What is the formula for Inverting op-amp calculator?

Inverting op-amp calculator

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Inverting op-amp stage: derive the voltage gain (A = −Rf/Rin) and input impedance from Rf/Rin, or pick standard resistors for a target gain, then use the resistor tolerance to bound the gain / output error and maximum mismatch error, and check noise-gain bandwidth and slew rate.

Key points

An inverting amplifier feeds the signal through input resistor Rin into the − input, with feedback resistor Rf from the output back to − and the + input grounded; the voltage gain is A = −Rf/Rin, the output is inverted 180° from the input, and |A| = Rf/Rin. The − input is a virtual ground (≈0 V) and the input impedance equals Rin — the key difference from a non-inverting stage. The closed-loop bandwidth uses the noise gain: BW = GBW/(1+|A|). For a sine output with peak voltage Vpk the required slew rate is SR = 2π·f·Vpk, and the full-power bandwidth is FPBW = SR/(2π·Vpk). The tool solves gain and input impedance from Rf/Rin, or standard resistors for a target gain, and bounds the gain / output error and maximum mismatch error with the resistor tolerance, together with bandwidth and slew-rate checks.

Inputs

DirectionFeedback resistor RfkΩOutput → inverting input (−)Input resistor RinkΩSource → inverting input (−); also sets the input impedanceResistor tolerance%Used to bound the gain error from the chosen resistors (1% common; 0.1% / 0.01% for precision)Gain-bandwidth product GBWMHzGBW / unity-gain bandwidth from the op-amp datasheet; closed-loop BW = GBW/(1+|A|)Slew rate SRV/µsAbout 0.5 for the LM358, 13 for the TL072; high-speed op amps reach hundreds of V/µsInput signal amplitude (peak)VSine peak; output peak = input peak × |A|Signal frequency fHzUsed for the slew-rate and bandwidth checksPositive supply V+VFor the output-clipping check (single supply: fill in Vcc; negative rail: 0)Negative supply V−VDual supply: a negative value (e.g. −15); single supply / ground: 0

Calculation model (updates with parameters)

Bode plot (magnitude / phase, updates with parameters)

Inverting voltage gain A	−10.000V/V	A = −Rf/Rin; ≈ 20.00 dB · phase 180°
Gain (dB)	20.00 dB	20 · log10(\|A\|)
Feedback ratio Rf / Rin	10.000	Rf = \|A\| · Rin
\|Gain\| range (resistor tolerance)	9.802 ~ 10.202V/V	±1.00% resistor worst case: -1.98% ~ +2.02%
Output amplitude range (resistor tolerance)	0.980 ~ 1.020 V	input peak 100 mV unchanged
Maximum resistor-mismatch error	±2.02%	gain error -1.98% ~ +2.02%; output peak 0.980 ~ 1.020 V
Equivalent Rf / Rin	10 kΩ / 1 kΩ
Input impedance Rin	1 kΩ	The inverting input is a virtual ground, so the input impedance = Rin (a low input impedance is inherent to this circuit)
Noise gain 1 + \|A\|	11.000	Sets the closed-loop bandwidth and noise gain
Closed-loop bandwidth BW = GBW/(1+\|A\|)	90.91 kHz	GBW 1 MHz; single-pole model -3 dB
Output amplitude (peak / peak-to-peak)	1.000 / 2.000 V	Input 100 mV × \|A\|
Required slew rate SR_req	62.83 mV/µs	2π · f · Vpk @ 10 kHz
Device SR / margin	×7.96	Device 500 mV/µs \| required 62.83 mV/µs
Full-power bandwidth FPBW	79.58 kHz	Highest sine frequency the slew rate allows
Small-signal rise time tr	3.85 µs	≈ 0.35 / BW (10–90%)
Slew-limited rise time	4 µs	peak-to-peak 2.000 V / SR
f = 10 kHz actual output amplitude	0.994 V	Bandwidth attenuates to 99.4% \| phase lag 6.3°

Engineering notes

Inverting amplifier: the signal enters the − input through Rin and Rf feeds back from the output to −, with the + input grounded. The gain is A = −Rf/Rin (output inverted 180°), with |A| set by Rf/Rin.
The inverting input is a virtual ground (≈0 V) and the input impedance equals Rin — the key difference from a non-inverting amplifier: for a high source impedance increase Rin or switch to the non-inverting input.
The closed-loop bandwidth uses the noise gain 1 + |A|: BW = GBW/(1+|A|); compared with a non-inverting stage of the same gain the bandwidth is the same but the input impedance is low.
A sine output needs a slew rate SR = 2π·f·Vpk, and the highest sine frequency a given SR supports (full-power bandwidth) is FPBW = SR/(2π·Vpk); beyond it slope distortion appears.
Rf and Rin set the noise gain and noise: a smaller Rin means higher noise gain and lower input impedance; for precision use 0.1% resistors and keep Rf/Rin accurate.

FAQ

What is Inverting op-amp calculator for?: Inverting op-amp stage: derive the voltage gain (A = −Rf/Rin) and input impedance from Rf/Rin, or pick standard resistors for a target gain, then use the resistor tolerance to bound the gain / output error and maximum mismatch error, and check noise-gain bandwidth and slew rate.
What is the formula for Inverting op-amp calculator?: Core formula: A = −Rf/Rin (|A| = Rf/Rin) | Zin = Rin | BW = GBW/(1+|A|) | SR = 2π·f·Vpk | FPBW = SR/(2π·Vpk). The tool returns results instantly using this formula and the selected parameters.
What engineering notes should I keep in mind when using Inverting op-amp calculator?: Inverting amplifier: the signal enters the − input through Rin and Rf feeds back from the output to −, with the + input grounded. The gain is A = −Rf/Rin (output inverted 180°), with |A| set by Rf/Rin. The inverting input is a virtual ground (≈0 V) and the input impedance equals Rin — the key difference from a non-inverting amplifier: for a high source impedance increase Rin or switch to the non-inverting input. The closed-loop bandwidth uses the noise gain 1 + |A|: BW = GBW…