Formula & Calculator
Non-Inverting Op-Amp Gain
The closed-loop voltage gain of a non-inverting operational amplifier configuration.
Interpretation
Non‑inverting op‑amp gain: V_out = (1 + R_f/R_in)·V_in produces an output that is in phase with the input and amplified by 1 plus the resistance ratio.
The input impedance is very high (ideally infinite).
Example: R_f=9kΩ, R_in=1kΩ, V_in=1V → V_out = (1+9)×1 = 10V.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V_out | Output voltage | V |
| R_f | Feedback resistor | Ω |
| R_in | Input resistor | Ω |
| V_in | Input voltage | V |
What it means
The non‑inverting operational amplifier produces an output that is in phase with the input, with a gain given by V_out = (1 + R_f/R_in) · V_in. The gain is always greater than or equal to 1. The input impedance is very high (ideally infinite), making it suitable for buffering. This configuration is used in buffer amplifiers, voltage followers (when R_f=0), and as a building block for active filters. The gain is set by the ratio of feedback resistor to input resistor. Example: With R_f=9kΩ and R_in=1kΩ, the gain is 1 + 9 = 10. A 1V input gives V_out = 10V. This circuit is often used for impedance transformation without inversion.
Worked example
Non‑Inverting Op‑Amp – Practical Example
Real‑World| Parameter | Value |
|---|---|
| Rf | 100 kΩ |
| Rin | 10 kΩ |
| Vin | 1 V |
| Formula | Vout = (1 + Rf/Rin)·Vin |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
Non‑inverting op‑amp gain V_out = (1 + R_f/R_in)·V_in amplifies the input without inversion. It offers high input impedance and is used in buffer and amplifier stages. Engineers use it to boost signals while maintaining phase, to provide high impedance inputs, and to drive loads. This configuration is widely used in sensor and audio applications.
- Buffer and unity‑gain amplifier (voltage follower)
- Signal amplification without inversion
- High‑impedance input stage for sensors
- Audio and RF amplifier stages
- Educational understanding of non‑inverting amplifiers
Frequently Asked Questions
The voltage gain is V_out = (1 + R_f / R_in)·V_in. The output is in phase with the input (no inversion).
The input impedance is very high (ideally infinite) because the input is directly connected to the non‑inverting op‑amp input.
For a gain of G, set R_f = (G − 1)·R_in. Choose R_in to balance bias currents (often a few kΩ to 100 kΩ).
Common errors: 1) using the inverting formula, 2) forgetting that the gain is always ≥ 1, 3) not accounting for the input bias current, 4) applying the formula to an inverting circuit.
A voltage follower has R_f = 0 (or shorted) and R_in = ∞ (open). The gain is 1, and it provides high input impedance and low output impedance.
Used for impedance buffering, active filters, and scaling signals where high input impedance is required.
The bandwidth is BW = GBW / Gain. It is similar to the inverting case for the same gain.
Higher gain reduces the loop gain, which may improve stability but also reduces bandwidth. Compensation may be needed for unity‑gain stability.