Op-Amp Gain Calculator
Voltage gain, output, and clipping for the two basic op-amp configurations.
Always at least 1: a non-inverting amplifier cannot attenuate.
Within the ±12 V rails.
These are the ideal-op-amp results, which assume infinite open-loop gain and no input current. Real devices also have a gain-bandwidth product — a part rated at 1 MHz gives a gain of 10 only up to about 100 kHz, so high gain and high frequency trade against each other.
A non-inverting amplifier has a gain of 1 + Rf/R₁, so 1 kΩ and 10 kΩ give 11×. The inverting configuration gives −Rf/Rin, so the same resistors give −10×. The minus sign means the output moves opposite to the input.
Gain is set by two resistors, not by the chip
An op-amp on its own has enormous gain — often 100,000 or more — which makes it useless as an amplifier by itself, since any input beyond a fraction of a millivolt slams the output into the supply rail. Negative feedback tames it: by feeding part of the output back to the inverting input, the circuit's gain becomes a ratio of two resistors and the chip's own variability stops mattering.
That is the central idea worth carrying away. Two op-amps from different manufacturers, with wildly different open-loop gains, produce the same closed-loop gain from the same two resistors.
The two configurations
The non-inverting amplifier feeds the signal into the + input. Its gain is 1 + Rf/R₁, so it can never go below 1 — it cannot attenuate. Its input impedance is very high, which makes it the right choice for a weak or high-impedance source such as a sensor.
The inverting amplifier feeds the signal through a resistor into the − input. Its gain is −Rf/Rin, which can be less than 1, so it can attenuate as well as amplify. Its input impedance is just Rin, which loads the source more heavily.
Both assume an ideal op-amp: infinite open-loop gain, no input current, and no offset. Real devices approach this closely at low frequencies.
Worked example: 1 kΩ and 10 kΩ
The same two resistors give different answers in each configuration:
- 1 Identify the configuration. Signal into the + input is non-inverting; signal through a resistor into the − input is inverting.
- 2 Take the resistor ratio. 10 kΩ ÷ 1 kΩ = 10.
- 3 Apply the right formula. Non-inverting: 1 + 10 = 11×. Inverting: −10×.
- 4 Multiply by the input. At 0.5 V in, the non-inverting output is 5.5 V and the inverting output is −5 V.
- 5 Check against the rails. Both fit inside ±12 V. An output beyond the supply simply clips at the rail.
- 6 Convert to decibels if needed. 20 × log₁₀(11) ≈ 20.8 dB.
Gain from common resistor ratios
The non-inverting gain is always one more than the ratio, which is why the two configurations never give the same magnitude.
| Rf : Rin | Inverting | Non-inverting | Non-inverting in dB |
|---|---|---|---|
| 1 : 1 | −1× | 2× | 6.0 dB |
| 2 : 1 | −2× | 3× | 9.5 dB |
| 10 : 1 | −10× | 11× | 20.8 dB |
| 47 : 1 | −47× | 48× | 33.6 dB |
| 100 : 1 | −100× | 101× | 40.1 dB |
| 1 : 10 | −0.1× | 1.1× | 0.8 dB |
What the ideal formulas leave out
The most important real-world limit is the gain-bandwidth product. An op-amp specified at 1 MHz can deliver a gain of 10 only up to about 100 kHz, or a gain of 100 up to 10 kHz — gain and bandwidth trade directly against each other. A circuit that measures perfectly at DC can fall apart at audio frequencies for this reason alone.
Slew rate is the other common surprise: it limits how fast the output can move regardless of gain, so a large fast signal distorts even when the frequency is well inside the bandwidth.
Finally, a single-supply circuit cannot produce a negative output. Running an op-amp from 0 V and +12 V means the inverting configuration has nothing to swing towards for a positive input unless the inputs are biased to a mid-rail reference — one of the most common reasons a first op-amp circuit outputs nothing at all.