ECAD Workbench

Part of Analogue and filter calculators

Op-Amp Gain Calculator

Calculate gain, resistor values, dB gain, and ideal output voltage for inverting and non-inverting amplifiers.

Inputs

Enter gain as a positive magnitude. Inverting mode applies the negative sign automatically.

Results

Closed-loop gain2 V/V
Gain magnitude6.021dB
Ideal output voltage2V
Rf10kΩ
Rg10kΩ

This is an ideal closed-loop estimate. It does not model rail limits, output current, gain-bandwidth, slew rate, noise, bias current, or stability.

When to use it

Use ideal op-amp gain calculations as the first resistor-ratio check

This calculator helps choose resistor ratios for inverting and non-inverting amplifier stages, calculate gain in V/V and dB, and estimate the ideal output voltage from an input signal. Treat it as the starting point before checking the real op-amp limits.

Non-inverting stages

Choose feedback values for positive gain while preserving high input impedance.

Inverting stages

Set negative gain from input and feedback resistor ratio.

Signal-chain budgeting

Convert gain to dB and estimate output swing before checking real device limits.

Equations and ideal model

The calculator assumes an ideal op-amp with enough open-loop gain, bandwidth, slew rate, input range, and output swing to support the requested closed-loop result.

Av = 1 + Rf / Rg

Non-inverting gain

Positive gain where the input drives the non-inverting terminal and the feedback divider sets gain.

Av = -Rf / Rin

Inverting gain

Negative gain where the input resistor and feedback resistor set the closed-loop magnitude.

Gain dB = 20 log10(|Av|)

Gain in dB

Convert voltage gain magnitude to decibels for analogue signal-chain budgeting.

Av - Closed-loop gain

Unit: V/V

The ideal voltage gain from input to output.

Rf - Feedback resistor

Unit: ohms (Ω)

Resistor from output back to the inverting input or feedback node.

Rg / Rin - Ground or input resistor

Unit: ohms (Ω)

The lower feedback resistor for non-inverting mode, or input resistor for inverting mode.

Vout - Ideal output voltage

Unit: volts (V)

The calculated output before real output-swing, load-current, and bandwidth limits are checked.

Worked examples

These examples are covered by the shared analogue calculation test suite.

Non-inverting gain

Design question: Rf = 30 kΩ and Rg = 10 kΩ with a 0.5 V input.

Gain: Av = 1 + 30 kΩ / 10 kΩ = 4 V/V.

Output: Vout = 4 × 0.5 V = 2.0 V ideal.

dB gain: 20 log10(4) = 12.04 dB.

Inverting gain

Design question: Rf = 20 kΩ and Rin = 10 kΩ with a 0.5 V input.

Gain: Av = -20 kΩ / 10 kΩ = -2 V/V.

Output: Vout = -2 × 0.5 V = -1.0 V ideal.

dB gain: 20 log10(2) = 6.02 dB.

What the ideal result does not prove

A valid resistor ratio does not guarantee the stage will behave correctly with a real op-amp and real signals.

Output and input limits

  • Output may clip before the ideal Vout is reached.
  • Input common-mode range may not include the requested signal.
  • Load current can reduce output swing or increase distortion.

Dynamic limits

  • Gain-bandwidth limits closed-loop bandwidth.
  • Slew rate limits large-signal speed.
  • Feedback networks and capacitive loads can affect stability.

Assumptions and limitations

Ideal op-amp model

The calculation ignores open-loop gain error, output impedance, input bias current, input offset, and finite common-mode range.

Tolerance affects ratio

Actual gain follows actual resistor ratio, so independent resistor tolerance and temperature drift can move the realised gain.

Topology context matters

Input impedance, source impedance, biasing, noise, and filtering differ between inverting and non-inverting stages.

Related calculators and next checks

Follow the next check based on whether the concern is gain units, input coupling, filtering, or resistor-related limits.

FAQ

Does this calculator tell me whether the op-amp will actually work?

No. It calculates ideal closed-loop gain and output voltage. You still need to check input common-mode range, output swing, load current, gain-bandwidth, slew rate, stability, noise, offset, and bias current.

Why enter gain as a positive magnitude for inverting mode?

The resistor ratio is positive. Inverting mode automatically applies the negative sign to the closed-loop gain and output voltage.

How do resistor tolerances affect gain?

Closed-loop gain depends on resistor ratio. Independent resistor tolerances can move the ratio and therefore the actual gain. Matched resistor networks or tighter tolerance parts may be needed for precision gain.

Engineering reference

Equations, assumptions, and design guidance

Exact equation

Solves ideal inverting and non-inverting closed-loop op-amp gain relationships.

Equations and variables
Non-inverting gainAv = 1 + Rf / Rg
Inverting gainAv = -Rf / Rin
Output voltageVout = Av * Vin
Rf
Feedback resistor (ohm)
Rg/Rin
Ground or input resistor (ohm)
Av
Closed-loop gain (V/V)
Assumptions and limitations

Assumptions

  • The op amp is ideal and remains in linear operation.
  • Input and output ranges are not limiting the result.

Limitations

  • Rail limits, output current, gain bandwidth, slew rate, noise, offset, bias current, and stability are not modelled.
Worked example and design use

Non-inverting gain of 11

Inputs: Rf = 100 kOhm, Rg = 10 kOhm, Vin = 100 mV

Outputs: Av = 11 V/V, gain = 20.8 dB, Vout = 1.1 V

Design guidance

  • Check output swing and common-mode input range against the selected op amp.
  • Use preferred-value and tolerance analysis when gain accuracy matters.