Inverting amplifier

Op-amp inverting amplifier

Rs tolerance

Rf tolerance

SI prefixes accepted (4k7 / 1M / 10m / 220). Upper-case M = mega, lower-case m = milli

Gain

—×

Gain

—dB

History

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Formula

Gain (×): G = Rf / Rs
Gain (dB): G[dB] = 20 × log₁₀(Rf / Rs)
The output is inverted with respect to the input

Design notes

The inverting amplifier is everywhere: amplifying sensor signals, scaling to an ADC's full scale, building active filters. Its appeal is that the gain depends on nothing but a ratio of two resistors.

Design notes:
• The input impedance is Rs — pick it with the source in mind
• The more gain you ask for, the less bandwidth you get (the gain-bandwidth product is fixed)
• Where gain error matters, use 0.1% resistors

For a non-inverting amplifier the gain is 1 + Rf/Rs instead.

When you need this

For setting the gain of an inverting op-amp stage. The circuit is simple — gain is a resistor ratio — but you still need to check the gain error once tolerance is included, and whether the op-amp can actually deliver that gain over your bandwidth.

Gain is set purely by the ratio

The gain is −Rf/Rs. The op-amp itself barely enters into it, which is exactly why the topology is popular: resistor accuracy becomes gain accuracy.

The output is inverted relative to the input. This calculator reports the magnitude, so remember the sign. On a single supply, bias the non-inverting input to set the output midpoint.

How tolerance propagates

Because gain is Rf/Rs, the worst case is the two resistors erring in opposite directions. Two ±1% parts give up to about ±2% gain error — twice the effect it has in a divider.

Higher gains spread the two values further apart. Gain of 100 with Rs = 1kΩ means Rf = 100kΩ, which is the region where input bias current offset starts to matter.

What to check

Gain-bandwidth product. Gain times bandwidth is fixed. A 1MHz GBW op-amp at a gain of 100 leaves only 10kHz of usable bandwidth. Choose a part where required bandwidth × gain is at most a fifth of GBW.
Input impedance is Rs. The inverting input is a virtual earth, so the stage presents Rs to the source. For a high-impedance source, raise Rs or use a non-inverting stage or a buffer.
Add a balancing resistor. Conventionally, put Rs in parallel with Rf between the non-inverting input and the reference to cancel input bias current offset. With CMOS-input op-amps the bias current is tiny and the resistor's own noise can be the bigger problem, so it is sometimes omitted.
A small capacitor across Rf stops oscillation. Input capacitance working against Rs adds phase shift. A few to a few tens of picofarads across Rf stabilises it, at the cost of bandwidth.

Common mistakes

Using it single-supply referenced to ground. The output inverts, so a positive input drives the output below ground and it saturates. On a single supply, bias the non-inverting input to something like Vcc/2.
Making the resistors too large. In the megohm range, thermal noise and input bias current become significant. For low noise, keep the values down while holding the ratio.
Exceeding the output swing. Even rail-to-rail outputs do not quite reach the rails. Check that the gained-up signal stays inside the supply at maximum input.

Frequently asked questions

Why is the gain negative?

The signal enters the inverting (−) input, so a rising input produces a falling output — a 180° phase reversal. For the same phase, use a non-inverting stage, which has high input impedance but cannot have a gain below one.

Is there a point to unity gain (Rf = Rs)?

Yes, when you want phase inversion or are generating a differential signal. If you only want a buffer, a non-inverting voltage follower uses fewer parts and has higher input impedance.

How do I read the gain in dB?

It is a voltage ratio, so 20·log₁₀(Rf/Rs). Two times is about 6dB, ten times is 20dB, a hundred times is 40dB. dB makes it easier to compare against the open-loop gain and GBW curves in the datasheet.

Why does gain fall at high frequency?

The op-amp's open-loop gain falls with frequency, and you need ample open-loop gain to hold a given closed-loop gain. Above GBW divided by your gain, the amplifier can no longer sustain it. That quotient is the practical upper frequency limit.

Standards and references

IEC 60747-5 — Characterisation of semiconductor devices including operational amplifiers.

Last updated: 2026-08-29