This calculator covers four of the most common op-amp and RC building blocks used throughout analog and mixed-signal circuit design: inverting and non-inverting amplifier gain, and single-pole RC low-pass and high-pass filter cutoff frequency. These four circuits are the basic vocabulary most larger analog signal-conditioning chains are built from.
An inverting amplifier applies the input signal through Rin to the op-amp's inverting (β) input, with Rf feeding back from the output to that same node β assuming an ideal op-amp with infinite open-loop gain, the closed-loop voltage gain is Av = βRf / Rin, and the negative sign reflects that the output is 180Β° out of phase with the input. A non-inverting amplifier instead applies the input directly to the non-inverting (+) input, with Rin and Rf forming a feedback divider from the output back to the inverting input β its gain is Av = 1 + Rf / Rin, always at least 1 (unity), and in phase with the input. The inverting configuration additionally has an input impedance equal to Rin (relatively low, and a real design constraint for high-impedance sources), while the non-inverting configuration has very high input impedance (the op-amp's own input impedance, typically megaohms or more) β this difference is often the deciding factor in which topology to use, independent of the gain value itself.
A single-pole (first-order) RC low-pass filter passes frequencies below its cutoff and attenuates frequencies above it at a rate of β20 dB/decade (roughly β6 dB/octave) beyond the cutoff. A single-pole RC high-pass filter does the opposite β attenuating below cutoff, passing above it, also at β20 dB/decade below the cutoff. Both share the identical cutoff-frequency formula fc = 1/(2ΟRC), because the cutoff is simply the frequency at which the resistor's impedance equals the capacitor's impedance (1/2ΟfC) β only the circuit topology (which component the output is taken across) determines whether that transition is a low-pass or high-pass response. A single pole gives a gentle roll-off; steeper filters (Butterworth, Chebyshev, etc.) cascade multiple poles, commonly implemented as active Sallen-Key or multiple-feedback op-amp stages rather than simple passive RC sections.
Real signal-conditioning chains frequently combine both functions β for example, an inverting amplifier stage with a capacitor in parallel with Rf turns it into an active low-pass filter with gain, useful for amplifying a sensor signal while rejecting high-frequency noise in the same stage. The DC/low-frequency gain in that combined circuit is still set by βRf/Rin exactly as in the plain inverting amplifier, while the cutoff frequency where the filtering kicks in is set by the Rf/C time constant. Recognizing these two calculations as independently reusable building blocks β rather than memorizing every combined topology separately β is the practical value of understanding both formulas on their own.
For amplifier gain, select inverting or non-inverting, and enter Rin and Rf in kΞ© β the tool returns both the linear gain and the equivalent gain in dB (20 logββ|Av|), useful when working with datasheets or filter specifications that quote gain in dB. For filter cutoff, select low-pass or high-pass, enter R in kΞ© and C in nF, and read the resulting cutoff frequency. Note that this models an ideal op-amp (infinite open-loop gain, infinite input impedance, zero output impedance) and a passive RC filter stage β real op-amps have finite gain-bandwidth product, which limits how much gain you can realize at high frequency, and real filter response depends on the op-amp's own bandwidth if the RC network is combined with an amplifying stage.
The inverting configuration drives the op-amp's inverting input through Rin while feedback comes through Rf to the same node β the op-amp's output has to swing in the opposite direction from the input to hold that node at virtual ground (0V, assuming a grounded non-inverting input), which is why the transfer function carries a negative sign. The non-inverting configuration applies the input directly to the non-inverting input and uses Rin/Rf purely as a feedback voltage divider, which mathematically can only add gain on top of a minimum of 1 (unity, when Rf = 0) β it structurally cannot produce a gain below 1 or invert phase, unlike the inverting topology which can produce any gain magnitude including exactly 0 or fractional attenuation.
The gain formulas (Av = βRf/Rin and Av = 1 + Rf/Rin) and the RC cutoff formula are all derived assuming an ideal op-amp with infinite open-loop gain and infinite input impedance β a good approximation for general-purpose op-amps operating well within their gain-bandwidth product and at typical audio/instrumentation frequencies. At high frequencies approaching a fraction of the op-amp's gain-bandwidth product (GBW), or when very high precision is required, the real (non-ideal) open-loop gain starts to matter and actual gain will be somewhat lower than these ideal formulas predict β check your specific op-amp's GBW against your target gain Γ bandwidth product to confirm you have adequate margin.
The cutoff frequency is defined purely by where the resistor and capacitor have equal impedance magnitude (R = 1/2ΟfC), which is a property of the RC pair alone, independent of which component the output is measured across. Whether that crossover produces a low-pass or high-pass response is entirely a matter of circuit topology β taking the output across the capacitor (voltage divider with R first) gives low-pass, taking it across the resistor (C first) gives high-pass β but the frequency at which the transition happens is identical either way for the same R and C values.
This calculator gives an exact mathematical result, but real designs should round to standard component values (the E12 or E24 resistor series, and standard capacitor values like 1nF, 2.2nF, 4.7nF, 10nF) rather than requesting a non-standard exact value from a distributor. After picking the nearest standard values, plug them back into this calculator to see the actual resulting gain or cutoff frequency you'll get in the real circuit, which will be close to but not exactly your original target.
A single RC pole rolls off at β20 dB/decade (a factor of 10 attenuation for each 10Γ increase in frequency beyond cutoff) β adequate for gentle noise rejection but not a sharp separation between passband and stopband. Cascading two poles doubles the roll-off to β40 dB/decade, three poles to β60 dB/decade, and so on; standard filter families (Butterworth for maximally flat passband, Chebyshev for a sharper transition at the cost of passband ripple, Bessel for preserved pulse shape/phase linearity) define specific pole placements to achieve a desired trade-off between flatness, transition sharpness, and phase behavior when more than one pole is needed.
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