Summing Amplifier Calculator (Inverting Op-Amp Adder)
By Santaji GadepatilinUpdated November 6, 2026
An inverting summing amplifier adds several input voltages, each weighted by the ratio of the feedback resistor to its own input resistor, because the inverting input sits at a virtual ground. This summing amplifier calculator gives the output voltage and input current for three inputs — the circuit builds on the inverting amplifier gain formula covered in op-amp basics.
How to use the summing amplifier calculator
Enter up to three input voltages with their input resistors, and the feedback resistor. Set an unused input voltage to 0. The calculator returns the current into the summing node and the output voltage. To weight the inputs equally, make all input resistors the same; to scale the sum, change Rf.
Summing amplifier formula
Vout = −Rf (V₁/R₁ + V₂/R₂ + V₃/R₃)
Each input contributes a gain of −Rf/Rn. Choose the non-inverting input resistor (to ground) ≈ R₁ ∥ R₂ ∥ R₃ ∥ Rf to cancel bias-current offset in bipolar op-amps.
Worked example
V₁ = 1 V and V₂ = 0.5 V through 10 kΩ, V₃ = −0.2 V through 20 kΩ, Rf = 10 kΩ:
- Current = 1/10k + 0.5/10k − 0.2/20k = 0.14 mA
- Vout = −10 kΩ × 0.14 mA = -1.40 V
Binary-weighted 4-bit DAC (5 V logic, R = 10 kΩ, 2R, 4R, 8R, Rf = 10 kΩ)
| Code | Bits | Output |
|---|---|---|
| 1 | 0001 | -0.6250 V |
| 2 | 0010 | -1.2500 V |
| 4 | 0100 | -2.5000 V |
| 8 | 1000 | -5.0000 V |
| 5 | 0101 | -3.1250 V |
| 10 | 1010 | -6.2500 V |
| 15 | 1111 | -9.3750 V |
A summing amplifier with binary-weighted input resistors is the simplest digital-to-analogue converter; practical DACs use an R-2R ladder because it needs only two resistor values.
Design notes
- Keep input resistors in the 1 kΩ–100 kΩ range: lower values load the sources, higher values add noise and offset.
- For a mixer, use equal input resistors and a potentiometer in series with each input.
- An averaging amplifier uses Rf = R/N for N equal inputs.
Frequently asked questions
What is the formula for an inverting summing amplifier?
Vout = −R_f × (V₁/R₁ + V₂/R₂ + V₃/R₃). With all resistors equal it is simply −(V₁ + V₂ + V₃).
Why is the output negative?
The inputs drive the inverting terminal, so the sum is inverted. Follow it with a unity-gain inverting stage, or use a non-inverting summing circuit, if you need a positive sum.
Do the inputs interact with each other?
No. The inverting input is held at virtual ground, so each input current depends only on its own voltage and resistor. That isolation is why the circuit is used in audio mixers.
What limits the output?
The op-amp supply rails. The result is only valid while |Vout| stays below the output swing limit — typically 1–2 V inside the rails, or close to the rails for rail-to-rail parts.