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Inverting Op-Amp Gain

An inverting op-amp circuit produces an output that is the input multiplied by the ratio of the feedback resistor to the input resistor, and then inverted (phase shifted by 180 degrees). The gain is negative, meaning a positive input gives a negative output. The input impedance is set by the input resistor. This configuration is widely used for amplification, summing, and signal inversion.

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Instrumentation Op-Amps

Inverting Op-Amp Calculator

Gain, resistor values, output voltage and error budget for an inverting amplifier.

Gain & dBE24 / E96 resistorsOffset errorBandwidth & slew
Vout = −(Rf / Rin) · Vin

Inputs

Results

Variables

Symbol Quantity Unit
V_out Output voltage V
R_f Feedback resistor Ω
R_in Input resistor Ω
V_in Input voltage V

What it means

The inverting operational amplifier configuration has the output voltage V_out = −(R_f / R_in) · V_in. The negative sign indicates phase inversion. The gain is set by the ratio of the feedback resistor R_f to the input resistor R_in. The input impedance is approximately R_in. This configuration is widely used for summing amplifiers, integrators, and active filters. Because the non‑inverting input is grounded, the inverting input is a virtual ground (V− ≈ 0). The gain can be made less than, equal to, or greater than one (in magnitude). Example: With R_f=10kΩ and R_in=1kΩ, the gain is −10. A 0.5V input gives V_out = −10 * 0.5 = −5V. This is used for signal inversion and amplification.

Worked example

Inverting Op‑Amp – Practical Example

Real‑World
Scenario: An inverting amplifier uses Rf = 100 kΩ and Rin = 10 kΩ. Find the gain for a 1 V input.
ParameterValue
Rf100 kΩ
Rin10 kΩ
Vin1 V
FormulaVout = −(Rf/Rin)·Vin
1Gain = −100/10 = −10
2Vout = −10 × 1 = −10 V
Final Design Vout = −10 V ✓ Inverted gain
Why: The inverting configuration provides gain with phase inversion, determined by the resistor ratio.

Common mistakes

Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.

Applications

Inverting op‑amp gain V_out = −(R_f/R_in)·V_in inverts and scales the input signal. This is a standard building block for analog signal processing. Engineers use it for signal inversion, scaling, and summing. By selecting resistor values, they set the desired gain. This circuit is fundamental in analog electronics.

  • Signal inversion and phase shifting
  • Precision scaling and attenuator circuits
  • Summing amplifiers and analog computation
  • Active filter implementation
  • Educational understanding of op‑amp applications

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  • Published July 10, 2026
  • Last updated July 12, 2026