Op-Amp Gain Calculator (inverting, non-inverting, summing, differential)

Understanding the op-amp gain calculator — concept and principle

An op-amp with two resistors is the most common amplifier stage, used in sensor front ends, audio preamps and active filters. This calculator gives the voltage gain of the inverting and non-inverting configurations for a feedback resistor Rf and input resistor Rin, the output voltage for a given input, and the gain in decibels.

The 10:1 resistor ratio turns 0.1 V into −1 V, upside down; non-inverting gives 1.1 V.

How it is calculated

Inverting gain: A = −Rf / Rin; output V_out = −(Rf / Rin) × V_in.
Non-inverting gain: A = 1 + Rf / Rin; output V_out = (1 + Rf / Rin) × V_in.
Gain in dB: inverting 20 log₁₀(Rf / Rin) (magnitude) and non-inverting 20 log₁₀(1 + Rf / Rin).

In every case the output cannot swing beyond the supply rails.

The principle

An ideal op-amp has enormous open-loop gain, so with negative feedback it adjusts its output until the voltage difference between its two inputs is essentially zero (the "virtual short"), while drawing no input current. In the inverting circuit the inverting input sits at 0 V, so the input current V_in / Rin must flow through Rf, giving V_out = −Rf × V_in / Rin. In the non-inverting circuit the inverting input must equal V_in, and Rf and Rin form a divider from the output, so V_out × Rin / (Rin + Rf) = V_in, which rearranges to 1 + Rf / Rin. The gain therefore depends on resistor ratios, not on the op-amp's unstable internal gain.

Worked example

Ratio: Rf / Rin = 100,000 / 10,000 = 10.
Inverting gain: −10; output: −10 × 0.1 V = −1 V.
Non-inverting gain: 1 + 10 = 11; output: 11 × 0.1 V = 1.1 V.
Gain in dB: inverting 20 log₁₀(10) = 20 dB; non-inverting 20 log₁₀(11) = 20.8278537 dB.

Each point is the calculator re-run with only “Input R (Ω)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Input R (Ω)	Inverting gain
2,500	-40
5,000	-20
7,500	-13.33333333
10,000	-10
12,500	-8
15,000	-6.666666667
20,000	-5

How to read the result

A negative gain means the output is inverted (a 180° phase shift for AC signals). The inverting stage's input resistance equals Rin, so a low Rin loads the source; the non-inverting stage has very high input resistance. Bandwidth falls as gain rises: closed-loop bandwidth is roughly the op-amp's gain-bandwidth product divided by the noise gain, 1 + Rf / Rin, which is 11 here for both circuits.

Common mistakes

Expecting an output larger than the supply allows; a ±5 V supply cannot deliver 8 V.
Forgetting that a single-supply op-amp needs a bias point for AC signals.
Mixing up the two dB rows: 20 dB belongs to the inverting gain of −10, 20.83 dB to the non-inverting gain of 11.

Keep in mind: These formulas assume an ideal op-amp. Real parts have limited bandwidth, slew rate, offset voltage, bias current and output swing, so check the datasheet and test the circuit.

Frequently asked questions

Why is the inverting amplifier's gain negative?

The input current flows into the virtual-ground node and out through Rf, so the output must go below 0 V when the input is positive.

How do I get a gain of exactly 1?

Use a voltage follower: the non-inverting circuit with Rf = 0 and Rin left open gives gain 1 with very high input impedance.

Sources: Horowitz and Hill, The Art of Electronics, 3rd edition, chapter on operational amplifiers · Texas Instruments, Op Amps for Everyone (Ron Mancini, editor)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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