Calculators
Op-Amp Gain Calculator
Calculate ideal op-amp gain, output voltage, or feedback resistance.
Op-Amp Gain Calculator tool
Loading tool…
Jump to a section
About This Tool
Operational amplifiers are commonly configured with feedback resistors to set a predictable closed-loop voltage gain. This calculator covers two foundational ideal circuits: the inverting amplifier and the non-inverting amplifier. It can calculate closed-loop gain and ideal output from resistor values, or rearrange the gain equation to find the feedback resistor for a target gain. The results are useful for learning and first-pass resistor selection, while real circuits must still be checked against the chosen op-amp's electrical limits.
How To Use It
- Choose the inverting or non-inverting amplifier configuration.
- To calculate gain and ideal output, enter the input voltage and the two resistor values in ohms.
- To design for a target gain, choose feedback resistor mode, enter the desired gain and Rin or Rg, and read the ideal Rf value.
- Treat the calculated output as an ideal mathematical result; verify supply rails, input/output ranges, bandwidth and other datasheet limits before using a real device.
Examples
Inverting gain of -10
With Rin = 10 kΩ and Rf = 100 kΩ, Av = -Rf/Rin = -10. An ideal 0.5 V input therefore gives -5 V output.
Non-inverting gain of 10
With Rg = 10 kΩ and Rf = 90 kΩ, Av = 1 + Rf/Rg = 10. An ideal 0.5 V input gives 5 V output.
Choose Rf for gain 8
For a non-inverting amplifier with Rg = 10 kΩ and desired gain 8, Rf = (8 - 1) × 10 kΩ = 70 kΩ.
Useful Notes
Inverting amplifier equation
For the ideal inverting configuration, Av = Vout/Vin = -Rf/Rin. The negative sign indicates a 180-degree polarity inversion: a positive input produces a negative output relative to the circuit reference. The gain magnitude is the feedback-to-input resistance ratio.
Non-inverting amplifier equation
For the ideal non-inverting configuration, Av = 1 + Rf/Rg, where Rf runs from output to the inverting node and Rg runs from that node to the reference. The ideal closed-loop gain is always greater than or equal to 1; this calculator requires greater than 1 when solving for a positive finite Rf.
Solving for the feedback resistor
Rearranging the inverting equation gives Rf = |Av| × Rin. Rearranging the non-inverting equation gives Rf = (Av - 1) × Rg. The exact calculated resistance may not be a standard resistor value, so practical design normally chooses a nearby available value and recalculates the actual gain.
Output voltage is not unlimited
The ideal equation multiplies input voltage by closed-loop gain without modeling supply rails. A real op-amp cannot generally drive its output beyond its powered output-voltage range, and many devices cannot swing exactly to either rail. If the ideal result exceeds the usable range, the real output clips or saturates.
Frequency and slew-rate limits
Closed-loop gain formulas do not guarantee the same behavior at every frequency. Gain-bandwidth product, phase margin, compensation, capacitive loading, and slew rate can limit signal amplitude or accuracy as frequency rises. Consult the datasheet and stability guidance for the selected device.
Other real-world errors
Input bias current, input offset voltage, common-mode range, noise, resistor tolerance, temperature drift, source impedance, load current, and PCB layout can all shift a real result away from the ideal calculation. This tool is for the basic resistive feedback model, not device selection or safety qualification.
FAQ
Why is inverting op-amp gain negative?
The negative sign represents polarity inversion. In the ideal inverting circuit, a positive input change produces a negative output change while the gain magnitude is Rf/Rin.
Can a non-inverting amplifier have a gain below 1?
Not with the standard two-resistor non-inverting configuration modeled here. Its ideal gain is 1 + Rf/Rg. A voltage follower has gain 1 when the output is connected directly to the inverting input.
Does the calculated output include supply-voltage clipping?
No. The displayed output is the ideal equation result. Compare it with the chosen op-amp's supply rails and specified output swing under the intended load.
Can I enter resistor values in kΩ instead of Ω?
The UI labels values in ohms, but gain depends on a resistance ratio. You can multiply both resistor values by the same scale factor and obtain the same gain; the feedback-resistor result is displayed in ohms.
Is this enough to choose an op-amp for a circuit?
No. Device selection also depends on supply voltage, input common-mode range, output swing/current, bandwidth, slew rate, noise, offset, stability, temperature and other application requirements.