Op Amp Gain Calculator (Non-inverting, Inverting, Differential)

Formulas

• Non-inverting: Vout = (1 + Rf/Rg) × Vin
• Inverting: Vout = −(Rf/Rin) × Vin
• Differential (matched Rf, Rin top and bottom): Vout = (Rf/Rin) × (E2 − E1)
• Summing (inverting): Vout = −Rf × (E1/R1 + E2/R2 + …)
• dB = 20 × log10|G| (×10 = 20 dB, ×100 = 40 dB)
• With open-loop gain A: G ≈ ideal gain ÷ (1 + noise gain ÷ A)
• Closed-loop bandwidth ≈ GBW ÷ (1 + Rf/Rg)

Common E12 resistor pairs (GBW 1 MHz)

Inverting amplifiers also divide GBW by the noise gain 1 + Rf/Rin — a gain −1 inverter has noise gain 2, so half the bandwidth of a follower (gain 1) (TI handbook figures 40 and 41).

Finite open-loop gain (TI handbook figure 30 example)

TI's handbook takes an op amp with open-loop gain A = 10,000, 50 kΩ input impedance and 100 Ω output impedance, builds an inverting amplifier with ZI = 10 kΩ and ZO = 100 kΩ (ideal gain −10) driving 10 kΩ, and finds an error term δ ≈ 0.0013, so the real gain is −9.987 (0.13 % off). It notes the error can be trimmed out with the feedback resistor, after which a 10 % change in A moves the gain by less than 0.02 %. The calculator above uses the same expression with infinite input and zero output impedance (δ = noise gain ÷ A).

How to read it

• A non-inverting amplifier cannot have gain below 1. To attenuate, put a divider in front or use an inverting stage.
• A differential amplifier cancels common-mode voltage only if the top and bottom resistor ratios match. A mismatch within resistor tolerance leaves some common mode in the output.
• The op amp's input pins must stay within the common-mode range. In a differential amplifier they sit at E2 × Rf/(Rin + Rf); check that too (TI handbook p.25).
• The output clips near the supply rails. If the calculated output is beyond the supply, check the datasheet's output swing.

Where it is used

• Amplifying mV-level signals from thermocouples, load cells or shunt resistors to an ADC or PLC analog input range (non-inverting, differential).
• Scaling the voltage across a 4–20 mA receiver resistor to 0–10 V or 0–3.3 V.
• Amplifying only the difference between two points (a bridge output) while rejecting the common voltage (differential).

FAQ

What is the op amp gain formula?

Non-inverting: 1 + Rf/Rg; inverting: −Rf/Rin. With Rf = 100 kΩ and Rg = 10 kΩ, non-inverting gain is 11 (20.8 dB) and inverting −10 (20 dB).

Inverting vs non-inverting?

An inverting amplifier flips the sign and has an input impedance of Rin. A non-inverting amplifier keeps the sign and has very high input impedance, so it barely loads a sensor.

How do I convert gain to dB?

20 × log10(gain). ×10 = 20 dB, ×100 = 40 dB, ×1000 = 60 dB.

What happens to bandwidth at high gain?

Bandwidth ≈ GBW ÷ noise gain. A 1 MHz GBW op amp at a non-inverting gain of 101 is flat to about 9.9 kHz. For more bandwidth use a higher-GBW op amp or split the gain into two stages.

To turn the amplified voltage into ADC counts, use the ADC Resolution Calculator. To make a value from two resistors, use the Parallel & Series Resistor Calculator.

Basis

Formulas are from Texas Instruments' «Handbook of Operational Amplifier Applications» (SBOA092B) pp.15, 17, 18 (non-inverting, inverting), pp.23–25 (summing, differential), pp.27–28 (figure 30 — finite-gain example −9.987), p.31 (dB) and pp.36–37 (figures 40, 41 — bandwidth). Tests check that this calculator reproduces its example. Standard resistor values: Vishay 28372 (IEC 60063 tables). For open-loop gain, GBW and common-mode range, check your op amp's datasheet.