Op-Amps Formulas

Op-amp formulas set the gain, bandwidth, and response of amplifier and filter stages built around operational amplifiers. These calculators turn feedback resistor values into precise gain and frequency limits. They are foundational to analog signal conditioning.

Op-Amps Formula Calculators

Worked result for every Op-Amps formula

Formula Expression Worked result
Non-Inverting Amplifier Vout = Vin × (1 + Rf/Ri) Input Voltage 0.726 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → Output Voltage = 1.056 V
Inverting Amplifier Vout = −Vin × Rf/Ri Input Voltage 0.726 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → Output Voltage = -0.33 V
Summing Amplifier Vout = −Rf × (V1/R1 + V2/R2 + V3/R3) Input V1 0.726 V, Input V2 1.55 V, Input V3 155 mV, R1 100 Ω, R2 0.22 kΩ, R3 0.47 kΩ, Feedback Resistor 47 Ω → Output Voltage = -0.6879 V
Difference Amplifier Vout = (Rf/Ri) × (V2 − V1) Input V1 0.726 V, Input V2 1.55 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → Output Voltage = 0.3745 V
Gain-Bandwidth Product GBW = Gain × f Voltage Gain 0.025, Frequency 100 Hz → Gain-Bandwidth Product = 2.5 Hz
Common-Mode Rejection Ratio CMRR = 20 × log10(Ad / Acm) Differential Gain 0.025, Common-Mode Gain 0.055 → CMRR = -6.848 dB
Op-Amp Integrator Gain |Vout| = Vin / (2πfRC) Input Voltage 0.726 V, Frequency 5 Hz, Input Resistor 100 Ω, Feedback Capacitor 100 pF → Output Voltage = 2311 kV
Op-Amp Differentiator Gain |Vout| = Vin × 2πfRC Input Voltage 0.726 V, Frequency 5 Hz, Feedback Resistor 100 Ω, Input Capacitor 100 pF → Output Voltage = 0.2281 µV
Instrumentation Amplifier Gain G = (1 + 2R1/Rg) × (R3/R2) R1 (input stage) 100 Ω, Gain Resistor 1 Ω, R3 (diff stage) 0.22 kΩ, R2 (diff stage) 0.47 kΩ → Gain = 94.09
Op-Amp Schmitt Trigger Hysteresis Vhyst = Vref × R1 / (R1 + R2) Saturation Voltage 0.726 V, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → Hysteresis Voltage = 0.2269 V
Transimpedance Amplifier Bandwidth f3dB = √(GBW / (2π × Rf × Cd)) Op-Amp GBW 0.22 MHz, Feedback Resistor 100 Ω, Input Capacitance (Cd) 1 pF → −3 dB Bandwidth = 18.71 MHz
TIA Feedback Capacitor (Stability) Cf = √(Cin / (2π · Rf · fGBW)) Input Capacitance 2.2 pF, Feedback Resistor 100 kΩ, Gain-Bandwidth 100 kHz → Feedback Capacitor = 5.917 pF
TIA Optimal Bandwidth f−3dB = √(fGBW / (2π · Rf · Cin)) Gain-Bandwidth 100 kHz, Feedback Resistor 100 kΩ, Input Capacitance 1 pF → Bandwidth = 0.3989 MHz
Settling Time to N-Bit Accuracy ts = (N + 1) · ln2 · τ Resolution (bits) 0.025, Time Constant 0.22 µs → Settling Time = 156.3 ns
Op-Amp RMS Noise Vn = en · √(NEB) Noise Density 0.1 nV/√Hz, Noise Bandwidth 100 Hz → RMS Noise = 1 nV

Variables used across Op-Amps formulas

  • Vout — Output voltage (V)
  • Vin — Input voltage (V)
  • Rf — Feedback resistor (Ω)
  • Ri — Input resistor from inverting input to ground (Ω)
  • V1 — Input voltage 1 (V)
  • V2 — Input voltage 2 (V)
  • V3 — Input voltage 3 (V)
  • R1 — Input resistor for V1 (Ω)
  • R2 — Input resistor for V2 (Ω)
  • R3 — Input resistor for V3 (Ω)
  • GBW — Gain-bandwidth product (Hz)
  • Gain — Closed-loop voltage gain (V/V, dimensionless)
  • f — Maximum usable frequency at that gain (Hz)
  • CMRR — Common-mode rejection ratio (dB)
  • Ad — Differential gain (V/V, linear)
  • Acm — Common-mode gain (V/V, linear)
  • V_out — Output voltage magnitude (V)
  • V_in — Input voltage magnitude (V)
  • R — Input resistor (Ω)
  • C — Feedback capacitor (F)
  • G — Total voltage gain (V/V)
  • R₁ — Input stage resistors (Ω, both equal)
  • Rg — Gain-setting resistor (Ω)
  • R₃ — Difference stage feedback resistor (Ω)
  • R₂ — Difference stage input resistor (Ω)
  • V_hyst — Half the hysteresis window (V)
  • V_ref — Output saturation voltage (V, typically V+ or V+ − 1.5 V for rail-to-rail)
  • f_3dB — Amplifier −3 dB bandwidth (Hz)
  • Cd — Total input capacitance, photodiode plus parasitic (F)
  • Cf — Feedback capacitor (F)
  • Cin — Total input capacitance (photodiode + amp) (F)
  • fGBW — Amplifier gain-bandwidth product (Hz)
  • f−3dB — Closed-loop bandwidth (Hz)
  • ts — Settling time to ½ LSB (s)
  • N — Resolution in bits
  • τ — Dominant time constant of the response (s)
  • Vn — Total RMS noise (V)
  • en — Input-referred noise density (V/√Hz)
  • NEB — Noise-equivalent bandwidth (Hz)

Questions people ask about Op-Amps

Related Formula Categories

Basic Electronics Resistors Capacitors Inductors AC Circuits Signal & dB

Browse the full formulas index for all 32 categories.