Inverting Op-Amp Gain Calculator
This Inverting Op-Amp Gain Calculator finds the ideal closed-loop voltage gain set by the input resistor and feedback resistor in an inverting amplifier.
Use it for first-pass analog gain planning, signal conditioning, summing amplifier preparation, sensor interface review, and lab checks where the ideal inverting op-amp equation is appropriate.
Engineering tool
Inverting Op-Amp Gain Calculator
Calculate ideal closed-loop gain for an inverting op-amp amplifier from the input resistor and feedback resistor.
Resistor between the input signal and the inverting input.
Resistor from op-amp output to the inverting input.
Closed-loop gain (Av)
-10 V/V
Result console
- Closed-loop gain (Av)
- -10V/V
- Gain magnitude
- 10V/V
- Gain
- 20dB
- Phase shift
- 180°
- Input resistor (Rin)
- 1kΩ
- Feedback resistor (Rf)
- 10kΩ
Gain is valid for the ideal inverting op-amp model.
Formula reference
Inverting Op-Amp Gain Formula
The ideal inverting amplifier assumes negative feedback, a virtual ground at the inverting input, zero input current into the op-amp, unlimited output swing, and enough bandwidth for the selected gain magnitude.
Av = -Rf / Rin|Av| = Rf / RinGain(dB) = 20 × log10(|Av|)Phase shift = 180°Variable definitions
- Av
- Signed closed-loop voltage gain in V/V
- |Av|
- Gain magnitude without the negative sign
- Rin
- Input resistor from the signal source to the inverting input
- Rf
- Feedback resistor from output to the inverting input
- Gain(dB)
- Voltage gain magnitude expressed in decibels
- Phase shift
- Output phase inversion relative to the input
Variable Description
- Input resistor (Rin)
- The resistor connected between the input signal and the inverting input. It sets input impedance and appears in the denominator of the gain equation.
- Feedback resistor (Rf)
- The resistor connected between the op-amp output and the inverting input. Increasing Rf increases gain magnitude.
- Closed-loop gain (Av)
- The signed ideal voltage gain. The negative sign means the output is inverted relative to the input.
- Gain magnitude and dB
- The absolute value of Av is used for gain magnitude and dB conversion.
Worked Examples
Example 1: Gain of -10
- Rf
- 10 kΩ
- Rin
- 1 kΩ
Av = -Rf / Rin
Av = -10 kΩ / 1 kΩ = -10
Gain = -10 V/V, |Av| = 10, Gain ≈ 20 dB, Phase = 180°
The output magnitude is ten times the input magnitude, but the signal polarity is inverted in the ideal model.
Example 2: Gain of -50
- Rf
- 100 kΩ
- Rin
- 2 kΩ
Av = -Rf / Rin
Av = -100 kΩ / 2 kΩ = -50
Gain = -50 V/V, |Av| = 50, Gain ≈ 33.98 dB, Phase = 180°
A gain magnitude of 50 can amplify low-level signals, but bandwidth, noise, offset, and output swing must be checked.
Ideal op-amp assumption
The equation assumes infinite open-loop gain, zero input current, zero offset, unlimited output swing, and stable negative feedback.
Negative feedback
The feedback resistor returns output voltage to the inverting input and creates a virtual ground when the non-inverting input is grounded.
Closed-loop gain
The resistor ratio sets signed gain. The negative sign describes inversion, while the magnitude describes amplification or attenuation.
Input impedance
The input resistor largely sets the input impedance seen by the signal source in the ideal inverting configuration.
Output phase inversion
The output is ideally 180° out of phase with the input signal, so polarity matters in signal-chain and feedback designs.
Gain-bandwidth tradeoff
Higher gain magnitude reduces available closed-loop bandwidth for a fixed op-amp gain bandwidth product.
Common Mistakes
Confusing inverting and non-inverting formulas
The inverting formula is Av = -Rf/Rin. The non-inverting formula is Av = 1 + Rf/Rg.
Ignoring the negative sign
The negative sign is not a calculation error. It indicates output inversion.
Confusing gain and gain magnitude
Use signed gain for polarity and gain magnitude for dB conversion.
Calculating dB from negative gain
Use 20 × log10(|Av|), not 20 × log10(Av), because logarithms require a positive magnitude.
Swapping Rin and Rf
Reversing the input and feedback resistors changes the gain magnitude and source loading.
Support reference
FAQ
What is an inverting amplifier?
An inverting amplifier is an op-amp circuit where the input signal is applied through an input resistor to the inverting input, producing an output with opposite polarity.
Why is the gain negative?
The negative sign in Av = -Rf/Rin indicates phase inversion. A positive input produces a negative output in the ideal inverting amplifier model.
Why is the output 180° out of phase?
The inverting input and negative feedback force the output to move in the opposite direction of the input signal, which corresponds to a 180° phase shift for sinusoidal signals.
How is gain in dB calculated?
Use the gain magnitude, not the negative signed gain: Gain(dB) = 20 × log10(|Av|).
Can the gain be less than one?
Yes. If Rf is smaller than Rin, the magnitude of the inverting gain is below one, so the circuit attenuates while still inverting the signal.
What happens if Rf is zero?
In the ideal equation, Rf = 0 gives Av = 0. In real circuits this is not normally used as a practical amplifier gain setting.
Why must Rin be greater than zero?
Rin is in the denominator of -Rf/Rin and also sets the input impedance. A zero-ohm Rin would create division by zero and an invalid ideal gain calculation.
Related Engineering Guides
Dedicated op-amp guides are planned for this topic cluster. These guide topics are reserved for future publication and are shown without links until the pages exist.
Planned Engineering Guide
Operational Amplifier Basics
Planned guide covering ideal op-amp behavior, feedback, input terminals, output behavior, and common gain stages.
Planned Engineering Guide
Negative Feedback in Op-Amps
Planned guide explaining virtual ground behavior, feedback networks, stability, and practical resistor selection.
Planned Engineering Guide
Understanding Closed-Loop Gain
Planned guide covering gain magnitude, phase inversion, dB conversion, bandwidth tradeoff, and real op-amp limits.
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Engineering Disclaimer
This calculator uses the ideal inverting op-amp gain equation. Verify resistor tolerance, source impedance, op-amp gain bandwidth product, slew rate, input common-mode range, output swing, offset, noise, supply rails, and stability before using the design in production hardware.