Op-Amp Inverting Gain Calculator

Find the closed-loop gain, output voltage, and input impedance of an inverting op-amp circuit from its feedback and input resistors.

🔌 Op-Amp Inverting Gain Calculator
Input voltage (Vin)0.50 V
V
-10 V10 V
Ω
Ω
Output voltage (Vout)
—
Gain (Av)
—
Input impedance (Zin)
—
Step-by-step working

🔌 What is the Op-Amp Inverting Gain Calculator?

The Op-Amp Inverting Gain Calculator finds the closed-loop voltage gain, output voltage, and input impedance of an inverting operational amplifier circuit, one of the two fundamental op-amp amplifier topologies, from its feedback resistor Rf and input resistor Rin.

Electronics designers use this calculation to set the gain of audio preamplifiers and signal conditioning stages, build summing amplifiers and active filters that use the same inverting-configuration math, and choose resistor values that keep output voltage within the op-amp's supply rails for a given input signal range.

A common point of confusion is that the inverting amplifier's input impedance is not infinite, unlike the non-inverting configuration. Because negative feedback holds the inverting input at virtual ground, the impedance seen by the signal source equals Rin itself, which matters when the source cannot drive a low-impedance load.

This calculator applies the ideal op-amp approximation (infinite open-loop gain, no input bias current, zero output impedance), which is accurate for the vast majority of practical designs operating well within the op-amp's bandwidth and voltage swing limits.

📐 Formula

Av = −Rf / Rin      Vout = Av × Vin
Av = closed-loop voltage gain (dimensionless)
Rf = feedback resistor (Ω), Rin = input resistor (Ω)
Zin ≈ Rin (virtual ground approximation)
Example: Vin = 0.5 V, Rin = 1,000 Ω, Rf = 10,000 Ω → Av = -10, Vout = -5 V.

📖 How to Use This Calculator

Steps

1
Enter the input voltage. Type Vin, the signal voltage applied to the input resistor.
2
Enter the input resistor. Type Rin, the resistor connecting the signal source to the inverting input.
3
Enter the feedback resistor. Type Rf, the resistor connecting the output back to the inverting input.

💡 Example Calculations

Example 1 — 10x Inverting Gain Stage

Vin = 0.5 V, Rin = 1,000 Ω, Rf = 10,000 Ω

1
Av = −10,000 / 1,000 = -10
2
Vout = -10 × 0.5 V = -5 V
Av = -10, Vout = -5 V
Try this example →

Example 2 — Same Ratio, Larger Resistors

Vin = 2 V, Rin = 2,200 Ω, Rf = 22,000 Ω

1
Av = −22,000 / 2,200 = -10
2
Vout = -10 × 2 V = -20 V
Av = -10, Vout = -20 V
Try this example →

Example 3 — Unity-Gain Inverter

Vin = 1 V, Rin = 4,700 Ω, Rf = 4,700 Ω

1
Av = −4,700 / 4,700 = -1
2
Vout = -1 × 1 V = -1 V
Av = -1, Vout = -1 V
Try this example →

❓ Frequently Asked Questions

What is the formula for inverting op-amp gain?+
The closed-loop gain of an inverting amplifier is Av = -Rf/Rin, where Rf is the feedback resistor from output to the inverting input, and Rin is the input resistor from the signal source to the inverting input. The negative sign indicates a 180-degree phase inversion.
Why is the gain negative?+
In an inverting amplifier, the input signal enters the inverting terminal, so negative feedback drives the output in the opposite direction to the input to hold the inverting node at virtual ground. This produces an output that is inverted (180 degrees out of phase) relative to the input.
What is virtual ground in an inverting amplifier?+
Virtual ground is the condition where the op-amp's negative feedback holds the inverting input at approximately the same voltage as the non-inverting input (usually 0 V or ground), even though no physical ground connection exists there, which is why the input impedance seen by the source equals Rin.
What is the input impedance of an inverting amplifier?+
The input impedance looking into the input resistor is approximately Rin, because the inverting input is held at virtual ground by feedback. This is lower than a non-inverting amplifier's near-infinite input impedance, and matters when the signal source has significant output impedance.
How do I get a gain of exactly -1?+
Set the feedback resistor Rf equal to the input resistor Rin. This configuration is called a unity-gain inverter and is commonly used to flip a signal's polarity without changing its amplitude.
What happens if Rin is very small?+
A very small Rin increases the gain magnitude (since Av = -Rf/Rin) but also lowers the input impedance the source must drive, and increases the current the op-amp's output stage must supply, which can push the circuit toward its output current limits for larger input voltages.
Can Vin and Vout be AC signals?+
Yes, this formula applies equally to DC and AC signals within the op-amp's bandwidth, at higher frequencies the real (non-ideal) op-amp's finite gain-bandwidth product will reduce the actual gain below the ideal Av = -Rf/Rin value.
What limits the maximum output voltage?+
The op-amp's output voltage swing is limited by its supply rails, typically to within 1 to 2 volts of the positive and negative supply for standard op-amps, or much closer to the rails for rail-to-rail output parts. Vout calculated here assumes no clipping against those limits.
Does source resistance affect the gain?+
Yes, if the signal source has nonzero output resistance, it effectively adds in series with Rin, slightly reducing the actual gain magnitude below -Rf/Rin. For most practical designs with a low-impedance source, this effect is negligible.
What units does this calculator use?+
Input and output voltages are in volts, and both resistors are in ohms. Gain Av is dimensionless (a ratio), and input impedance is reported in ohms.
Tags: Op-Amp Gain Calculator Inverting Amplifier Calculator Op Amp Output Voltage Calculator Feedback Resistor Calculator Operational Amplifier Calculator Calculator Formula Free Online

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What is the formula for inverting op-amp gain?

The closed-loop gain of an inverting amplifier is Av = -Rf/Rin, where Rf is the feedback resistor from output to the inverting input, and Rin is the input resistor from the signal source to the inverting input. The negative sign indicates a 180-degree phase inversion.

Why is the gain negative?

In an inverting amplifier, the input signal enters the inverting terminal, so negative feedback drives the output in the opposite direction to the input to hold the inverting node at virtual ground. This produces an output that is inverted (180 degrees out of phase) relative to the input.

What is virtual ground in an inverting amplifier?

Virtual ground is the condition where the op-amp's negative feedback holds the inverting input at approximately the same voltage as the non-inverting input (usually 0 V or ground), even though no physical ground connection exists there, which is why the input impedance seen by the source equals Rin.

What is the input impedance of an inverting amplifier?

The input impedance looking into the input resistor is approximately Rin, because the inverting input is held at virtual ground by feedback. This is lower than a non-inverting amplifier's near-infinite input impedance, and matters when the signal source has significant output impedance.

How do I get a gain of exactly -1?

Set the feedback resistor Rf equal to the input resistor Rin. This configuration is called a unity-gain inverter and is commonly used to flip a signal's polarity without changing its amplitude.

What happens if Rin is very small?

A very small Rin increases the gain magnitude (since Av = -Rf/Rin) but also lowers the input impedance the source must drive, and increases the current the op-amp's output stage must supply, which can push the circuit toward its output current limits for larger input voltages.

Can Vin and Vout be AC signals?

Yes, this formula applies equally to DC and AC signals within the op-amp's bandwidth, at higher frequencies the real (non-ideal) op-amp's finite gain-bandwidth product will reduce the actual gain below the ideal Av = -Rf/Rin value.

What limits the maximum output voltage?

The op-amp's output voltage swing is limited by its supply rails, typically to within 1 to 2 volts of the positive and negative supply for standard op-amps, or much closer to the rails for rail-to-rail output parts. Vout calculated here assumes no clipping against those limits.

Does source resistance affect the gain?

Yes, if the signal source has nonzero output resistance, it effectively adds in series with Rin, slightly reducing the actual gain magnitude below -Rf/Rin. For most practical designs with a low-impedance source, this effect is negligible.

What units does this calculator use?

Input and output voltages are in volts, and both resistors are in ohms. Gain Av is dimensionless (a ratio), and input impedance is reported in ohms.

📌 Quick Tips

💡The inverting gain formula assumes an ideal op-amp: infinite open-loop gain, infinite input impedance, and zero output impedance, real op-amps approximate this well within their bandwidth and output swing limits.
💡The negative sign in Av means the output is 180 degrees out of phase with the input, a positive input produces a negative output and vice versa.
💡Input impedance at the inverting input equals Rin, not infinity, because the inverting node is held at a virtual ground rather than being a true high-impedance node like the non-inverting input.
💡Keep Rf below about 1 megohm in practical designs, very large feedback resistors increase noise gain and make the circuit more sensitive to input bias current errors.
💡For a unity-gain inverter (Av = -1), simply set Rf equal to Rin.