Op-Amp Integrator
Ideal integrator
Enter input amplitude, frequency, R and C; output amplitude and phase appear live with a waveform.
Integrator output
How to use this calculator
An ideal op-amp integrator has a capacitor in the feedback path and a resistor at the input. For a sinusoidal input Vs·sin(2πft), the output is Vout = Vs/(2πf·R·C)·cos(2πft) — the amplitude scales as 1/f and the output lags the input by 90°. Enter the input amplitude, frequency, R and C, and the calculator shows the output amplitude, phase, and a live plot of both waveforms.
What it means in a real circuit
For Vs = 1 V, f = 1 kHz, R = 10 kΩ, C = 100 nF, the output amplitude is 1/(2π×1000×1000×1e-7) ≈ 1.59 V and lags by 90°. The integrator is used for wave-shaping (turning a square wave into a triangle), analog computation, and as part of active filters. In practice, a real integrator has a finite DC gain (a large resistor in parallel with C) to prevent the output from drifting to the rails due to input bias current — the ideal model shown here assumes that compensation is in place. Use this to size R and C for a target output amplitude at a given frequency, or to check that the output won't clip.