Op-amp integrator calculator

Enter the input voltage in volts, the input resistor in ohms, and the feedback capacitor in farads. The calculator applies the inverting-integrator relationship, so a positive constant input produces a negative output slope and a negative input produces a positive slope. The result is deterministic, uses explicit SI units, and is suitable for circuit study, first-pass design checks, lab preparation, and automated calculations through the API at $0.002 per request.

Understand what the integrator slope means

An ideal inverting op-amp integrator places a resistor between the input source and the inverting terminal, with a capacitor in the feedback path from output to that terminal. The non-inverting terminal is normally tied to a reference, and ideal negative feedback holds the inverting node at the same potential while drawing no current into the op-amp input. Current through the resistor therefore charges or discharges the feedback capacitor. For a constant input voltage, that capacitor current is constant, so the output changes linearly rather than settling at a fixed gain. The calculator reports this change as output_slope_v_per_s in volts per second. Its sign is important: the topology is inverting, so positive Vin gives a negative slope and negative Vin gives a positive slope. A zero input gives a zero slope. The result describes a rate, not an absolute output voltage. To find output after an interval, start with a known initial output and add the slope multiplied by elapsed time, provided the ideal assumptions remain reasonable and the output has not reached a supply rail.

How resistance, capacitance, and time constant determine the result

The calculation first forms the time constant tau = R*C. Ohms multiplied by farads reduce to seconds, which makes tau a convenient measure of how aggressively the integrator responds. The signed slope is then dVout/dt = -Vin/(R*C), or equivalently -Vin/tau. Increasing either resistance or capacitance increases the time constant and reduces the magnitude of the slope. Doubling R while keeping Vin and C unchanged halves the rate of output change; doubling C has the same effect. Changing the sign of Vin reverses the slope without changing tau. Inputs use explicit SI units to avoid hidden scaling: resistance_ohm is in ohms and capacitance_f is in farads, so a value entered in kilohms or microfarads must first be converted. For example, ten kilohms is 10000 ohms and one microfarad is 0.000001 farad. Both R and C must be finite and greater than zero because a zero or negative passive component would make this ideal formula undefined or outside its intended physical meaning. Precision controls stable numeric rounding without changing the underlying formula.

Use the ideal calculation within real circuit limits

This result is a first-order design and verification aid, not a complete op-amp simulation. A real integrator cannot ramp forever: its output eventually approaches a supply rail, and its usable behavior depends on output swing, input common-mode range, gain-bandwidth product, slew rate, bias currents, capacitor leakage, dielectric absorption, and component tolerances. Practical integrators often place a resistor in parallel with the feedback capacitor to limit low-frequency gain and prevent tiny offsets from driving the output into saturation. That resistor changes the low-frequency transfer function and is intentionally outside this ideal calculation. The endpoint also does not accept a sampled waveform or numerically integrate a changing input; it computes the constant-input slope that applies over an interval where Vin can be treated as fixed. Use the returned time_constant_s and output_slope_v_per_s to check a hand calculation, select an initial R-C pair, prepare expected lab traces, or create deterministic software fixtures. Then confirm a physical design against the selected op-amp data sheet, supply voltages, expected signal range, capacitor behavior, and the required duration before relying on the predicted ramp.