What does this calculator do?
A non-inverting amplifier produces an output with the same polarity as its input. Its ideal gain depends only on the ratio of the feedback resistors R2 (Rf) and R1 (Rg).
Av = 1 + R2 / R1
Divide R2 by R1 and add 1: that is the ideal voltage gain. In a real circuit, also check the supply rails, common-mode input range, GBW, slew rate and output drive of the op-amp.
Worked example
With R1 = 1 kΩ and R2 = 10 kΩ, Av = 11 V/V (about 20.8 dB).
Practical tips
- Make sure Vout stays inside the supply rails.
- Bandwidth falls as the closed-loop gain rises.
- Use tight-tolerance resistors when the gain must be accurate.
Common mistake to avoid
Check that the calculated output does not exceed the op-amp’s rails and that the bandwidth is enough for the gain you chose.
Complete non-inverting amplifier formulas
The signal enters the non-inverting input (+) and the R2–R1 network feeds a fraction of the output back to the inverting input (−). With negative feedback, the op-amp adjusts its output until both inputs sit at practically the same voltage:
- Voltage gain: Av = Vout / Vin = 1 + R2 / R1
- Output: Vout = Vin · (1 + R2 / R1)
- Gain in decibels: G = 20 · log₁₀(Av)
- Design: R2 = R1 · (Av − 1)
- Approximate bandwidth: BW ≈ GBW / Av (GBW = the op-amp’s gain-bandwidth product)
- Voltage follower: with R2 = 0 (or R1 open), Av = 1
R2 is the feedback resistor (between the output and the − input) and R1 goes from the − input to ground. The input impedance is very high because the signal goes straight into the op-amp’s + input.
Typical values
| R1 | R2 | Gain | Gain (dB) | BW with GBW = 1 MHz |
|---|---|---|---|---|
| — | 0 Ω | 1 V/V | 0 dB | ≈ 1 MHz |
| 10 kΩ | 10 kΩ | 2 V/V | 6.02 dB | ≈ 500 kHz |
| 10 kΩ | 47 kΩ | 5.7 V/V | 15.12 dB | ≈ 175 kHz |
| 1 kΩ | 9.1 kΩ | 10.1 V/V | 20.09 dB | ≈ 99 kHz |
| 1 kΩ | 10 kΩ | 11 V/V | 20.83 dB | ≈ 91 kHz |
| 1 kΩ | 100 kΩ | 101 V/V | 40.09 dB | ≈ 9.9 kHz |
Bandwidth is estimated for a general-purpose op-amp with a 1 MHz GBW; for another part, divide its GBW by the gain.
Worked example: scaling a 0–0.5 V sensor for an ADC
A sensor outputs 0 to 0.5 V and the microcontroller’s ADC accepts 0 to 3.3 V.
- Maximum possible gain: 3.3 / 0.5 = 6.6. Aim slightly lower to keep away from the op-amp’s output limits.
- With R1 = 10 kΩ and R2 = 47 kΩ: Av = 1 + 47 / 10 = 5.7.
- Full-scale output: 0.5 × 5.7 = 2.85 V, leaving 0.45 V of headroom.
- Bandwidth with a 1 MHz op-amp: 1 MHz / 5.7 ≈ 175 kHz, plenty for a slow sensor.
- Use a rail-to-rail output op-amp if it runs from 3.3 V, so the output can get close to 0 V.
Then convert the reading with the ADC calculator and divide by 5.7 to recover the sensor voltage.
Common mistakes
- Swapping R1 and R2: with R1 = 10 kΩ and R2 = 1 kΩ you get 1.1 instead of 11.
- Expecting a gain below 1: a non-inverting stage never attenuates; use a divider before the amplifier or an inverting stage instead.
- Forgetting the rails: the output saturates near the supply; many classic op-amps cannot get closer than 1–2 V to each rail.
- Ignoring the common-mode range: the + input must also stay within the range the op-amp accepts.
- Using extreme resistor values: below 1 kΩ they load the output; above 1 MΩ they add noise and magnify the effect of bias currents.
Frequently asked questions
Why is the gain 1 + R2/R1 and not R2/R1?
Because the output must develop a voltage equal to Vin across R1; the resulting current also flows through R2, so Vout = Vin + Vin · R2 / R1. That sum is the “1 +”.
How is it different from the inverting amplifier?
The non-inverting stage keeps the phase and has a very high input impedance; the inverting stage flips the sign, allows gains below 1 and has an input impedance of Rin. Compare them with the inverting gain calculator.
How do I express the gain in dB?
With G = 20 · log₁₀(Av): a gain of 10 is 20 dB and a gain of 100 is 40 dB. Convert it with the dB gain calculator.
To understand negative feedback and the virtual short, read the non-inverting amplifier guide.
Educational tool. Check tolerances, datasheets, standards and real operating conditions before using the results in critical applications.