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Ideal Op-Amp Gain from Resistor Ratio

Calculate ideal inverting gain magnitude or non-inverting voltage gain from the input and feedback resistors, with reverse resistance calculations.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 10 kΩ input resistor and 100 kΩ feedback resistor give an inverting gain magnitude of 10 (signed gain −10 V/V), or non-inverting gain 11 V/V.

Inverting magnitude = Rf / Rin; signed inverting gain = −Rf / Rin; non-inverting gain = 1 + Rf / Rin

Worked example

Enter these known values and leave the other values blank.

Input / gain-setting resistance
10000 Ω
Feedback resistance
100000 Ω
Inverting gain magnitude (signed gain is negative)
10

Assumptions and limitations

  • The captured inverting equation gives a positive magnitude. Its signed voltage gain is the negative of that result because the output is inverted.
  • These formulas assume an ideal voltage-feedback amplifier in its linear operating range with negative feedback and positive resistances.
  • The model omits finite open-loop gain, bandwidth, stability, slew rate, offsets, loading, resistor tolerances, supply rails and output saturation.
  • For a non-inverting amplifier, the gain-setting resistor connects the inverting node to the reference node. Circuit topology matters; the equations are not a universal amplifier model.

Common questions

Why is the inverting result positive?

The field displays magnitude, matching the captured ratio equation. A magnitude of 10 means a signed ideal voltage gain of −10 V/V.

Can I solve for a resistor?

Yes. Enter one resistance and the gain for the selected configuration. The other resistance is calculated when the inputs define a valid positive value.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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