Op Amp Gain Calculator results give the gain in V/V and dB, along with the output voltage. Pick an inverting, non-inverting or differential stage, then enter Rf, Rin and the input.
Rf runs from the output back to the - input. Rin is the resistor on the - input, to ground or to the signal.
Supply, Tolerance and Capacitor
Cf is an optional capacitor across Rf that rolls the gain off above a cutoff. Enter 0 if there is none.
Op-Amp Limits
Headroom is how far the output or the inputs must stay from each rail. Picking a part fills in its figures.
Gain in Decibels and Rf Needed
| In dB | Gain | Exact Rf | E96 Rf |
|---|---|---|---|
| 1.00 dB | 1.122 V/V | 244.0 Ω | 243 Ω |
| 3.00 dB | 1.413 V/V | 825.1 Ω | 825 Ω |
| 6.00 dB | 1.995 V/V | 1.991 kΩ | 2 kΩ |
| 10.00 dB | 3.162 V/V | 4.325 kΩ | 4.32 kΩ |
| 15.56 dB | 6.000 V/V | 10.00 kΩ | 10 kΩ |
| 20.00 dB | 10.00 V/V | 18.00 kΩ | 18.2 kΩ |
| 40.00 dB | 100.0 V/V | 198.0 kΩ | 200 kΩ |
| 60.00 dB | 1,000 V/V | 1.998 MΩ | 2 MΩ |
Op Amp Gain Calculator Formulas
Op-amp gain is the ratio of the output voltage to the input voltage. The op-amp on its own has a huge gain, so two resistors and negative feedback set a smaller, exact one. The Op Amp Gain Calculator covers the three stages built that way, and each has its own formula.
Rf is the feedback resistor, from the output back to the - input. Rin is the other resistor on the - input. This is a voltage gain calculator, so the result is a voltage ratio. Current gain and power gain are different quantities.
Op-amp gain formula, non-inverting
In a non-inverting stage the signal goes straight to the + input and Rin runs from the - input to ground. The gain is 1 plus the resistor ratio, so it can never be below 1.
With Rf = 10 kΩ and Rin = 2 kΩ the Op Amp Gain Calculator returns 6.000 V/V, or 15.56 dB. A 0.5 V input gives 3.000 V at the output. The first card reads In Phase (0°) and Op-Amp Input Only, because the source drives nothing but the op-amp's own input.
Inverting op amp gain formula
In an inverting stage the signal enters through Rin to the - input, and the + input sits at ground. The gain is the resistor ratio with a minus sign, which means the output is flipped.
The same 10 kΩ and 2 kΩ now give -5.000 V/V, and 0.5 V in becomes -2.500 V out. The card reads Inverted (180°). It also reads Same as Rin, since TI's inverting amplifier circuit note points out that the input resistor sets the input impedance. The source has to drive 2 kΩ.
Differential op amp gain formula
A differential stage amplifies the difference between two inputs. It uses two matched pairs of resistors. One Rin feeds each input, one Rf is the feedback, and one Rf runs from the + input to ground.
With V1 at 0.5 V and V2 at 0.8 V, the 0.3 V difference times 5 gives 1.500 V. The two inputs are not loaded equally. Analog Devices notes in its MT-061 tutorial that V1 sees Rin while V2 sees Rin plus Rf, and the card shows Rin Plus Rf for V2.
That same tutorial gives the worst-case rejection of a signal common to both inputs. With ±1% resistors, the differential example in the Op Amp Gain Calculator comes out at 43.52 dB. A source that cannot drive those resistors needs the buffered version in the Instrumentation Amplifier Gain Calculator.
Setting the Gain With Rf or Rin
To set an amp gain, fix one resistor and solve for the other. Solve For offers Rf for a Target Gain and Rin for a Target Gain, and the target can be typed in V/V or dB. For a non-inverting stage the Op Amp Gain Calculator rearranges the formula for Rf.
A target of 20 V/V with Rin at 2 kΩ needs exactly 38.00 kΩ. The nearest E96 part is 38.3 kΩ, which gives 20.15 V/V. For an inverting or differential stage, Rf is simply Rin times the gain. An inverting gain of 20 with Rf at 10 kΩ needs Rin = 500.0 Ω, and the 499 Ω part gives 20.04 V/V.
The Resistor Tolerance setting picks the series. A ±1% setting searches E96 values, ±5% searches E24 and ±0.1% searches E192. For a stage that also needs its output shifted by an offset, the Non-Inverting Op-Amp Resistor Calculator sizes the extra resistors.
Converting Gain to Decibels
To convert gain to decibels, take 20 times the base-10 log of the voltage ratio. The Op Amp Gain Calculator shows both forms in the main result, and its Gain in Decibels table lists the resistor needed at each common dB step.
| Gain in dB | Voltage Gain | Rf With Rin = 2 kΩ | E96 Rf |
|---|---|---|---|
| 1 dB | 1.122 V/V | 244.0 Ω | 243 Ω |
| 3 dB | 1.413 V/V | 825.1 Ω | 825 Ω |
| 6 dB | 1.995 V/V | 1.991 kΩ | 2 kΩ |
| 20 dB | 10.00 V/V | 18.00 kΩ | 18.2 kΩ |
| 40 dB | 100.0 V/V | 198.0 kΩ | 200 kΩ |
| 60 dB | 1,000 V/V | 1.998 MΩ | 2 MΩ |
The table is for a non-inverting stage. A 20 dB gain multiplies the voltage by 10, and a 40 dB gain means the output is 100 times the input. A gain of 3 dB is 1.413 times and 1 dB is 1.122 times. Every extra 20 dB is another factor of ten.
Gain is measured in dB because the numbers add. Two stages of 20 dB each make 40 dB, where the ratios would have to be multiplied as 10 times 10. A wide range also fits in small numbers, since 1,000,000 V/V is only 120 dB.
Bandwidth at a Given Gain
More gain leaves less bandwidth. The second card in the Op Amp Gain Calculator multiplies the op-amp's gain bandwidth product by the feedback fraction β. That fraction is the share of the output fed back to the - input. Analog Devices covers the relationship in its MT-033 tutorial.
With 10 kΩ and 2 kΩ, β is 16.67%, so a 1 MHz op-amp gives 166.7 kHz. At 40 dB the same op-amp is down to 10 kHz. The LM358 preset uses TI's typical 0.7 MHz, which brings the default stage to 116.7 kHz.
The inverting stage gets the same 166.7 kHz for a gain of only 5. Its bandwidth depends on 1 + Rf ÷ Rin, the same term as the non-inverting gain. An inverting gain of -1 therefore has half the bandwidth of a follower built on the same op-amp.
Op Amp Gain Calculator With Capacitor
A capacitor Cf across Rf makes the gain fall off above a cutoff frequency. Below the cutoff the Op Amp Gain Calculator result still holds. Enter Cf under Supply, Tolerance and Capacitor, or enter 0 if there is none.
The default 100 pF across 10 kΩ gives 159.2 kHz, just under the 166.7 kHz the op-amp allows. TI's low-pass inverting amplifier design uses 20 kΩ and 3.9 nF for a 2 kHz cutoff at a gain of 20. Entering those values returns 2.040 kHz.
In a non-inverting stage the gain falls toward 1 above the cutoff and stops there. In an inverting stage it keeps falling like a passive RC filter. A full filter with both a lower and an upper cutoff is sized in the Bandpass Filter Calculator.
Tolerance, Supply and Clipping
Real resistors shift the gain. With both parts at their ±1% limits, the default 6.000 V/V can land anywhere from 5.901 to 6.101 V/V, a spread of 1.7% each way. The third card in the Op Amp Gain Calculator also shows what that does to the output, 2.950 V to 3.051 V here.
The output cannot pass the supply rails. On ±15 V with a rail-to-rail part, the default stage accepts inputs from -2.500 V to 2.500 V before clipping. An inverting stage on a single 5 V supply clips at 0 V for any positive input, and the alert says to bias the + input above ground.
The Op-Amp setting adds real limits. Picking the LM358 or the µA741 fills in how far the output and the inputs must stay from each rail, and the card turns red when either one is exceeded. The last row shows the current the output must push through Rf, 250.0 µA in the default example.
Amplifier Gain Calculator Answers
How do you calculate amp gain?
Divide the output voltage by the input voltage. If 0.5 V in produces 3 V out, the gain is 6 V/V, or 15.56 dB. That works for any amplifier and needs only two measurements at the same frequency.
For an op-amp stage the resistors give the same answer before anything is built. The Op Amp Gain Calculator takes Rf and Rin and returns the gain, then multiplies it by the input voltage for the output.
What is the gain of a 741 op amp?
On its own, with no feedback, a 741 has a typical DC gain of 200,000 V/V, which is 106 dB. The TI µA741 data sheet lists it as 200 V/mV typical and 20 V/mV minimum. This is the open-loop gain, also called the DC gain of the op-amp.
In a circuit the gain is whatever Rf and Rin set, as long as it stays far below that figure. In the Op Amp Gain Calculator, a 741 wired with 10 kΩ and 2 kΩ shows a gain of 6, the same as any other op-amp. Only the bandwidth and the output swing differ.
What is VCC in an op amp?
VCC is the positive supply pin, and it carries a steady DC voltage. Its value depends on the part. TI specifies the µA741 for ±5 V to ±15 V, and the LM358 runs from a single supply as low as 3 V.
The Power Supply setting in the Op Amp Gain Calculator covers ±5 V to ±15 V dual supplies and 3.3 V to 12 V single supplies. The output can only move between those rails, less any headroom the op-amp needs.