Integrator Circuit Calculator

An integrator circuit uses a resistor and capacitor to mathematically integrate an input signal over time — a building block in analog electronics, signal processing, and waveform shaping. Select what to calculate — Resistor Value (R), Capacitor Value (C), Cutoff Frequency (fc), or Time Constant (τ) — then enter the known circuit parameters to get the calculated value. Secondary outputs include the Time Constant (τ), Cutoff Frequency, Gain at Input Frequency, and Integration Quality. Also try the Op-Amp Gain Calculator.

What to Calculate *

Results

Calculated Value

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Time Constant (τ)

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Cutoff Frequency (fc)

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Gain at Input Frequency

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Integration Quality

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Frequently Asked Questions

How does the op-amp perform integration?

The op-amp integrator uses a capacitor in the feedback loop instead of a resistor. As current flows through the input resistor, it charges the capacitor, creating an output voltage proportional to the integral of the input voltage over time. See also our Summing Amplifier Calculator.

What is the time constant in an RC integrator?

The time constant (τ) equals R × C and determines how quickly the circuit responds. It's measured in seconds and represents the time needed for the capacitor to charge to about 63% of its final value.

What is the optimal pulse time for integration?

For optimal integration, the pulse time should be about 5 times the time constant (t1 = 5τ). This ensures the capacitor has enough time to charge properly and produce a good ramp output.

Why is a feedback resistor sometimes needed?

A feedback resistor prevents DC saturation caused by input offset voltage and bias currents. Without it, the integrator may saturate to the supply rails, but it limits the low-frequency integration range. You might also find our Voltage Follower / Buffer Calculator useful.

What's the difference between ideal and practical integrators?

An ideal integrator has infinite gain at DC and integrates down to 0 Hz. A practical integrator includes a feedback resistor for stability, which limits the low-frequency response and creates a finite DC gain.

How do I choose the right capacitor value?

Choose the capacitor based on your desired time constant and available resistor values. Smaller capacitors work better at high frequencies, while larger capacitors are better for low-frequency integration and longer time constants.

What happens if the time constant is too small?

If τ is too small compared to the input pulse width, the integration will be incomplete, resulting in poor waveform shaping. The output may not reach the expected ramp voltage before the input changes.

Can an integrator work with AC signals?

Yes, integrators work with AC signals and are commonly used in analog computers, waveform generators, and filter circuits. The output will be the mathematical integral of the input waveform, shifted in phase by 90 degrees.