Op-Amp Gain Calculator
Calculate the ideal closed-loop voltage gain of a standard inverting or non-inverting operational-amplifier stage from its two feedback-network resistances.
Inputs
Select the standard closed-loop configuration.
Required. Positive resistance; U.S.-style decimal notation is accepted.
Required. Positive resistance; the unit may differ from the input-resistance unit.
Live result
Gain
10.00 V/V
Magnitude shown; the inverting transfer has a negative sign and a 180° phase reversal.
Current ideal relation
|A| = Rf / Rin = 10.00
Inverting gain magnitude: 10.00 volts per volt.
How to use this op-amp gain calculator
What this calculator does
This calculator estimates the ideal closed-loop voltage gain of the two most common resistive op-amp amplifier configurations. It uses the resistor ratio that sets feedback around an ideal operational amplifier. For an inverting stage, the transfer gain is negative and its magnitude is Rf/Rin. For a non-inverting stage, the gain is 1 + Rf/Rin. The displayed Gain is the positive magnitude in volts per volt, while the nearby note states whether the transfer is inverted. This is a resistor-network calculation, not a complete prediction of a real amplifier's bandwidth, slew rate, noise, offset, output swing, input common-mode limits, stability, or power-supply behavior.
When to use it
- Choose resistor values for a first-pass analog gain stage before checking a specific op-amp data sheet.
- Verify the intended gain of an existing inverting or non-inverting feedback network.
- Compare how changing one resistor alters closed-loop gain while keeping the other fixed.
- Check classroom, lab, or prototype calculations where the ideal-op-amp approximation is appropriate.
How to calculate
The calculator opens with a complete demonstration: an Inverting stage, Input resistance of 1 kΩ, and Feedback resistance of 10 kΩ. Its result is already calculated and its XLSX workbook is ready for download.
- Choose Op-amp type: Inverting or Non-inverting.
- Replace the demonstration Input resistance and choose its Input resistance unit. If you change the unit, the entered physical resistance is converted rather than merely relabeled.
- Enter Feedback resistance and choose its Feedback resistance unit. The two resistors may use different displayed units because the calculation converts both to ohms internally.
- Read Gain in V/V. Results update automatically. For an inverting stage, interpret the displayed number as gain magnitude; the signed transfer is negative. For a non-inverting stage, the signed transfer equals the displayed positive gain.
- Select Download Excel to export the current validated inputs and calculated result as a real XLSX workbook. Reset deliberately clears the demonstration resistance values; after Reset, export remains unavailable until both required resistances are valid again.
Input guide
Op-amp type is required and accepts exactly Inverting or Non-inverting. Use Inverting when the signal enters through the input resistor into the inverting terminal; use Non-inverting when the signal drives the non-inverting terminal and the resistor network closes feedback to the inverting terminal. Changing this control changes the formula itself. Analog Devices' inverting op-amp explanation shows why the ideal transfer gain is negative.
Input resistance is required and must be a finite positive number. The accepted numeric convention uses a period as the decimal separator; correctly grouped thousands such as 1,000 are accepted, while ambiguous decimal-comma input such as 1,5 is rejected. A realistic example is 1 with Input resistance unit set to kΩ. Increasing Rin while Rf stays fixed reduces the resistor ratio and therefore reduces gain. Zero and negative resistance entries are rejected because these simple ideal gain equations assume positive resistor magnitudes.
Input resistance unit is required and supports Ω, kΩ, and MΩ. It changes the scale of the displayed resistance, not the physical resistor. For example, switching 1 kΩ to Ω converts the input to 1000 Ω. A common mistake is to change a unit and then manually re-enter the old number, unintentionally changing the actual resistance by a factor of one thousand or one million.
Feedback resistance is also required, finite, and positive, with the same accepted numeric format. The demonstration uses 10 and Feedback resistance unit of kΩ. Increasing Rf while Rin stays fixed increases gain in either configuration. Feedback resistance unit supports Ω, kΩ, and MΩ and converts the current value when changed. The resistor units do not need to match; only their physical values matter to the ratio.
Output guide
Gain is a dimensionless voltage ratio presented as V/V. It is driven by the selected configuration and the physical values of Rf and Rin. In an inverting stage, a gain magnitude below 1 is possible when Rf is smaller than Rin; a magnitude of 1 means equal resistor values. In a non-inverting stage, ideal gain cannot fall below 1 because the formula contains the additional unity term. Analog Devices' non-inverting amplifier derivation gives the ideal relation 1 + Rf/Rin. A very high calculated gain is mathematically valid in this ideal model but may be unattainable in practice once a real device's gain-bandwidth product, output swing, stability, noise, and other limits are considered.
Worked example
With the startup values, Rin is 1 kΩ = 1000 Ω and Rf is 10 kΩ = 10,000 Ω. The resistor ratio is therefore 10,000 / 1000 = 10. Because the selected stage is Inverting, its signed ideal transfer gain is -10 V/V; the calculator displays the magnitude as 10.00 V/V and notes the 180° phase reversal. If you switch only Op-amp type to Non-inverting, the same resistor values produce 1 + 10 = 11.00 V/V.
Learn more
The ideal equations are useful because negative feedback makes a closed-loop amplifier's gain depend primarily on its external network, but a real op amp still has finite electrical limits. Texas Instruments' overview of operational amplifiers and gain is a practical next step before applying a resistor-only result to hardware.
How the ideal gain model works
For the classic inverting circuit, negative feedback holds the inverting node near the same potential as the grounded non-inverting node. Under the ideal assumptions, essentially no current enters the op-amp input, so the current through the input resistor also flows through the feedback resistor. That produces the familiar signed transfer relation A = -Rf/Rin. The negative sign represents polarity reversal, not a negative magnitude of amplification.
For the classic non-inverting circuit, the input signal is applied directly to the non-inverting terminal. The resistor divider at the inverting terminal returns a fraction of the output. Solving the ideal feedback condition gives A = 1 + Rf/Rin. Equal resistors therefore give an ideal non-inverting gain of 2 V/V, while equal resistors in an inverting circuit give a gain magnitude of 1 V/V.