Op-Amp Gain Calculator
Gain and E-series resistors for five op-amp circuits, with bandwidth, slew and clipping.
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Closed-loop gain against frequency
Gain across frequency
How it was calculated
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About the Op-Amp Gain Calculator
Choose the circuit — inverting, non-inverting, difference, summing or the three-op-amp instrumentation amplifier — and either type the resistors to get the gain, or type the gain you need to get the resistors, rounded to the standard values you stock (E12 to E192) with the error they leave and other standard pairs that come closer. Gains are given in V/V and in dB.
The calculator then checks the design against a real op amp. From the gain-bandwidth product it gives the closed-loop bandwidth (GBW ÷ noise gain) and how much gain is lost at your signal frequency; from the slew rate the full-power bandwidth and whether the output can follow a full-size sine; from the supply rails and the output swing whether the output — and, for the in-amp, the input stage — clips. The difference amplifier also gets its common-mode rejection from the resistor ratios and the worst case for 1% resistors.
Without a pass, the free preview works on your own values and shows the verdict of every check, the names of the table’s first rows and the chart under a watermark, without its numbers; the gain, the resistors, every other figure, the working, Copy result and the CSV come with a Pro pass.
How to use it
- Choose the circuit; the drawing shows which resistor is which.
- Gain from resistors: type the resistors (10k, 4.7k, 499). Resistors for a gain: type the gain you need and the resistor you want to fix, and pick the E-series.
- Under Signal, supply and op amp, type the input voltage (a DC level or the peak of a sine), the supply rails, how close the output gets to them, the GBW and the slew rate from the op amp’s datasheet, and the signal frequency.
- Read the gain and the checks. Copy result and the CSV of the frequency response need a pass, or unlocking this result.
Examples
Rin 10 kΩ, Rf 100 kΩ, GBW 1 MHz
G = −10 V/V (20 dB), noise gain 11, bandwidth 90.91 kHz
Rg 10 kΩ, E24
Rf 23 kΩ exact; best E24 pair 27 kΩ and 62 kΩ, G = 3.296 (−0.11%)
R1 = R3 = 10 kΩ, R2 = R4 = 100 kΩ, V1 1 V, V2 1.05 V
Vout = 10 × (1.05 − 1) = 0.5 V; worst-case CMRR with 1% resistors 48.8 dB
R1 24.7 kΩ, R2 = R3 = 10 kΩ, E96
RG = 2 × 24.7 kΩ ÷ 99 = 499 Ω
10 V peak, SR 0.5 V/µs
full-power bandwidth 0.5 V/µs ÷ (2π × 10 V) = 7.958 kHz
The five circuits
- Inverting: G = −Rf ÷ Rin. The source sees Rin as its load.
- Non-inverting: G = 1 + Rf ÷ Rg; Rf = 0 with Rg left open is a voltage follower (G = 1). The source sees the op amp’s own input.
- Difference: Vout = V2 × R4 ÷ (R3 + R4) × (1 + R2 ÷ R1) − V1 × R2 ÷ R1, which is (R2 ÷ R1)(V2 − V1) when R4 ÷ R3 = R2 ÷ R1. A reference voltage on the bottom of R4 shifts the output by exactly that voltage.
- Summing (inverting): Vout = −Rf × (V1 ÷ R1 + V2 ÷ R2 + …), so each input has its own gain −Rf ÷ Ri.
- Three-op-amp instrumentation amplifier: G = (1 + 2R1 ÷ RG) × R3 ÷ R2. With R2 = R3 only RG sets the gain; the input stage’s outputs swing to Vin± ± (R1 ÷ RG) × (Vin+ − Vin−) and must stay inside the rails too.
Noise gain and bandwidth
A voltage-feedback op amp’s open-loop gain falls by 20 dB per decade, so gain × frequency is constant: the gain-bandwidth product (GBW). The closed-loop bandwidth is GBW ÷ noise gain (Analog Devices MT-033), where the noise gain is 1 + Rf ÷ (the resistance to the inputs) — for an inverting ×10 that is 11, not 10. At the −3 dB point the gain is already 29% down. For a gain error under 1% the signal must stay below about a seventh of the closed-loop bandwidth (1 ÷ √(1 + (f ÷ f−3dB)²) ≥ 0.99 holds up to f = 0.1425 × f−3dB), so choose a GBW of at least about 7 × the noise gain × the highest signal frequency: 70 kHz for a 1 kHz signal at a noise gain of 10. The in-amp’s two stages each have their own bandwidth; the calculator combines them.
Slew rate and full-power bandwidth
The output cannot change faster than the slew rate SR. A sine of peak Vp at frequency f needs 2π × f × Vp, so the largest sine the op amp can give in full is at the full-power bandwidth FPBW = SR ÷ (2π × Vp) (Analog Devices MT-056). Above it the output turns into a triangle; at the FPBW itself the output is already at the slew limit, so keep the highest frequency at full amplitude below it with some margin.
Common-mode rejection of the difference amplifier
Only matched ratios cancel a voltage common to both inputs. With four resistors of tolerance Kr the worst-case CMRR is 20 × log((1 + R2 ÷ R1) ÷ 4Kr) (Analog Devices MT-061): about 34 dB with 1% resistors at unity gain and 48.8 dB at a gain of 10. The calculator also gives the CMRR of the exact values you type, so you can see what a mismatched resistor costs. A resistor network or an in-amp does far better.
Sources
- Texas Instruments SBOA092B, Handbook of Operational Amplifier Applications
- Analog Devices MT-033, Voltage Feedback Op Amp Gain and Bandwidth
- Analog Devices MT-056, High Speed Voltage Feedback Op Amps (slew rate and full-power bandwidth)
- Analog Devices MT-061, Instrumentation Amplifier (In-Amp) Basics
- Analog Devices MT-063, Basic Three Op Amp In-Amp Configuration
Limitations
- The op amp is ideal apart from its GBW, slew rate and output swing: input offset voltage, bias currents, noise, finite open-loop gain at DC and input common-mode limits are not included. Check the input common-mode range in the datasheet, above all on a single supply.
- The bandwidth uses a single-pole model of a voltage-feedback op amp; current-feedback op amps follow different rules.
- Resistor tolerance is not applied to the gain; the CMRR check shows its effect on a difference amplifier.
- Stability with capacitive loads and at low noise gain is not analysed. A follower (gain 1) needs an op amp that is stable at unity gain.
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Frequently asked questions
What do I get without a pass?
Without a pass, Op-Amp Gain Calculator shows each check’s verdict, the names of the table’s first rows and a watermarked chart, with the gain, the resistors and every other figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I calculate the gain of an inverting amplifier?
G = −Rf ÷ Rin. With Rin = 10 kΩ and Rf = 100 kΩ the gain is −10 V/V (20 dB): 0.5 V in gives −5 V out. The minus sign means the output is inverted.
What resistors give a non-inverting gain of 10?
Any pair with Rf ÷ Rg = 9, since G = 1 + Rf ÷ Rg: for example Rg = 10 kΩ and Rf = 90 kΩ. 90 kΩ is not an E24 value; 91 kΩ gives 10.1 (+1%), or use E96 parts. The calculator lists the standard pairs that come closest.
Why is the bandwidth lower than GBW ÷ gain?
Because the bandwidth depends on the noise gain, 1 + Rf ÷ Rin, which is one more than the inverting gain: an inverting ×1 has a noise gain of 2 and half the bandwidth of a follower. For a non-inverting amplifier the noise gain equals the gain.
How do I set the gain of an instrumentation amplifier?
With RG: G = 1 + 2R1 ÷ RG when R2 = R3. For a gain of 100 with R1 = 24.7 kΩ, RG = 2 × 24.7 kΩ ÷ 99 = 499 Ω. Integrated in-amps print their own formula in the datasheet; use it with their R1.
What is slew rate and why does it matter?
The fastest the output can change, in V/µs. A 10 V peak sine at 20 kHz needs 2π × 20 kHz × 10 V = 1.26 V/µs; an op amp with 0.5 V/µs can give that amplitude only up to 7.96 kHz. Above that the output distorts into a triangle.