Inverting Op-Amp Gain Calculator Formula

Understand the math behind the inverting op-amp gain calculator. Each variable explained with a worked example.

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Formulas Used

Voltage Gain

gain = -(r_feedback_kohm / r_input_kohm)

Gain (dB)

gain_db = 20 * log10(abs(r_feedback_kohm / r_input_kohm))

Output Voltage

v_output = -(r_feedback_kohm / r_input_kohm) * v_input

Variables

VariableDescriptionDefault
r_input_kohmInput Resistor (Rin)(kΩ)10
r_feedback_kohmFeedback Resistor (Rf)(kΩ)100
v_inputInput Voltage(V)0.5

How It Works

Inverting Op-Amp Configuration

Formula

Gain = -Rf / Rin

V_out = -(Rf / Rin) x V_in

The negative sign means the output is 180 degrees out of phase with the input. Input impedance equals Rin.

Worked Example

Rin = 10k, Rf = 100k, input signal is 0.5 V.

r_input_kohm = 10r_feedback_kohm = 100v_input = 0.5
  1. 01Gain = -100 / 10 = -10 V/V
  2. 02Gain in dB = 20 x log10(10) = 20 dB
  3. 03V_out = -10 x 0.5 = -5.0 V

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