Nearest E24 value: 100 kΩ
What Is an Inverting Op Amp?
An inverting operational amplifier is the most widely used op-amp configuration in analog electronics. The input signal is applied through an input resistor Rin to the inverting (−) input, a feedback resistor Rf connects the output back to that same input, and the non-inverting (+) input is grounded. Negative feedback forces the inverting input to sit at virtual ground (≈ 0 V), which makes the gain depend only on the two resistors — not on the op amp itself. The output is an amplified, 180°-inverted copy of the input: when the input swings up, the output swings down.
How to Use This Calculator
1. Set the input resistor (Rin) — the resistor between your signal source and the inverting (−) input. 2. Set the feedback resistor (Rf) — the resistor from the output back to the inverting input. 3. Enter your input signal peak and supply rails. The gain, gain in dB and output voltage update instantly, the circuit diagram relabels itself, and the waveform redraws — including clipping if the output would exceed the rails. 4. Designing to a target gain instead? Use the Reverse Design box: type the gain you need and the calculator returns the required Rf plus the nearest standard E24 resistor and its gain error.
Inverting Amplifier Gain Formula
Av = −Rf / Rin
Vout = −(Rf / Rin) × Vin
Gain (dB) = 20 × log10|Av|
Where Rf is the feedback resistor, Rin is the input resistor and Vin is the input signal. The minus sign is the inversion. Because the inverting node is a virtual ground, the input impedance seen by the source is simply Rin — one of the key trade-offs of this topology.
Calculate the Feedback Resistor (Reverse Design)
Most real design work runs the formula backwards: you know the gain you need and must calculate the feedback resistor. Rearranging the gain equation gives:
Rf = |Av| × Rin
Need a gain of −25 with Rin = 4.7 kΩ? Then Rf = 25 × 4.7 k = 117.5 kΩ, and the nearest standard E24 value is 120 kΩ (gain −25.5, about 2% high). The Reverse Design box in the calculator does this E24 rounding for you and reports the exact gain error — something most op amp calculators skip entirely.
Worked Examples
Example 1 — Gain of −10 (the classic 1 kΩ / 10 kΩ pair)
The textbook example: Rin = 1 kΩ and Rf = 10 kΩ give Av = −10, so a 1 V input produces −10 V out. The same ratio scales up for lower source loading: Rin = 10 kΩ, Rf = 100 kΩ, Vin = 0.5 V peak.
Av = −100k / 10k = −10 (20 dB). Vout = −10 × 0.5 V = −5 V peak. With ±12 V rails (saturation ≈ ±10.5 V) the amplifier stays perfectly linear.
Example 2 — Clipping at the rails
Same resistors, but Vin = 1.5 V peak. Ideal output = −15 V, yet the op amp can only swing to about ±10.5 V on ±12 V supplies. The waveform clips flat at −10.5 V — try it in the calculator and watch the orange trace flatten.
Example 3 — Attenuator (gain below 1)
Rin = 100 kΩ, Rf = 22 kΩ gives Av = −0.22 (−13.2 dB). Inverting stages work below unity gain too — unlike the non-inverting topology whose minimum gain is +1.
Quick Gain Reference Table
| Rin | Rf | Gain Av | Gain (dB) |
|---|---|---|---|
| 10 kΩ | 10 kΩ | −1 | 0 dB (unity inverter) |
| 10 kΩ | 22 kΩ | −2.2 | 6.8 dB |
| 10 kΩ | 47 kΩ | −4.7 | 13.4 dB |
| 10 kΩ | 100 kΩ | −10 | 20 dB |
| 1 kΩ | 100 kΩ | −100 | 40 dB |
| 100 kΩ | 10 kΩ | −0.1 | −20 dB (attenuator) |
Inverting vs Non-Inverting Amplifier
| Property | Inverting | Non-Inverting |
|---|---|---|
| Gain formula | −Rf/Rin | 1 + Rf/Rin |
| Phase | 180° inverted | In phase |
| Input impedance | ≈ Rin (low–moderate) | Very high (op-amp input) |
| Gain below 1 possible? | Yes | No (minimum +1) |
| Typical uses | Summing mixers, filters, transimpedance, audio stages | Buffers, sensor front-ends |
Need gain without the phase flip? Use the companion Non-Inverting Op Amp Gain Calculator (Av = 1 + Rf/Rin), which keeps the output in phase and offers very high input impedance.
Need a current output instead of a voltage? The same virtual-ground trick powers the Op-Amp Voltage to Current Converter Calculator (IL = Vin/Rin), used for constant-current LED drive and 4–20 mA loops.
Design Tips for Real Circuits
1. Choose sensible resistor values. Keep Rin and Rf in the 1 kΩ–1 MΩ range. Too low wastes signal current and loads your source (remember, input impedance = Rin); too high adds noise and interacts with the op amp input bias current. 2. Watch the gain-bandwidth product. Closed-loop bandwidth ≈ GBW ÷ noise gain (1 + Rf/Rin). A classic 1 MHz-GBW op amp at gain −100 leaves only ~10 kHz; an NE5532 (10 MHz GBW) at the same gain still covers the full audio band (~99 kHz). High gain costs speed — cascade two lower-gain stages if you need both. 3. Respect the rails. Classic op amps saturate roughly 1.5 V below each supply rail (rail-to-rail parts get much closer). This calculator clips the output at ±(VCC − 1.5 V) so you see the real limit, not the ideal one. 4. Balance bias currents by adding a resistor equal to Rin∥Rf from the + input to ground on precision designs.
Where Inverting Amplifiers Are Used
The inverting stage is everywhere: audio preamps and mixers (several inputs summed into one node), active filters (Sallen-Key and multiple-feedback), transimpedance amplifiers converting photodiode current to voltage, analog computation (integrators and differentiators are inverting stages with a capacitor swapped in), and signal conditioning before an ADC — pair this tool with our ADC Calculator to size the full chain. Working in dB? The Attenuation Calculator converts ratios both directions, and the basics of every resistor decision live in the Ohm’s Law Calculator and Parallel Resistor Calculator.
Frequently Asked Questions
What is the gain formula for an inverting op amp?
The closed-loop voltage gain is Av = −Rf / Rin. The minus sign means the output is inverted (180° out of phase). With Rf = 100 kΩ and Rin = 10 kΩ the gain is −10: a +0.5 V input produces a −5 V output.
Why is the output of an inverting amplifier negative?
The signal enters the inverting (−) input while the (+) input is grounded. Negative feedback holds the inverting input at virtual ground, so a rising input forces the output to move the opposite way to balance the currents through Rin and Rf — a 180° phase inversion.
What is virtual ground?
With high open-loop gain and negative feedback, the op amp drives the difference between its inputs to nearly zero. Since the (+) input is grounded, the (−) input also sits at ≈0 V without being physically connected to ground — a virtual ground. It is what makes the simple −Rf/Rin formula accurate.
What happens when the output hits the supply rails?
A real op amp cannot swing beyond its supplies. If −(Rf/Rin)×Vin exceeds the saturation limit (≈ VCC − 1.5 V for classic parts), the output clips flat at the rail. Raise the gain or input amplitude in the calculator and the waveform visibly flattens.
Can I use this calculator for real-world circuit design?
Yes — it gives the ideal closed-loop gain, which is what the resistors set. In hardware, expect small deviations from resistor tolerance (1% resistors give ~2% worst-case gain error), finite gain-bandwidth at high frequencies, and input bias/offset effects in precision work. The E24 rounding and gain-error readout in the Reverse Design box account for the biggest real-world factor: standard resistor values.
What is the difference between inverting and non-inverting gain?
Inverting: Av = −Rf/Rin, output 180° out of phase, input impedance ≈ Rin, gain can be below 1. Non-inverting: Av = 1 + Rf/Rin, output in phase, very high input impedance, minimum gain +1. See the full comparison table above.
What is the input impedance of an inverting amplifier?
Approximately Rin, because the inverting node is a virtual ground. That is much lower than the non-inverting topology, so pick Rin large enough not to load your signal source — typically 1 kΩ to 100 kΩ.