How to use the Op-Amp Gain Calculator
- 1. Pick the circuitInverting, non-inverting, follower, difference or summing.
- 2. Enter resistors and inputsAdd the output swing limit and the gain-bandwidth product if you know it.
- 3. See gain and outputWorking shows each formula with your numbers.
Op-amp gain formulas
For an ideal op-amp (infinite gain, no input current), the main formulas are:
- Inverting: Av = −Rf / Rin
- Non-inverting: Av = 1 + Rf / R1
- Voltage follower: Av = 1
- Difference (matched resistors): Vout = (Rf / R1)(V2 − V1)
- Inverting summer: Vout = −Rf (V1/R1 + V2/R2)
Worked example: inverting amplifier with Rin = 10 kΩ, Rf = 100 kΩ and Vin = 0.5 V. Av = −100k / 10k = −10, which is 20 dB with a 180° phase shift. Vout = −10 × 0.5 = −5 V. With a 741 (GBW about 1 MHz) the noise gain is 1 + Rf/Rin = 11, so the bandwidth is about 1 MHz / 11 = 91 kHz.
Saturation and exam questions
A real op-amp cannot swing its output beyond its supply rails. If the ideal answer is more than the output limit, the output clips. Enter the limit (often supply minus about 1.5 V for older op-amps) and the tool flags clipping.
- Find Rf for a gain of −20 with Rin = 4.7 kΩ.
- Find the output of a summing amplifier with two inputs.
- Why is the input resistance of a non-inverting amplifier very high?
- Find the bandwidth of a gain-of-100 stage using a 1 MHz GBW op-amp (10 kHz).
Frequently asked questions
Why is the inverting amplifier gain negative?
The input goes to the inverting (−) terminal, so the output moves in the opposite direction. A negative gain means a 180° phase shift for sine waves.
What is noise gain?
It is 1 + Rf / Rin (the gain seen by the non-inverting input). Bandwidth is set by noise gain, so an inverting amplifier with gain −1 has a noise gain of 2.
Does this include offset voltage and slew rate?
No. It uses the ideal op-amp model taught in exams, plus output clipping and gain-bandwidth. Slew rate and offset need the datasheet.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.