How to use the op-amp gain calculator
- Choose the amplifier type: inverting, non-inverting, summer, difference or instrumentation.
- Enter the resistor values with unit suffixes such as 4.7k or 1M, and the input voltages.
- In More options set the supply voltages and how close to each rail the output can get.
- Read the gain, the ideal output and the output after the supply limit. A warning appears when the output would clip.
Formula
Inverting: gain = -Rf / Rin
Non-inverting: gain = 1 + Rf / Rg
Summing: Vout = -Rf (V1 / R1 + V2 / R2 + V3 / R3)
Difference: Vout = (R2 / R1)(V2 - V1); instrumentation: gain = (1 + 2R / Rgain)(R3 / R2)
These are the results for an ideal op amp: infinite open-loop gain, no input current and a perfect output. Gain in decibels is 20 log10 of the size of the gain.
Five amplifiers
An inverting amplifier with Rin = 1k and Rf = 10k has a gain of -10, so 0.5 V in gives -5 V out. A non-inverting one with Rg = 1k and Rf = 10k has a gain of 11, and 0.5 V in gives 5.5 V. A summer with Rf = 10k and inputs of 1 V through 10k and 2 V through 20k gives -(1 + 1) = -2 V.
A difference amplifier with R1 = 10k and R2 = 100k has a gain of 10, so inputs of 1 V and 1.1 V give 1 V. An instrumentation amplifier with Rgain = 1k, R = 25k and a unity output stage has a gain of 51, so the same 0.1 V difference gives 5.1 V. Using 1k and 100k with 0.5 V gives a gain of -100 and an ideal -50 V, which clips at -10.5 V on a plus and minus 12 V supply with 1.5 V of headroom.
Choosing a configuration
An inverting amplifier flips the signal and has an input resistance set by Rin. A non-inverting amplifier keeps the sign and presents a very high input resistance. A summer adds several inputs with separate weights. A difference amplifier amplifies the difference between two inputs and rejects what they share, and an instrumentation amplifier improves on it with high input resistance and a gain set by one resistor.
For the related resistor basics, see the Ohm's law calculator, the voltage divider calculator, the RC filter calculator and the resistor network calculator.
Supply limits and clipping
An op amp cannot put out more than its supply allows. The output stops short of each rail by an amount that depends on the part, and the page lets you set it. The default 1.5 V is only an example, so use your datasheet. Beyond that point the output clips and the formula no longer holds. Real parts also limit bandwidth and speed, which the ideal model leaves out.
Assumptions and limits
- The op amp is ideal in the gain formulas, with no offset, bias current or finite bandwidth.
- Resistors are exact. Real resistor tolerance changes the gain, and a mismatch in a difference amplifier lets common signals through.
- The example headroom of 1.5 V and the plus and minus 12 V supply are editable and are not from a datasheet.
- The target gain option works for inverting, non-inverting and difference amplifiers.
Frequently asked questions
How do I calculate the gain of an inverting amplifier?
Divide the feedback resistor by the input resistor and make it negative. With 10k and 1k the gain is -10, and a 0.5 V input gives -5 V.
Why is the gain of a non-inverting amplifier always at least 1?
The gain is 1 plus Rf over Rg, and neither resistor can be negative, so the gain cannot fall below 1. A voltage follower is the case with no feedback resistor.
What is the output swing limit?
It is how close the output can get to each supply rail. Many parts stop a volt or two short of the rails, while rail-to-rail parts get within a few millivolts. Use the figure from your part's datasheet.
How do I pick resistors for a wanted gain?
Fix one resistor, such as 10k, then compute the other. For an inverting gain of -20 with Rin = 10k, Rf = 200k. Fill in the optional target gain field and the page does this for you.