Op-Amp Gain Calculator
Enter your resistor values and choose your amplifier configuration to get the voltage gain, gain in decibels, output voltage, and input impedance of your operational amplifier circuit. Supports inverting, non-inverting, and difference amplifier topologies. Results update instantly as you type.
How op-amp gain is calculated
An operational amplifier achieves a precise, predictable gain by using negative feedback. Without feedback, an ideal op-amp has infinite open-loop gain, which makes it impractical for analog amplification. Adding a feedback resistor (Rf) between the output and the inverting input reduces and controls the gain to a value set purely by the external resistors, not the op-amp chip itself. For a non-inverting amplifier, voltage gain Av = 1 + R2 / R1. For an inverting amplifier, Av = -Rf / Rin, where the negative sign means the output is 180 degrees out of phase with the input. These simple ratios are the foundation of almost every analog signal-conditioning circuit.
Inverting vs. non-inverting configurations
The two most common single-input configurations differ in two key ways: phase and input impedance. A non-inverting amplifier applies the input directly to the positive (+) terminal, so the output stays in phase with the input and the input impedance is very high (ideally infinite), making it ideal for buffering high-impedance sources like sensors. An inverting amplifier applies the input through Rin to the negative (-) terminal, so the output is flipped 180 degrees, and the input impedance is equal to Rin itself. This lower and predictable input impedance is an advantage in some circuit designs such as transimpedance amplifiers and summing circuits. Both configurations are equally accurate and stable when the resistors are matched with good tolerances.
Difference amplifiers and common-mode rejection
A difference amplifier uses four resistors to amplify the voltage difference between two inputs while rejecting any common signal they share (such as noise or ground offset). When the resistor ratios are perfectly balanced (R1/R2 = R3/R4), the common-mode rejection ratio (CMRR) is theoretically infinite, meaning only the differential signal appears at the output. In practice, 1% resistors limit CMRR to around 34 dB, while 0.1% precision resistors push it above 54 dB. For demanding instrumentation applications, a dedicated instrumentation amplifier IC (INA, AD, or similar) is preferred over a discrete difference amplifier because it maintains high CMRR internally.
Gain in decibels and resistor selection guidelines
Engineers often express gain in decibels (dB) because decibels are additive across cascaded stages, which makes system-level math simpler. Gain in dB = 20 x log10(|Av|). A gain of 10 V/V is 20 dB; a gain of 100 V/V is 40 dB; unity gain (1 V/V) is 0 dB. When selecting resistors, keep values between 1 kohm and 1 Mohm for general-purpose op-amps. Values below 1 kohm load the output and can exceed the op-amp drive capability; values above 1 Mohm increase noise and the effect of bias currents. For high gains, consider cascading two lower-gain stages rather than using a single stage with a 1000:1 resistor ratio, which is harder to lay out accurately and more sensitive to parasitic capacitance.
Common op-amp gain configurations
| Configuration | Gain formula | Typical gain range | Phase shift | Common use |
|---|---|---|---|---|
| Non-inverting | 1 + R2/R1 | 1 to 1000 V/V | 0 degrees | Sensor buffering, ADC driving |
| Inverting | -Rf/Rin | -1 to -1000 V/V | 180 degrees | Signal inversion, summing circuits |
| Voltage follower (buffer) | 1 (no feedback R) | 1 V/V (0 dB) | 0 degrees | Impedance matching |
| Difference amplifier | R2/R1 (balanced) | 1 to 100 V/V | Input-dependent | Bridge sensors, audio |
| Summing inverting | -Rf/Rin per input | Configurable | 180 degrees | DAC, audio mixing |
Standard resistor ratios and typical applications. Values shown are representative; real designs should account for bias current, bandwidth, and noise.
Frequently asked questions
What is the gain formula for a non-inverting op-amp?
The voltage gain of a non-inverting amplifier is Av = 1 + R2 / R1, where R2 is the feedback resistor and R1 is the resistor from the inverting input to ground. The minimum gain is 1 (when R2 = 0 or R1 is open), which gives a unity-gain buffer or voltage follower.
What is the gain formula for an inverting op-amp?
The voltage gain of an inverting amplifier is Av = -Rf / Rin, where Rf is the feedback resistor from the output to the inverting (-) terminal and Rin is the input resistor from the signal source to the inverting terminal. The negative sign means the output signal is flipped 180 degrees relative to the input.
How do I convert op-amp gain from V/V to decibels?
Use the formula: Gain (dB) = 20 x log10(|Av|). For example, a gain of 10 V/V is 20 dB, a gain of 100 V/V is 40 dB, and a gain of 0.5 V/V (attenuation) is -6 dB. The absolute value ensures you work with the magnitude before taking the logarithm.
What resistor values should I use for an op-amp gain circuit?
A good general rule is to keep resistor values between 1 kohm and 100 kohm. Values much below 1 kohm can draw more current than the op-amp can supply; values above 1 Mohm increase Johnson noise and make the circuit sensitive to input bias currents. For precise gain accuracy, use resistors with 0.1% or better tolerance. Thin-film resistors or matched resistor networks are preferred for low-drift applications.
What is the input impedance of an op-amp amplifier?
For a non-inverting amplifier, the input impedance is very high (ideally infinite, practically tens of megaohms or more due to the op-amp input stage). For an inverting amplifier, the input impedance is simply equal to Rin, because the inverting terminal is held at a virtual ground. For a difference amplifier, the input impedance is R1 + R2 as seen from each input.
What is the difference between open-loop and closed-loop gain?
Open-loop gain is the internal amplification of the op-amp chip with no feedback, typically 100 dB or more (100,000 V/V). It is huge, poorly controlled, and varies with temperature and frequency. Closed-loop gain is the gain after you apply negative feedback via external resistors; it is small, precise, and set entirely by the resistor ratio. Almost all practical circuits operate in closed-loop mode.