Op Amp Gain Calculator: Inverting & Non-Inverting
Calculate inverting and non-inverting op amp gain, find standard E24 resistor pairs, and prevent supply rail clipping with step-by-step formulas.
How it works
Operational Amplifiers (Op-Amps) configure fixed closed-loop voltage gain using negative feedback networks:
Non-Inverting Op Amp Gain Calculator
In a non-inverting configuration, input voltage Vin is applied directly to the non-inverting (+) input pin. The output remains in phase with the input:
Av = 1 + (Rf / Rg)
Because the ratio Rf/Rg is always positive, non-inverting gain is always greater than or equal to 1.
Inverting Op Amp Gain Calculator
In an inverting configuration, input voltage Vin is applied through resistor Rin to the inverting (-) pin, while the non-inverting (+) pin is held at ground (virtual ground):
Av = -Rf / Rin
The negative sign reflects the 180° phase inversion between input and output.
Supply-Rail Output Clipping
Real op-amps cannot output voltages higher than their positive supply rail (V+) or lower than their negative supply rail (V-). Standard rail-to-rail op-amps can swing within millivolts of the rails, while non-rail-to-rail models (like the LM358 or LM741) clip 1.5V to 2V inside the rails. If Av × Vin exceeds the rails, the waveform will be hard-clipped.
Worked example
Non-Inverting Worked Example
Suppose you choose Rf = 90 kΩ and Rg = 10 kΩ:
- Av = 1 + (Rf / Rg)
- Av = 1 + (90,000 / 10,000) = 1 + 9 = 10
- An input signal of +0.2V produces an in-phase output of +2.0V.
Inverting Worked Example
Suppose you choose Rf = 100 kΩ and Rin = 10 kΩ:
- Av = -Rf / Rin
- Av = -100,000 / 10,000 = -10
- An input signal of +0.2V produces an inverted output of -2.0V.
Common mistakes
- Swapping Rf and Rin: In both formulas, feedback resistor Rf is divided by Rin (or Rg). Swapping them inverts the ratio.
- Forgetting the +1 in non-inverting: A non-inverting amplifier's gain is always at least 1. Forgetting the +1 leads to incorrect resistor choices.
- Ignoring input bias currents: Resistors over 1 MΩ introduce significant DC voltage offsets due to op-amp input bias currents.
Frequently Asked Questions
Why is non-inverting gain always greater than or equal to 1?
The formula for non-inverting gain is Av = 1 + (Rf / Rg). Since resistance values cannot be negative, the term (Rf / Rg) is always ≥ 0, which means Av is always at least 1. If Rf is 0Ω (or Rg is open/infinite), the circuit becomes a unity-gain buffer (voltage follower) with Av = 1.
Can an op-amp output exceed its supply voltage rails?
No. An op-amp can only output voltages within its power supply rails (V+ and V-). For example, with a single 0V to 5V supply, the output can never rise above 5V or drop below 0V, regardless of calculated gain. Signals exceeding these bounds saturate and clip.
How do I choose practical resistor values for Rf and Rin?
Typical practical resistor values range from 1 kΩ to 100 kΩ. Values below 1 kΩ draw excessive current from the op-amp output stage, while values above 1 MΩ are sensitive to PCB leakage currents, input bias currents, and stray parasitic capacitance.
Related Tools
Sources
- Texas Instruments Application Report SLOA058: "A Single-Supply Op-Amp Circuit Collection".
- Horowitz, P., & Hill, W. The Art of Electronics (3rd ed., Chapter 4: Operational Amplifiers).
Results are for engineering assistance. Verify important calculations and check official datasheets. See the Engineering Disclaimer.