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
This is an ideal closed-loop estimate. It does not model rail limits, output current, gain-bandwidth, slew rate, noise, bias current, or stability.
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.
Non-inverting gain
Positive gain where the input drives the non-inverting terminal and the feedback divider sets gain.
Inverting gain
Negative gain where the input resistor and feedback resistor set the closed-loop magnitude.
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.
Engineering conversion calculator
Convert gain to dB, dB to ratio, RMS values, and SI-prefixed values.
RC low-pass filter calculator
Use when the amplifier input or feedback path includes first-order filtering.
AC coupling capacitor calculator
Use when the amplifier input is AC-coupled into a bias network.
Resistor power calculator
Check power only when feedback or load resistors dissipate meaningful heat.
Analogue and filter hub
Follow related analogue, RC, filter, and signal-chain workflows.
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
Solves ideal inverting and non-inverting closed-loop op-amp gain relationships.
Equations and variables
Av = 1 + Rf / RgAv = -Rf / RinVout = 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.