Work out the gain of an inverting, non-inverting, difference or summing circuit from its resistors with this op amp gain calculator, or get the feedback resistor for the gain you want, rounded to E24 or E96 values. Add the op amp’s gain-bandwidth product and supply rails to see the bandwidth, the frequency response and whether the output clips.
Optional: DC level or peak of the signal.
Optional: GBW or unity-gain bandwidth from the datasheet.
Optional, with V−: checks the output against the rails.
0 for a single supply.
Gain
-10 V/V
Enter the op amp’s gain-bandwidth product to get the closed-loop bandwidth and a frequency response.
For an inverting amplifier, G = −Rf ÷ Rin; for a non-inverting amplifier, G = 1 + Rf ÷ Rg. With Rf = 100 kΩ and 10 kΩ the gain is −10 inverting or 11 non-inverting (20.8 dB). The bandwidth is the op amp’s gain-bandwidth product divided by the noise gain, 1 + Rf ÷ Rin, so an LM358 (0.7 MHz typical) gives about 63.6 kHz in either case.
With negative feedback, an op amp drives its output until both inputs sit at the same voltage. The resistors then fix the ratio of output to input. These are the ideal-op-amp results; they hold while the open-loop gain at your frequency is much larger than the noise gain.
With four discrete resistors of tolerance t, the worst-case mismatch is Kr = 4t. V1 sees an input resistance of R1; V2 sees R3 + R4.
Rf = 100 kΩ and Rg = 10 kΩ give G = 1 + 100 ÷ 10 = 11 (20.8 dB), so 0.2 V in becomes 2.2 V. The noise gain is also 11, and with the LM358’s 0.7 MHz typical GBW the closed-loop bandwidth is 0.7 MHz ÷ 11 = 63.6 kHz.
With Rin = 10 kΩ, Rf = 4.7 × 10 kΩ = 47 kΩ, which is not an E96 value. The nearest E96 resistor is 47.5 kΩ, giving G = −4.75, 1.06% high. The noise gain is 1 + 4.75 = 5.75, so the same LM358 reaches 122 kHz.
R1 = R3 = 1 kΩ and R2 = R4 = 20 kΩ turn a 50 mV shunt drop into 1 V. The common-mode rejection is set by the resistors: worst case 54.4 dB with 1% parts and 74.4 dB with 0.1% parts. On a high-side shunt the inputs sit near the supply, so the input divider R3/R4 must bring them inside the op amp’s common-mode range.
Rf for common gains with Rg (non-inverting) or Rin (inverting) fixed at 10 kΩ, rounded to the nearest E96 value, and the gain it actually gives. For any other gain, the calculator solves for Rf.
| Gain | Non-inverting Rf | Actual gain | Inverting Rf | Actual gain |
|---|---|---|---|---|
| 2 | 10 kΩ | 2 | 20 kΩ | −2 |
| 3 | 20 kΩ | 3 | 30.1 kΩ | −3.01 |
| 5 | 40.2 kΩ | 5.02 | 49.9 kΩ | −4.99 |
| 10 | 90.9 kΩ | 10.09 | 100 kΩ | −10 |
| 20 | 191 kΩ | 20.1 | 200 kΩ | −20 |
| 50 | 487 kΩ | 49.7 | 499 kΩ | −49.9 |
| 100 | 1 MΩ | 101 | 1 MΩ | −100 |
Closed-loop −3 dB bandwidth for an op amp with a 1 MHz gain-bandwidth product. Scale the bandwidth columns by your op amp’s GBW ÷ 1 MHz.
| |Gain| | Non-inverting noise gain | Bandwidth | Inverting noise gain | Bandwidth |
|---|---|---|---|---|
| 1 | 1 | 1 MHz (follower) | 2 | 500 kHz |
| 2 | 2 | 500 kHz | 3 | 333 kHz |
| 5 | 5 | 200 kHz | 6 | 167 kHz |
| 10 | 10 | 100 kHz | 11 | 90.9 kHz |
| 20 | 20 | 50 kHz | 21 | 47.6 kHz |
| 50 | 50 | 20 kHz | 51 | 19.6 kHz |
| 100 | 100 | 10 kHz | 101 | 9.9 kHz |
The gain formulas assume infinite open-loop gain. In practice the closed-loop gain is the ideal gain divided by (1 + noise gain ÷ open-loop gain), so at frequencies where the open-loop gain has fallen toward the noise gain the gain drops and the phase shifts; keep the signal well below the closed-loop bandwidth if the gain must be accurate. Large output swings are also limited by slew rate, not just bandwidth. A summing amplifier of three equal 10 kΩ inputs and a 10 kΩ feedback resistor turns 0.5 V, 0.3 V and −0.2 V into -600 mV, but each extra input raises the noise gain (to 4 here) and cuts the bandwidth. Capacitance at the inverting input, including the op amp’s own few pF, makes the noise gain rise at high frequency and eats into the phase margin: with large feedback resistors a small capacitor across Rf keeps the stage stable. Finally, the output cannot swing past the rails, and most op amps stop well short of them, so enter your supplies to see the usable input range.
Inverting amplifier: G = −Rf / Rin. Non-inverting amplifier: G = 1 + Rf / Rg, where Rg runs from the inverting input to ground. Both assume an ideal op amp, which is accurate when the open-loop gain at your signal frequency is much larger than the noise gain.
Divide the feedback resistor by the input resistor and make it negative: G = −Rf / Rin. With Rin = 10 kΩ, the E96 value 47.5 kΩ gives −4.75. The calculator above also solves for Rf from a target gain.
G = 1 + Rf / Rg, with Rg from the inverting input to ground. Rf = 100 kΩ and Rg = 10 kΩ give 11 (20.8 dB), and the noise gain equals the signal gain, so the bandwidth is GBW ÷ G.
Vout = −Rf × (V1/R1 + V2/R2 + V3/R3). Three equal 10 kΩ inputs with a 10 kΩ feedback resistor turn 0.5 V, 0.3 V and −0.2 V into -600 mV, and the noise gain rises to 4.
As a non-inverting amplifier, 1 + 100 kΩ / 10 kΩ = 11 (20.8 dB). As an inverting amplifier, −100 kΩ / 10 kΩ = −10 (20.0 dB), with a 10 kΩ input resistance.
Bandwidth is set by the noise gain, 1 + Rf / Rin, not the signal gain. An inverting gain of −1 has a noise gain of 2, so on a 1 MHz GBW op amp it reaches 500 kHz, while a follower reaches the full 1 MHz.
The ratio sets the gain; the absolute value is a trade-off. Values from about 1 kΩ to 100 kΩ suit most op amps: much lower and the feedback network loads the output, much higher and bias current, leakage and stray capacitance across Rf start to matter. Use 1% (E96) resistors when the gain needs to be within a couple of percent.
The gain the op amp applies to its own input offset and noise voltage, 1 + Rf divided by everything connected from the inverting input to a source or ground. It sets the closed-loop bandwidth (GBW ÷ noise gain) and the stability margin, so it is the number to use with the gain-bandwidth product.
Resistor matching, not the op amp, sets the common-mode rejection. With four 1% resistors at unity gain the worst case is only 34 dB; 0.1% parts give 54 dB. For more, use a matched resistor network or an instrumentation amplifier.
An inverting amplifier can: make Rf smaller than Rin (Rf = 10 kΩ with Rin = 22 kΩ gives −0.45). A non-inverting amplifier cannot go below 1, so attenuate with a divider first and buffer it with a follower.
Only with a rail-to-rail output op amp, and even then it stops tens of millivolts short under load. A TL072 on ±15 V swings to ±13.5 V typical (±12 V minimum) into 10 kΩ. Enter the supplies in the op amp calculator to see the input range that keeps the output inside them.
See all free electronics tools →
ProtoFlow is free AI PCB design software: describe a circuit and get a schematic with real parts, PCB layout with an autorouter, SPICE simulation and Gerber files. Native KiCad, Altium and EAGLE import and export. Free on macOS, Windows and Linux.
Free to start. No card required.
Download ProtoFlow
