Op Amp Gain Interactive Calculator

Working out the right feedback resistor values for an op amp circuit by hand can be tedious and leaves plenty of room for mistakes—especially if you’re changing between inverting and non-inverting setups, or need to solve for a specific gain. This calculator lets you quickly figure out voltage gain, output voltage, and key resistor values (Rf, Rg, Rin) using common variables like Vin and desired gain. These calculations are routine if you’re conditioning sensor signals, amplifying audio, or designing precision analog gear—anywhere you need steady, predictable closed-loop gain. Here, you’ll find all the main formulas, a real-world example, discussion of configuration, and answers to practical engineering questions.

What is op amp gain?

Op amp gain is simply the ratio between output and input voltages—controlled by picking two resistor values. It's a straightforward process, needing no tuning beyond resistor choice.

Simple Explanation

A good way to picture an op amp is as a volume knob set by resistor values. Change the resistor ratio, and the amp changes how much the signal gets amplified. It’s immediate and direct—resistor values in, gain out.

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Op Amp Configuration Diagrams

Op Amp Gain Calculator

How to Use This Calculator

1. Pick your calculation mode—choose the circuit type (inverting/non-inverting) and decide what you want to solve for (gain, Rf, or Vout).
2. Enter the resistor values in ohms (Rf, Rg, or Rin depending on the mode) and any voltage values you have (Vin or Vout).
3. If you want to solve for Rf, give the desired gain and the other resistor value (Rg or Rin).
4. Click Calculate for the result.

Op Amp Gain Equations

Here’s the standard formula if you’re dealing with a non-inverting op amp.

If you’re using an inverting op amp, use the formula below.

To get the gain in decibels, use this equation.

Simple Example

Non-inverting configuration: Rf = 10,000 Ω, Rg = 1,000 Ω.
A_V = 1 + (10,000 / 1,000) = 11
With Vin = 1 V: Vout = 1 × 11 = 11 V
Gain in dB = 20 × log10(11) = 20.83 dB

Theory & Engineering Applications

Op amps handle analog signal amplification by relying on negative feedback and good resistor selection. Closed-loop gain in practice depends entirely on your resistor values—as long as your op amp has high enough open-loop gain (usually 100,000 or above). This makes it possible to set up circuits where the gain stays consistent, regardless of manufacturing or temperature differences between individual op amps.

Non-Inverting Amplifier Configuration

In a non-inverting setup, the input signal goes directly to the non-inverting (+) input. Part of the output gets fed back to the inverting (–) input via a resistor divider. Because of negative feedback, the voltage at the inverting terminal is forced to match the non-inverting input—often called the "virtual short." The textbook result is the familiar gain formula: A_V = 1 + R_f/R_g.

This approach gives you very high input impedance—often in the megohms or even higher—since the signal doesn’t see any series resistance before reaching the op amp’s input stage. The lowest gain you can get is 1 (no amplification), which happens if R_f is set to zero (making what’s called a voltage follower, or buffer).

Inverting Amplifier Configuration

In the inverting setup, the non-inverting input is grounded and the signal goes through R_in to the inverting pin. The feedback resistor R_f connects the output back to that same pin. Because the inverting input is held at virtual ground, all input current (I_in = Vin/R_in) must flow through the feedback path, producing an output voltage equal to -Vin × (R_f/R_in). The minus sign shows you get 180° phase inversion at the output.

This design sets your input impedance to R_in—typically 10kΩ to 100kΩ for most general circuits, though it can be adjusted. That means your source must be able to drive this resistance, which can load weak signal sources. However, the inverting amp often does a better job rejecting common-mode noise and is handy if you want to sum signals or handle differential conversion.

Resistor Selection and Practical Limitations

The equations for op amp gain look easy but the choices you make for resistor values have to account for trade-offs. Going too low (below 1kΩ) means the op amp pulls more current at the output—sometimes more than it can handle without distortion or excess heat. Pushing values too high (well over 1MΩ) raises noise, makes the circuit more sensitive to stray interference, and can introduce unwanted DC offsets through the op amp's input bias currents.

Input bias currents typically fall between 10nA and 10µA depending on the op amp. When those currents flow through big resistors, they induce voltage offsets (V_offset = I_bias × R) that quickly add up. If you need offset under 1mV and your op amp’s bias current is 100nA, you’ll want to keep total resistance seen by that pin below 10kΩ. As a rule of thumb, 1kΩ to 1MΩ covers almost all sensible choices, with 10kΩ to 100kΩ being the usual starting point for most circuits.

Frequency Response and Bandwidth Considerations

Op amp bandwidth gets set by the gain-bandwidth product (GBW), which is fixed by the chip itself. For example, with a 1MHz GBW, you’ll get up to 1MHz bandwidth at unity gain, but only 100kHz if you raise the gain to 10, and just 10kHz with gain of 100. Beyond those points, the frequency response drops off. Large resistor values and layout can also cause high-frequency instability. Sometimes you need to add a small capacitor (1pF–100pF) in parallel with R_f to keep the circuit stable, even though that narrows the bandwidth further. To figure out the cap size, start with C_f ≈ 1/(2πR_ff_-3dB).

Slew Rate and Large Signal Performance

Slew rate is how quickly the op amp output can change, typically in V/µs. This kicks in if you want high-amplitude or fast-changing signals. Say you want to output a 10Vpp (5V amplitude) sine at 16kHz: you’ll need at least 0.5V/µs of slew rate or you’ll see the signal distorting even if the small signal bandwidth looks high enough. This is often overlooked—audio and sensor applications where you swing several volts at high frequency will push up against these limits.

Worked Example: Precision Sensor Signal Conditioning

Suppose you have a strain gauge bridge that gives 3.73mV at full load, but your data system needs the signal to stretch from 0V up to 5V for accurate reads. You’ll want a non-inverting amp that boosts the signal by about 1340× (5V / 0.00373V). Resistor values have to keep offset currents low and bandwidth over 10kHz, with your op amp’s bias current capped at 50nA.

Step 1: Calculate Required Gain

Required gain: A_V = 5V / 0.00373V = 1340.2. Use 1340 for calculations.

Step 2: Select Resistor Values for Minimal Offset

Using A_V = 1 + R_f/R_g, rearrange to get R_f = (A_V - 1) × R_g = 1339 × R_g. To cut offset, keep R_g moderate—say, 100Ω. That gives R_f = 133900Ω (standard value: 133kΩ), so gain is actually 1331.

Step 3: Verify Offset Error

Total resistance at the input is about 100Ω (parallel combo), and the bias current of 50nA produces 5µV offset, which multiplies out to 6.66mV at the output—just 0.13% error on 5V, which is reasonable.

Step 4: Check Bandwidth Requirements

To maintain 10kHz bandwidth at gain of 1331, GBW should be at least 13.31MHz. A TL072 (3MHz GBW) won’t cut it—its real bandwidth here would just be 2.25kHz. An LM833 (15MHz GBW) can deliver about 11.27kHz, so it passes.

Step 5: Verify Slew Rate for Dynamic Signals

At 5V amplitude and 10kHz: minimum slew rate is 0.314V/µs. The LM833’s 7V/µs is far more than you’ll need.

Final Design: Non-inverting amp with R_g = 100Ω, R_f = 133kΩ; LM833 op amp. Gain = 1331; output up to 4.96V for full-scale sensor; bias-induced offset about 0.13% of span; bandwidth about 11.3kHz.

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Practical Applications

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