What the Operational Amplifier Gain Calculator does
This calculator gives the gain of the five standard op-amp configurations - inverting, non-inverting, unity buffer, summing and difference - in volts per volt and in decibels, together with the noise gain and the closed-loop bandwidth the amplifier's gain-bandwidth product allows.
Noise gain is the part worth paying attention to. Bandwidth, input offset error and output noise all follow the noise gain, not the signal gain, which is why an inverting stage at -1 V/V gets only half the bandwidth a unity buffer does from the same op-amp.
How to use it
- Choose the configuration. The resistor labels change to match: Rg to ground for a non-inverting stage, Rin from the source for an inverting one.
- Enter the feedback resistor and the input or ground resistor. Shorthand such as 100k and 4k7 is understood.
- Enter the gain-bandwidth product from the op-amp's data sheet - 1 MHz for an LM358, about 3 MHz for a TL072, tens of megahertz for a modern CMOS part.
- Read the gain, the noise gain and the bandwidth. For a summing amplifier, list one input per line as resistance and voltage.
- Check the slew-rate note before assuming the bandwidth applies to your signal: large outputs are limited by slew rate long before the small-signal bandwidth.
Reading the results
A negative gain simply means the output is inverted. A gain of -10 and a gain of +10 have the same magnitude and the same 20 dB figure; only the sign differs.
Closed-loop bandwidth is the gain-bandwidth product divided by the noise gain, and it is a small-signal figure measured at the -3 dB point. Response begins to droop well before it.
The resistor values themselves matter as much as their ratio. Very high values raise noise and make input bias current significant; very low values load the output. Ten kilohms to a hundred kilohms suits most general-purpose parts.
Worked example: a non-inverting stage of 11 on an LM358
With Rf = 100 kOhm and Rg = 10 kOhm the gain is 1 + 100/10 = 11 V/V, which is 20 log10(11) = 20.83 dB. An input of 0.1 V gives 1.1 V out.
The noise gain of a non-inverting stage equals its signal gain, so with a 1 MHz gain-bandwidth product the closed-loop bandwidth is 1,000,000 / 11 = 90.9 kHz.
Build the same gain magnitude as an inverting stage - Rf = 100 kOhm, Rin = 10 kOhm - and the signal gain is -10 while the noise gain is 1 + 10 = 11. The bandwidth is the same 90.9 kHz, but you get one less unit of signal gain for it. That asymmetry is exactly why noise gain, not signal gain, is the figure to design with.
Formulas and scoring rules
- Non-inverting gain
G = 1 + Rf / RgNever below 1. Noise gain equals signal gain.- Inverting gain
G = -Rf / RinCan be below 1. Noise gain is 1 + Rf/Rin, which is always one more than the magnitude.- Buffer
G = 1Noise gain 1, so it gets the full gain-bandwidth product.- Summing
Vout = -Rf x (V1/R1 + V2/R2 + ...)Each input has its own gain; the noise gain is 1 + Rf x sum(1/Rn).- Difference
Vout = (Rf / Rin) x (V+ - V-)With both dividers matched. Mismatch, not the op-amp, sets the common-mode rejection.- Gain in decibels
dB = 20 log10(|G|)A voltage ratio, so 20 log and not 10 log.- Closed-loop bandwidth
f-3dB = GBW / noise gain- Full-power bandwidth
f = slew rate / (2 pi Vpeak)The limit for large signals, usually well below the small-signal bandwidth.
Noise gain, and why it is not the gain you asked for
Noise gain is the gain the amplifier applies to anything appearing at its own input - its offset voltage, its input noise, and the feedback network's noise. It is set by the feedback network alone: 1 + Rf/Rg, regardless of where the signal enters.
For a non-inverting stage that happens to equal the signal gain. For an inverting stage it is one higher, and for a summing amplifier it grows with every input you add, even inputs that are sitting at zero. The consequences are practical: a five-input summing amplifier has a noise gain of six or more, so it has six times less bandwidth and six times more output offset than its per-input gain of one would suggest.
The difference amplifier's real limitation
A one-op-amp difference amplifier rejects common-mode voltage only as well as its two resistor dividers match. With 1% resistors the worst-case common-mode rejection ratio is about 46 dB - far below the 100 dB the op-amp itself manages - and it is the resistors, not the silicon, that set it.
This is why instrumentation amplifiers exist: they use a matched network trimmed at manufacture, or a three-amplifier topology that removes the dependence. If you need to measure a small difference riding on a large common-mode voltage, use one; a discrete difference amplifier is for undemanding work.
Limitations: what the result does not prove
- This is ideal op-amp analysis: infinite open-loop gain, no input current, no offset. Real parts add offset voltage, bias current and a finite open-loop gain that reduces accuracy at high closed-loop gain.
- Bandwidth assumes a single-pole op-amp and unity-gain stability. Decompensated parts, capacitive loads and stray capacitance at the inverting node all change the picture, sometimes into oscillation.
- Slew rate, output current, output swing near the rails and input common-mode range are not modelled and frequently decide whether a design works.
- The result is indicative. Check the data sheet for the part and, for anything precision or high-frequency, simulate before building.
Privacy: where your data goes
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Standards and sources
- Texas Instruments - Op amps for everyone design reference - checked 19 Sep 2026
- Analog Devices - Op amp noise gain and stability (MT-047, MT-059)
- Analog Devices - Difference amplifiers and CMRR versus resistor matching
Frequently asked questions
How do I calculate op-amp gain?
For a non-inverting stage, G = 1 + Rf/Rg. For an inverting stage, G = -Rf/Rin. Those two formulas cover most circuits; the difference amplifier uses Rf/Rin applied to the difference of its inputs, and a summing amplifier gives each input its own -Rf/Rn.
Why does gain reduce bandwidth?
Because an op-amp has a fixed gain-bandwidth product: the product of closed-loop gain and bandwidth is constant. A part with 1 MHz GBW gives 1 MHz at unity gain, 100 kHz at a gain of 10 and 10 kHz at a gain of 100. Splitting a large gain across two stages gives more total bandwidth.
What is noise gain and why does it matter?
The gain the circuit applies to the op-amp's own offset and noise, equal to 1 + Rf/Rg. It sets bandwidth, output offset and output noise. An inverting stage's noise gain is one higher than its signal gain magnitude, which is why -1 V/V costs the same bandwidth as +2 V/V.
Can a non-inverting amplifier have a gain less than one?
No. Its gain is 1 + Rf/Rg, so unity is the floor. To attenuate, use an inverting stage with Rf smaller than Rin, or put a resistive divider in front of a unity buffer.
What resistor values should I use around an op-amp?
Usually 1 kOhm to 100 kOhm. Too low loads the output and wastes power; too high raises Johnson noise and makes input bias current a real error, and combines with stray capacitance to create an unintended pole at the inverting node.
Why is my amplifier's output clipping before the calculated voltage?
Output swing is limited by the supply rails, and many op-amps cannot get within a volt or two of them. Check whether the part is rail-to-rail on the output, whether the load current is within its capability, and whether the input common-mode range covers your signal.
What limits an op-amp at large output swings?
Slew rate. The full-power bandwidth is SR / (2 pi Vpeak): a 1 V/us part producing a 10 V peak sine can only manage about 16 kHz, no matter what the small-signal bandwidth says. Above that the output turns into a triangle wave.
How good is the common-mode rejection of a difference amplifier?
Only as good as the resistor matching. With 1% resistors, roughly 46 dB; with 0.1% resistors, about 66 dB. The op-amp's own CMRR is usually 100 dB or more, so the resistors are always the limit. Use a matched network or an instrumentation amplifier when it matters.
Last reviewed by the A2Z.Tools team against the sources listed above.
