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Op-Amp Voltage and Gain Calculator

Vout = V2·R4/(R3+R4)·(1+R2/R1) − V1·R2/R1. Equal 10 kΩ, 1 V and 1.5 V is 0.5 V.

By Jasper · Updated

Calculator

PASS0.5 Videal 0.5 V

Vout = V2 · R4/(R3+R4) · (1 + R2/R1) − V1 · R2/R1, then clip to [V−, V+]. Non-inverting drives the +input directly (divider = 1; R3/R4 unused). Saturated when ideal is beyond the rails — real parts need headroom unless they are rail-to-rail.

Ideal Vout
0.5 V
Clipped
0.5 V
Saturated
no
  • Pass Ideal Vout: Vout = 0.500000 V, clipped 0.500000 V

Formula

Ideal closed-loop Vout

Vout=V2⋅R4R3+R4⋅(1+R2R1)-V1⋅R2R1 Vout = V2 · R4/(R3+R4) · (1 + R2/R1) − V1 · R2/R1

Rail clip

Vclip=min(V+,max(V-,Vout)) Clip to [V−, V+]

Saturation

sat=(Vout<V-)∨(Vout>V+) Saturated when ideal is beyond the rails

Variables

Symbol Meaning Unit Typical range Precision Default
preset Preset — — 1 sig differential
V1 Inverting input V — 4 sig 1 V
V2 Non-inverting input V — 4 sig 1.5 V
R1 Inverting gain resistor Ω ≥ 0 mΩ R1 must be > 0 4 sig 10 kΩ
R2 Feedback Ω ≥ 0 mΩ 4 sig 10 kΩ
R3 +input series Ω ≥ 0 mΩ 4 sig 10 kΩ
R4 +input to ground Ω ≥ 0 mΩ 4 sig 10 kΩ
Vp Positive rail V — 4 sig 15 V
Vn Negative rail V — 4 sig -15 V
Vout Ideal output V — 4 sig —
Vclip Clipped output V — 4 sig —
sat Saturated — — 1 sig —
G R2/R1 — — 4 sig —
div Non-inverting divider — — 4 sig —

Worked example

Differential 10 kΩ × 4

Input Value
preset · Preset differential
V1 · Inverting input 1 V
V2 · Non-inverting input 1.5 V
R1 · Inverting gain resistor 10 kΩ
R2 · Feedback 10 kΩ
R3 · +input series 10 kΩ
R4 · +input to ground 10 kΩ
Vp · Positive rail 15 V
Vn · Negative rail -15 V
Output Value
Vout · Ideal output 0.5 V
Vclip · Clipped output 0.5 V
sat · Saturated no
G · R2/R1 1

Inverting 1 kΩ / 47 kΩ clips

Input Value
preset · Preset inverting
V1 · Inverting input 0.5 V
V2 · Non-inverting input 0 V
R1 · Inverting gain resistor 1 kΩ
R2 · Feedback 47 kΩ
R3 · +input series 1 kΩ
R4 · +input to ground 1000 MΩ
Vp · Positive rail 15 V
Vn · Negative rail -15 V
Output Value
Vout · Ideal output -23.5 V
Vclip · Clipped output -15 V

How it works

The four-resistor op-amp is the superposition you actually write on a whiteboard: the +input is a divider, the −input is an inverting gain, and the closed-loop output is their sum. This page evaluates that formula and then clips to the rails so a wild gain does not print ±∞.

Use the inverting resistor page when you already know G and only need R2 and R3.

Pitfalls

  • Treating the clip as a real output — most op-amps need headroom unless they are rail-to-rail.
  • Leaving R1 at 0 Ω. Gain R2/R1 is not a finite number.
  • Using R3 = R4 = 0 without the non-inverting unused-divider path.

FAQ

What is Vout for four equal 10 kΩ resistors at 1 V and 1.5 V?

0.5 V. The differential pair with matched resistors has gain 1.

How do I run a non-inverting stage?

Choose the Non-inverting preset. V1 is grounded, R3/R4 are unused so the divider is 1, and R2/R1 sets the gain.

Why is the output stuck at the rail?

The ideal Vout is outside [V−, V+]. The page clips and marks saturated.

Does this model input bias current?

No. It is the ideal superposition from Sedra/Smith.

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