Op-Amp Gain Calculator: Inverting, Non-Inverting and Summing

How to use it

Choose Circuit: inverting, non-inverting, voltage follower, differential or summing, or Pick resistors for a gain.
Type the resistor boxes that the circuit uses, for example Feedback resistor Rf 10k and Input resistor R1 1k. Other boxes are ignored.
Type the input voltage or voltages. Read Gain and Output voltage Vout, then open Working, step by step.
For Pick resistors for a gain, type the Target gain and the circuit it is for. The Nearest resistor pairs table lists the closest E12 or E24 pairs.

The circuits

An op-amp with negative feedback keeps its two inputs at the same voltage. In the inverting circuit the inverting input is a virtual ground, so the input current flows through Rf, and the gain is the ratio of the two resistors.

Inverting:      Vout = −(Rf ÷ R1) × Vin
Non-inverting:  Vout = (1 + Rf ÷ Rg) × Vin
Follower:       Vout = Vin
Differential:   Vout = ((Rf + R1) ÷ R1) × (Rg ÷ (Rg + R2)) × V2 − (Rf ÷ R1) × V1
                gain Rf ÷ R1 when R1 ÷ Rf = R2 ÷ Rg
Summing:        Vout = −Rf × (V1 ÷ R1 + V2 ÷ R2 + V3 ÷ R3)

The inverting gain is negative, so the output is flipped, and its size can be below 1. The non-inverting gain is never below 1.
The follower has a gain of exactly 1 and a high input impedance, so it isolates a source from the load it drives.

Choosing preferred resistors

Resistors come in preferred values: E12 has 12 values in each decade and E24 has 24. The ratio of two preferred values gives a gain close to the target, and the calculator searches the pairs for the smallest error.

Inverting:      Rf ÷ R1 = |G|
Non-inverting:  Rf ÷ Rg = G − 1

Each preferred value is the nearest one in its series, so the real gain differs from the target by a few per cent. That difference is the error in the table.
A larger resistor loads the output less, but a very large one adds more noise and makes the input bias current error bigger. A resistance in the kilohm range is a common compromise.

What the calculator does not cover

The limits of the op-amp: its finite gain and bandwidth, the offset voltage and the bias current, and the output swing near the supply rails. Near the rails the output saturates and the formula no longer holds.
Frequency response: above the bandwidth of the op-amp the gain falls, so these formulas give the DC or low-frequency gain only.
Stability and capacitive loads, which can make a circuit oscillate.

Worked example: inverting, Rf 10 kΩ, R1 1 kΩ, input 0.5 V

The gain is G = −Rf ÷ R1 = −10 kΩ ÷ 1 kΩ = −10, which is 20 dB in size.

The output is Vout = G × Vin = −10 × 0.5 V = −5 V. The sign is inverted.

For a target gain of 10 with the inverting circuit, the pairs 1 kΩ with 10 kΩ and 10 kΩ with 100 kΩ are both exact in E24, so their error is 0 %.

Frequently asked questions

Why does the inverting gain have a minus sign?

The input current flows through Rin and then through Rf. The output has to draw that same current back the other way, so it has the opposite sign to the input.

What is a virtual ground?

With negative feedback the inverting input follows the non-inverting input. When the latter is grounded, the inverting input also sits at 0 V. Current enters it through Rin but does not flow into the op-amp.

Why can a non-inverting gain not be below 1?

The input goes straight into the non-inverting input, so the output is at least the input: Vout = (1 + Rf ÷ Rg) × Vin, and Rf ÷ Rg is never negative. The lowest gain is 1, which is the follower.

Why does the calculator show an error for the resistor pairs?

The pairs use preferred values, which come in fixed steps. Few pairs hit the target exactly, so the error shows how far the real gain is from the target.

What happens if the output would exceed the supply?

The op-amp saturates: the output stops near the supply rail and the formula no longer applies. Check that the calculated output is within the range the op-amp can reach from its supply.

Sources

Figures and text last checked on Tuesday, November 10, 2026.

Result

Working, step by step