors has only half the bandwidth of a plain follower built on the same chip. Showing noise gain beside signal gain is meant to make that trade visible before it turns up on an oscilloscope.

What is op amp gain calculator?

Closed-loop gain is the ratio of an amplifier's output voltage to its input voltage once negative feedback is connected. With enough open-loop gain inside the loop, the op-amp drives its output to whatever level keeps its two inputs at almost the same voltage. In the non-inverting circuit that means the feedback divider Ri and Rf must return exactly the input voltage to the − input, so the output must be (1 + Rf/Ri) times larger. In the inverting circuit the + input is grounded, the − input sits at a virtual ground, and the current through Ri has nowhere to go but through Rf, so the output is −Rf/Ri times the input. The voltage follower is the non-inverting circuit with the divider removed, giving a gain of exactly 1. The difference amplifier combines both paths and multiplies V₊ − V₋ by Rf/Ri. Noise gain, 1 + Rf/Ri, is the gain the feedback loop itself works against, and it is that figure, not the signal gain, that sets the bandwidth.

How to use this calculator.

1. 01Pick the configuration. Non-inverting suits high-impedance sources and gets the most bandwidth for a given gain; inverting gives a virtual-ground summing node and a defined input resistance; the follower converts impedance at unity gain; the difference amplifier subtracts one voltage from another.
2. 02Enter Ri and Rf, each with its own unit. The gain depends only on their ratio, but keep both somewhere between about 1 kΩ and 100 kΩ. The follower ignores these two fields entirely.
3. 03Enter the input voltage. For an AC signal, use the peak value rather than RMS when you want the rail check to mean anything: 1 V RMS is about 1.414 V peak. In difference mode this field is V₋ and the second field is V₊.
4. 04Copy the gain-bandwidth product from the datasheet's first page, where it may be called unity-gain bandwidth, and set its unit. Use the typical figure at your supply voltage if the datasheet gives several.
5. 05Enter one rail of a symmetric supply, so ±12 V is entered as 12. For a single-supply stage biased at mid-supply, half the supply voltage is the closest equivalent.
6. 06Read the signed gain, the noise gain beside it, the bandwidth, and the verdict, which states how much of the rail-to-rail swing the output uses.

The formula.

Signal gain depends on the configuration. Non-inverting: Av = 1 + Rf/Ri. Inverting: Av = −Rf/Ri. Follower: Av = 1. Difference: Vout = (Rf/Ri) × (V₊ − V₋), with the gain shown as Rf/Ri and the voltage actually amplified shown separately as V₊ − V₋. These are Equations 4.1, 4.2 and 6.1 in James Fiore's Operational Amplifiers and Linear Integrated Circuits. The output is Av multiplied by the amplified voltage, and the decibel figure is 20·log₁₀|Av|, taken on the magnitude because a negative number has no logarithm; the sign stays in the signed gain.

Noise gain is 1 + Rf/Ri for every configuration that uses resistors, and 1 for the follower. Its reciprocal is the feedback factor β, the fraction of the output returned to the inverting input. Bandwidth follows from the way most op-amps are compensated: open-loop gain rolls off at 20 dB per decade, so gain multiplied by frequency stays roughly constant at the gain-bandwidth product. The closed-loop response stays flat until the falling open-loop gain meets the noise gain, which happens at f₂ = GBW ÷ A_noise (Fiore Eq. 5.1), the point where the response is 3 dB down. Use the linear noise gain there, never the decibel value: 1 MHz divided by 20 gives 50 kHz, half the true answer for a gain of 10.

The op-amp model is ideal except for that one finite parameter: infinite open-loop gain at low frequency, infinite input impedance, zero output impedance, no offset, bias current or noise. The rail verdict compares |Vout| with the rail you entered — clipping at or above it, a warning from 90% upward, comfortable below — and assumes the output could reach the rail, which most parts cannot. Slew rate, offset, common-mode and supply rejection, output current limits and stability margin are all outside the calculation.

A worked example.

Frequently asked questions.

References& sources.

1. [1]James M. Fiore, Operational Amplifiers and Linear Integrated Circuits: Theory and Application, §4.2 'Inverting and Noninverting Amplifiers' (Engineering LibreTexts). Source of the two core gain equations: Eq. 4.1 Av = 1 + Rf/Ri for the non-inverting configuration and Eq. 4.2 Av = −Rf/Ri for the inverting one, with the printed explanation that 'There is a change in polarity because we reference the output signal to ground'. Also the source of the differential-amplifier statement at §4.2.8 and Eq. 4.11 — 'the output voltage is found by multiplying the differential input signal by Rf/Ri' — and of the input-impedance contrast between the two configurations. Open access; retrieved 2026-07-29.
2. [2]James M. Fiore, Operational Amplifiers and Linear Integrated Circuits, §5.3 'Gain-Bandwidth Product' (Engineering LibreTexts). Source of Eq. 5.1, f₂ = GBW/A_noise, and of the noise-gain definition A_noise = 1 + Rf/Ri. Contains the statement this page's noise-gain output exists to make visible: 'Noise gain is the same as ordinary voltage gain for the noninverting voltage amplifier, but is one unit larger than the inverting amplifier's ordinary gain (Rf/Ri)', and therefore 'for the same gain, noninverting amplifiers will exhibit a higher break frequency than inverting types'. Also the warning 'Never use the gain in dB form for this calculation!'. Open access; retrieved 2026-07-29.
3. [3]James M. Fiore, Operational Amplifiers and Linear Integrated Circuits, §5.4 'Slew Rate and Power Bandwidth' (Engineering LibreTexts). Source of the slew-rate definition ('the rate of change of voltage versus time', dv/dt), of the power-bandwidth relation f_max = Slew Rate/(2πVp), of the instruction 'To be on the conservative side, set Vp to the op amp's clipping level', and of the worked figure of 'a ±15 V supply yielding approximately ±13 V clipping levels' — which is the basis for this page's statement that a real op-amp does not swing to its rails. Open access; retrieved 2026-07-29.
4. [4]James M. Fiore, Operational Amplifiers and Linear Integrated Circuits, §6.2 'Instrumentation Amplifiers' (Engineering LibreTexts). Source of Eq. 6.1, Vout = (Rf/Ri)(V_b − V_a), the exact difference-amplifier expression implemented here, together with the limitations that make this page's difference mode an idealisation: 'the input impedances are not isolated; indeed, the impedance of one input may very well be a function of the signal present on the other input', and 'Any mismatch in gain between the two inputs will result in a degradation of CMRR... For high CMRR systems, resistor matching may need to be better than 0.01%'. Open access; retrieved 2026-07-29.
5. [5]James M. Fiore, AC Electrical Circuit Analysis: A Practical Approach, §10.3 'Bode Plots' (Engineering LibreTexts). Cited for the decibel and break-frequency conventions this page's gain-in-dB and closed-loop-bandwidth outputs rest on: Eq. 10.15 fc = 1/(2πRC), Eq. 10.14 the lag-network gain −10·log₁₀(1 + f²/fc²), and the statement that break frequencies are 'also known as the half-power points, or corner frequencies'. Open access; retrieved 2026-07-29.