Differential Amplifier Calculator
This Differential Amplifier Calculator estimates the ideal output voltage of a classic four-resistor op-amp difference amplifier. It assumes matched resistor pairs where R1 equals R3 and R2 equals R4.
Use it for first-pass analog front-end planning, differential signal scaling, sensor interface review, and comparison with instrumentation amplifier requirements.
Engineering tool
Differential Amplifier Calculator
Calculate ideal differential gain and output voltage for a classic four-resistor differential amplifier with matched resistor ratios.
Voltage applied to the subtracting side of the ideal differential equation.
Voltage applied to the non-inverting side of the ideal differential equation.
Input resistor value. The matched opposite resistor is assumed to equal R1.
Feedback resistor value. The matched opposite resistor is assumed to equal R2.
Output voltage (Vout)
10 V
Result console
- Differential gain
- 10V/V
- Output voltage (Vout)
- 10V
- Voltage difference (V2 - V1)
- 1V
- Input voltage V1
- 1V
- Input voltage V2
- 2V
- Input resistor (R1)
- 10kΩ
- Feedback resistor (R2)
- 100kΩ
Result is valid for the ideal matched-resistor differential amplifier model.
Formula reference
Differential Amplifier Formula
The classic ideal differential amplifier model assumes matched resistor ratios, ideal op-amp behavior, and valid input and output voltage ranges.
Matched resistor assumption: R1 = R3 and R2 = R4Ad = R2 / R1Vdiff = V2 - V1Vout = (R2 / R1) × (V2 - V1)Variable definitions
- V1
- Input voltage on the subtracting side
- V2
- Input voltage on the non-inverting side
- R1
- Input resistor value, with R3 assumed equal to R1
- R2
- Feedback resistor value, with R4 assumed equal to R2
- Ad
- Differential gain
- Vout
- Ideal output voltage
Variable Description
- Input voltage V1
- The input voltage subtracted from V2 in the ideal differential equation.
- Input voltage V2
- The input voltage compared against V1. If V2 is greater than V1, the ideal output is positive.
- Input resistor R1
- The input resistor used to set the matched resistor ratio. The opposite resistor R3 is assumed equal to R1.
- Feedback resistor R2
- The feedback resistor used to set gain. The opposite resistor R4 is assumed equal to R2.
- Differential gain
- The ideal gain applied to the voltage difference V2 - V1.
- Output voltage
- The ideal amplified difference voltage before real op-amp swing, common-mode, and bandwidth limits are applied.
Worked Examples
Example 1: 10 V Output
- V1
- 1 V
- V2
- 2 V
- R1
- 10 kΩ
- R2
- 100 kΩ
Vout = (R2 / R1) × (V2 - V1)
Gain = 100 kΩ / 10 kΩ = 10; Vout = 10 × (2 V - 1 V)
Gain = 10 V/V, Vout = 10 V
The input difference is 1 V and the matched resistor ratio applies a gain of ten.
Example 2: Small Differential Signal
- V1
- 2.5 V
- V2
- 2.7 V
- R1
- 5 kΩ
- R2
- 50 kΩ
Vout = (R2 / R1) × (V2 - V1)
Gain = 50 kΩ / 5 kΩ = 10; Vdiff = 2.7 V - 2.5 V = 0.2 V; Vout = 2 V
Gain = 10 V/V, Voltage Difference = 0.2 V, Vout = 2 V
A small 200 mV differential input becomes a 2 V ideal output when resistor ratios are perfectly matched.
Ideal differential amplifier
The calculator uses the ideal four-resistor difference amplifier model and does not include input range, output swing, offset, or bandwidth limits.
Differential gain
Differential gain is set by the matched resistor ratio R2/R1 and applies only to the difference V2 - V1.
Common-mode rejection
Good common-mode rejection depends strongly on matched resistor ratios and real op-amp common-mode behavior.
Matched resistor requirement
The model assumes R1 = R3 and R2 = R4. Precision resistor networks are often used when CMRR matters.
Precision applications
Small differential signals need low offset voltage, low drift, good resistor matching, and careful PCB layout.
Instrumentation front-end
For high input impedance or high CMRR sensor inputs, an instrumentation amplifier may be more suitable than a simple difference amplifier.
Common Mistakes
Ignoring resistor matching
Using loose resistor tolerances can reduce common-mode rejection and create output error.
Swapping V1 and V2
The equation uses V2 - V1. Reversing the inputs changes output polarity.
Treating differential gain as single-ended gain
Differential gain applies to the input difference, not to each input independently.
Ignoring common-mode input effects
Real op-amps have input common-mode limits and finite common-mode rejection.
Mixing units
Convert mV to V and kΩ to Ω consistently before checking manual calculations.
Support reference
FAQ
What is a differential amplifier?
A differential amplifier is an op-amp circuit that amplifies the voltage difference between two input signals while ideally rejecting voltage common to both inputs.
How is differential gain calculated?
For the matched four-resistor model where R1 = R3 and R2 = R4, differential gain is calculated as R2 / R1.
Why should resistor ratios be matched?
Matched resistor ratios are required for good common-mode rejection. Ratio mismatch converts common-mode voltage into output error.
What is common-mode rejection?
Common-mode rejection is the ability of a differential amplifier to reject voltage that appears equally on both inputs while amplifying the difference between them.
Can this calculator model a real op-amp?
No. It uses an ideal matched-resistor model. Real op-amps also require checks for common-mode range, output swing, offset, bias current, bandwidth, and resistor tolerance.
Why is my output negative?
The output becomes negative when V2 is lower than V1 because the ideal equation uses Vout = (R2 / R1) × (V2 - V1).
Is a differential amplifier the same as an instrumentation amplifier?
No. An instrumentation amplifier is usually a more precise differential front end with high input impedance and better common-mode rejection.
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
Differential Amplifier Basics
Planned guide covering four-resistor differential amplifiers, resistor ratios, input polarity, and output voltage.
Planned Engineering Guide
Understanding Common-Mode Rejection
Planned guide explaining CMRR, resistor matching, common-mode voltage, and real op-amp limitations.
Planned Engineering Guide
Choosing Precision Resistors
Planned guide covering resistor tolerance, ratio matching, temperature drift, and precision analog design.
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Engineering Disclaimer
This calculator uses an ideal matched-resistor differential amplifier equation. Verify resistor ratio tolerance, common-mode range, input impedance, op-amp offset, bias current, bandwidth, output swing, supply rails, and stability before using the design in production hardware.