Summing Amplifier Calculator
This Summing Amplifier Calculator estimates the ideal output voltage of a two-input inverting op-amp summing amplifier. It shows the contribution from each input and the effective weighted gain.
Use it for first-pass analog mixing, weighted signal summation, sensor signal conditioning, level scaling, and lab checks where the ideal virtual-ground model is appropriate.
Engineering tool
Summing Amplifier Calculator
Calculate ideal output voltage and per-input contributions for a two-input inverting op-amp summing amplifier.
First voltage input to the inverting summing node.
Second voltage input to the inverting summing node.
Input resistor for V1. This sets the weighting of V1.
Input resistor for V2. This sets the weighting of V2.
Feedback resistor from output to the inverting summing node.
Output voltage (Vout)
-3 V
Result console
- Output voltage (Vout)
- -3V
- Contribution of V1
- -1V
- Contribution of V2
- -2V
- Overall gain
- -1V/V
- Input 1 gain
- -1V/V
- Input 2 gain
- -1V/V
- Input resistor R1
- 10kΩ
- Input resistor R2
- 10kΩ
- Feedback resistor Rf
- 10kΩ
Result is valid for the ideal two-input inverting summing amplifier model.
Formula reference
Summing Amplifier Formula
The ideal inverting summing amplifier assumes negative feedback, a virtual ground at the inverting input, zero op-amp input current, and valid output swing for the calculated result.
Vout = -Rf × (V1 / R1 + V2 / R2)Contribution of V1 = -(Rf / R1) × V1Contribution of V2 = -(Rf / R2) × V2Vout = Contribution of V1 + Contribution of V2Variable definitions
- V1
- First input voltage
- V2
- Second input voltage
- R1
- Input resistor for V1
- R2
- Input resistor for V2
- Rf
- Feedback resistor from output to the summing node
- Vout
- Ideal output voltage
Variable Description
- Input voltage V1
- The first voltage source connected to the inverting summing node through R1.
- Input voltage V2
- The second voltage source connected to the inverting summing node through R2.
- Input resistor R1
- The resistor that sets the weighting of V1. Smaller R1 gives V1 a larger magnitude contribution.
- Input resistor R2
- The resistor that sets the weighting of V2. Smaller R2 gives V2 a larger magnitude contribution.
- Feedback resistor Rf
- The resistor from output to the inverting input. Increasing Rf increases all input contribution magnitudes.
- Overall gain
- The calculated output voltage divided by the arithmetic sum of V1 and V2. Weighted circuits should also review each contribution separately.
Worked Examples
Example 1: Equal Resistor Summing
- V1
- 1 V
- V2
- 2 V
- R1
- 10 kΩ
- R2
- 10 kΩ
- Rf
- 10 kΩ
Vout = -Rf × (V1 / R1 + V2 / R2)
Vout = -10 kΩ × (1 V / 10 kΩ + 2 V / 10 kΩ)
Vout = -3 V
With equal resistor values, the ideal output is the negative sum of the two input voltages.
Example 2: Weighted Summing
- V1
- 0.5 V
- V2
- 1.5 V
- R1
- 5 kΩ
- R2
- 10 kΩ
- Rf
- 20 kΩ
Contribution = -(Rf / Rin) × Vin
V1 contribution = -(20 kΩ / 5 kΩ) × 0.5 V = -2 V; V2 contribution = -(20 kΩ / 10 kΩ) × 1.5 V = -3 V
Contribution of V1 = -2 V, Contribution of V2 = -3 V, Vout = -5 V
Different input resistor values weight each input differently before the inverted contributions are added.
Ideal summing amplifier
The calculator uses the ideal two-input inverting summing amplifier equation and does not include output swing, offset, input bias current, bandwidth, or stability limits.
Weighted summation
Each input contribution is weighted by its own ratio of -Rf/Rin, so different input resistors create different gains.
Negative feedback
Negative feedback keeps the inverting input near virtual ground when the op-amp operates within its valid linear range.
Virtual ground
The summing node is ideally held near the non-inverting input reference, but it should not be treated as a high-current ground node.
Audio mixing applications
Inverting summing amplifiers are commonly used for analog audio mixing and signal addition when inversion is acceptable or corrected later.
Sensor signal conditioning
Weighted summing can combine offsets, sensor signals, and scaling terms before ADC input stages or analog control circuits.
Common Mistakes
Ignoring output inversion
The ideal inverting summing amplifier produces negative contributions for positive inputs.
Connecting input resistors incorrectly
Each input must feed the summing node through its own resistor, not directly shorted together.
Calculating feedback resistance incorrectly
Rf controls every input weighting. Changing Rf changes all input gains at once.
Mixing units
Convert mV to V and kΩ to Ω consistently before checking manual calculations.
Assuming simple voltage addition
The circuit sums currents into a virtual ground node and converts them through Rf, so resistor ratios determine the output.
Support reference
FAQ
What is a summing amplifier?
A summing amplifier is an op-amp circuit that combines multiple input voltages into one output. In the inverting version, each input contributes through its own resistor to a virtual ground node.
Why is the output negative?
The output is negative because this calculator models an inverting summing amplifier. Each input contribution is multiplied by a negative gain set by -Rf/Rin.
Can the inputs have different resistor values?
Yes. Different input resistor values create weighted summing, where each input has a different gain contribution.
How do resistor values affect weighting?
For each input, the weighting gain is -Rf divided by that input resistor. A smaller input resistor gives that input a larger magnitude contribution.
Can this calculator support more than two inputs?
This first version models two inputs. The same ideal method can be extended by adding more terms of the form Vn/Rn inside the summation.
What happens if all resistor values are equal?
If R1, R2, and Rf are all equal, the ideal output is the negative sum of the two input voltages: Vout = -(V1 + V2).
Does this calculator include real op-amp limits?
No. It uses the ideal inverting summing amplifier equation. Real designs must check output swing, bandwidth, slew rate, input bias current, resistor tolerance, and stability.
Related Engineering Guides
Dedicated op-amp guides are planned for this topic cluster. These guide topics are reserved for future publication and are shown without links until the pages exist.
Planned Engineering Guide
Summing Amplifier Basics
Planned guide covering inverting summing amplifier operation, virtual ground behavior, and output polarity.
Planned Engineering Guide
Weighted Summing Circuits
Planned guide explaining input weighting, resistor selection, scaling, and practical signal mixing.
Planned Engineering Guide
Operational Amplifier Applications
Planned guide covering analog mixing, sensor signal conditioning, scaling, filtering, and active analog interfaces.
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Engineering Disclaimer
This calculator uses an ideal two-input inverting summing amplifier equation. Verify op-amp supply rails, output swing, gain bandwidth product, slew rate, input bias current, resistor tolerance, source impedance, noise, and stability before using the design in production hardware.