Op-amp gain calculator — inverting / non-inverting / differential

Work out the closed-loop gain of the three classic op-amp configurations from your resistor values — or the resistor ratio for a target gain.

Configuration

R1 (input to inverting pin)Ohms — from the input to the summing nodeR2 (feedback resistor)Ohms — from the output back to the summing nodeInput voltage (V_in)Volts — to see the output swing

Closed-loop gain

Reverse: target gain → R2

Gain (×)

1 + R2/R1 — output in phase

Gain

20·log10(|gain|)

9.54 dB

Output voltage

gain × V_in

0.3 V

Quick reference

×1 buffer

R2 = 0, any R1 (unity gain, output follows input)

×2

R2 = R1, e.g. 10k + 10k

×10

R2 = 9×R1, e.g. 90k + 10k

×11

R2 = 10×R1, e.g. 100k + 10k

About the model

These are the closed-loop gain formulas for an ideal op-amp: infinite open-loop gain, infinite input impedance and zero output impedance, so the feedback network alone sets the gain. Real op-amps are limited by the gain-bandwidth product (GBW): gain × bandwidth ≤ GBW, so a high-gain stage is also a low-bandwidth one — and the input bias current and offset voltage shift the output by a few millivolts that you should account for in precision designs.

For the parts themselves: operational amplifiers and precision resistors carry the GBW and tolerance specs this math assumes.

Browse related parts:

operational amplifiers resistor kits precision resistors

Frequently asked questions

How is the gain of a non-inverting op-amp circuit calculated?

A non-inverting stage has gain = 1 + R2/R1, with the output in phase with the input. With the defaults R1 = 10 kΩ and R2 = 20 kΩ that is 1 + 20/10 = ×3, which the tool also reports in dB as 20·log10(|gain|). For a ×11 stage use R2 = 10×R1, e.g. 100 kΩ feedback on 10 kΩ.

How do I pick a feedback resistor for a target gain?

Switch on Reverse mode and the calculator works the algebra backwards from a target gain and a fixed R1: a non-inverting target needs R2 = (gain − 1)·R1, an inverting one needs R2 = |gain|·R1, and a differential stage sets both R2 and R4 with R3 kept equal to R1 for best common-mode rejection.

What are the gain formulas for the three classic op-amp configurations?

Non-inverting gain is 1 + R2/R1, inverting gain is −R2/R1 (output inverted), and a differential stage has gain R2/R1 with R3 = R1 and R4 = R2 for CMRR. The tool assumes an ideal op-amp — real parts are limited by the gain-bandwidth product, so gain × bandwidth ≤ GBW and a high-gain stage is also a low-bandwidth one.

Voltage divider calculator Ohm's law calculator ← Back to all calculators

Ideal-op-amp model: real parts are limited by gain-bandwidth product and finite slew rate.ICBOMS provides this tool for reference only.