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Op Amp Formulas Cheat Sheet

All the common op amp circuit equations on one page, with the golden rules, bandwidth and slew rate limits and practical design tips.

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Op Amp Formulas Cheat Sheet PDF preview

A one page A4 sheet to print, pin up in the workshop or keep on your phone. Everything on it is also shown below.

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Golden rules (ideal op amp with feedback)

  • No current flows into the inputs
  • The output adjusts so both inputs are at the same voltage
  • Inverting input of an inverting stage is a virtual ground

Inverting amplifier

GainA = −Rf ÷ Rin
Input impedanceZin = Rin

Non inverting amplifier

GainA = 1 + Rf ÷ Rg
Voltage followerA = 1 (Rf = 0, Rg open)
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Summing amplifier

OutputVout = −Rf (V1/R1 + V2/R2 + V3/R3)

Difference amplifier

Matched (R1 = R3, R2 = R4)Vout = (R2 ÷ R1) × (V2 − V1)
CMRRset by resistor ratio matching

Instrumentation amplifier

3 op ampG = 1 + 2R ÷ RG
AD620, AD8221, INA129G = 1 + 49.4 kΩ ÷ RG
INA128G = 1 + 50 kΩ ÷ RG
INA333G = 1 + 100 kΩ ÷ RG

Integrator and differentiator

IntegratorVout = −(1 ÷ RC) ∫ Vin dt
DifferentiatorVout = −RC × dVin/dt
Active low passfc = 1 ÷ (2π Rf Cf)

Transimpedance (current to voltage)

OutputVout = −Iin × Rf
Example4 to 20 mA through 250 Ω gives 1 to 5 V (passive)

Speed limits

Bandwidthf−3dB = GBW ÷ noise gain
Noise gain1 + Rf ÷ Rg (both configurations)
Full power bandwidthfp = SR ÷ (2π Vpeak)
Rise timetr ≈ 0.35 ÷ f−3dB

Comparator with hysteresis (Schmitt)

Hysteresis width (non inverting)ΔV = (R1 ÷ R2) × (VOH − VOL)
UseStops chattering on slow or noisy signals

Practical tips

  • Resistors 1 kΩ to 100 kΩ
  • Decouple each supply pin with 100 nF close to the IC
  • Use rail to rail output parts on single 3.3 V or 5 V supplies
  • Bias current × feedback resistance = offset; balance with a resistor on the + input

Related Calculators and Tools

Inverting Amplifier CalculatorFree on instrumentationblog.inNon Inverting Amplifier CalculatorFree on instrumentationblog.inInstrumentation Amplifier Gain CalculatorFree on instrumentationblog.inOp Amp Gain Bandwidth CalculatorFree on instrumentationblog.in
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Frequently Asked Questions

What is the gain of a non inverting amplifier?

1 + Rf ÷ Rg.

Why does an inverting amplifier have a negative gain?

The signal enters the inverting input, so the output is 180° out of phase.

What limits op amp bandwidth?

The gain bandwidth product for small signals and the slew rate for large signals.

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