Op-Amp Calculator: Inverting, Non-Inverting, Summing, Integrator and Filter Circuits

Work out the gain, output and frequency response of common op-amp circuits.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose the circuit and enter the resistors, the capacitor where there is one, the input voltages and the supply limit.

The calculator gives the gain and the output voltage and warns if the output would saturate. For an integrator it gives the rate of change of the output and the time to reach the limit.

For filters it gives the pass-band gain and the corner frequency, and for amplifiers the bandwidth from the gain-bandwidth product.

Formulas used

  • A_v = -\frac{R_f}{R_{in}}
  • A_v = 1 + \frac{R_f}{R_{in}}
  • V_o = -R_f\left(\frac{V_1}{R_1} + \frac{V_2}{R_2}\right)
  • f_c = \frac{1}{2\pi RC}
  • f_{BW} = \frac{GBW}{1 + |A_v|}

Worked example

With the default numbers in the calculator above:

  1. Gain: -10.00 (20.00 dB)
  2. Output voltage: -1.00 V
  3. Input resistance seen by the source: 10.00 kohm
  4. Bandwidth limit set by the gain-bandwidth product: 90.91 kHz

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Circuit Non-inverting amplifier.

  1. Gain: 11.00 (20.83 dB)
  2. Output voltage: 1.10 V
  3. Input resistance seen by the source: Very high (the input of the op-amp itself)
  4. Bandwidth limit set by the gain-bandwidth product: 90.91 kHz

Common questions

Why does the inverting amplifier invert?

The input goes to the inverting terminal, so the output moves in the opposite direction to hold the two inputs at the same voltage.

What limits the bandwidth?

The gain-bandwidth product of the op-amp. The higher the gain, the lower the bandwidth.

Why does an integrator need a resistor across the capacitor?

Without it a tiny offset voltage is integrated forever and the output drifts to the supply rail.

What is the output limit?

The output cannot go beyond the supply rails, and in many op-amps it stops 1 to 2 V short of them.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Sedra and Smith, Microelectronic Circuits (operational amplifiers); Horowitz and Hill, The Art of Electronics.

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