Instrumentation Amplifier Calculator
This Instrumentation Amplifier Calculator estimates the ideal gain, differential input voltage, and output voltage of a classic three-op-amp instrumentation amplifier.
Use it for first-pass bridge sensor signal conditioning, precision measurement front ends, low-level differential signals, and analog design reviews where the ideal gain equation is appropriate.
Engineering tool
Instrumentation Amplifier Calculator
Calculate ideal three-op-amp instrumentation amplifier gain, differential voltage, and output voltage from V+, V−, Rg, and R.
Non-inverting differential input voltage.
Inverting differential input voltage.
External gain-setting resistor between the first-stage amplifier nodes.
Matched internal resistor used by the ideal three-op-amp gain model.
Output voltage (Vout)
1.05 V
Result console
- Output voltage (Vout)
- 1.05V
- Instrumentation gain
- 21V/V
- Differential voltage (V+ - V−)
- 50mV
- Positive input (V+)
- 150mV
- Negative input (V−)
- 100mV
- Gain resistor Rg
- 1kΩ
- Internal resistor R
- 10kΩ
Result is valid for the ideal three-op-amp instrumentation amplifier model.
Formula reference
Instrumentation Amplifier Formula
The ideal three-op-amp instrumentation amplifier model assumes matched internal resistors, high input impedance, high common-mode rejection, and valid linear output swing.
Gain = 1 + (2R / Rg)Vdiff = V+ − V−Vout = Gain × (V+ − V−)Vout = Gain × VdiffVariable definitions
- V+
- Positive instrumentation amplifier input
- V−
- Negative instrumentation amplifier input
- Rg
- External gain-setting resistor
- R
- Matched internal gain resistor
- Gain
- Ideal differential gain
- Vout
- Ideal output voltage
Variable Description
- Positive input V+
- The non-inverting measurement input of the instrumentation amplifier.
- Negative input V−
- The inverting measurement input. The calculator subtracts this value from V+.
- Gain resistor Rg
- The external resistor that programs the differential gain. Smaller Rg values increase gain.
- Internal resistor R
- The matched resistor value used in the classic three-op-amp gain equation.
- Differential voltage
- The measured input difference, calculated as V+ minus V−.
- Output voltage
- The ideal output voltage before checking real supply rail, output swing, and common-mode limits.
Worked Examples
Example 1: Bridge Sensor Signal
- V+
- 0.15 V
- V−
- 0.10 V
- R
- 10 kΩ
- Rg
- 1 kΩ
Gain = 1 + (2R / Rg); Vout = Gain × (V+ − V−)
Gain = 1 + (2 × 10 kΩ / 1 kΩ) = 21; Vdiff = 0.15 V − 0.10 V = 0.05 V
Vout = 21 × 0.05 V = 1.05 V
A 50 mV bridge signal becomes a 1.05 V ideal output when the instrumentation gain is 21.
Example 2: Small Differential Measurement
- V+
- 2.520 V
- V−
- 2.500 V
- R
- 10 kΩ
- Rg
- 500 Ω
Gain = 1 + (2R / Rg); Vout = Gain × Vdiff
Gain = 1 + (2 × 10 kΩ / 500 Ω) = 41; Vdiff = 2.520 V − 2.500 V = 0.020 V
Vout = 41 × 0.020 V = 0.82 V
A 20 mV differential signal is amplified to 0.82 V in the ideal model.
Instrumentation amplifier basics
The classic topology uses two input buffer amplifiers followed by a differential amplifier stage.
High input impedance
Instrumentation amplifiers are useful with sensors because the inputs load the signal source much less than a simple resistor difference amplifier.
High CMRR
High common-mode rejection helps recover small differential signals even when both inputs sit on a large shared common-mode voltage.
Gain programming
Many instrumentation amplifier circuits set gain with a single external Rg, but real ICs may use manufacturer-specific equations.
Precision measurement
Offset voltage, drift, noise, resistor tolerance, and ADC range become important when amplifying millivolt-level signals.
Bridge sensor applications
Instrumentation amplifiers are common front ends for strain gauges, pressure sensors, load cells, and other bridge-based sensors.
Common Mistakes
Confusing instrumentation and differential amplifiers
A simple differential amplifier does not provide the same high input impedance or CMRR as a classic instrumentation amplifier.
Setting Rg incorrectly
Rg has a strong effect on gain. A value that is too small can create excessive gain and unusable bandwidth.
Ignoring output saturation
The ideal output voltage still must fit within the real amplifier output swing and supply rails.
Ignoring input common-mode range
The inputs may be valid differentially but still outside the real amplifier common-mode operating range.
Assuming all INAs use the same formula
Integrated instrumentation amplifiers often use device-specific gain resistor equations and internal resistor values.
Support reference
FAQ
What is an instrumentation amplifier?
An instrumentation amplifier is a precision differential amplifier with high input impedance and strong common-mode rejection. It is commonly used for sensors, bridge circuits, and low-level measurement signals.
How is instrumentation amplifier gain set?
In the classic three-op-amp model used here, gain is set by the external gain resistor Rg and matched internal resistor R using Gain = 1 + 2R/Rg.
Why is CMRR important?
CMRR describes how well the amplifier rejects voltage that is common to both inputs. High CMRR is important when measuring small differential signals in the presence of large common-mode voltage.
What is the purpose of Rg?
Rg programs the first-stage gain. A smaller Rg produces higher gain, while a larger Rg produces gain closer to one.
Can this calculator model AD620 or INA128?
It can provide a first-pass ideal estimate, but real instrumentation amplifier ICs use device-specific gain equations, resistor values, input range limits, output swing limits, and bandwidth constraints.
Why is my calculated output unrealistic?
The calculated output may exceed the real amplifier supply rails or output swing. Real circuits must also check common-mode input range, load current, offset, noise, and gain bandwidth.
Is an instrumentation amplifier the same as a differential amplifier?
No. Both amplify a voltage difference, but a three-op-amp instrumentation amplifier usually provides much higher input impedance and better common-mode rejection than a simple four-resistor difference amplifier.
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
Instrumentation Amplifier Basics
Planned guide covering three-op-amp instrumentation amplifier structure, input buffering, and differential output behavior.
Planned Engineering Guide
Understanding CMRR
Planned guide explaining common-mode rejection ratio, resistor matching, common-mode voltage, and measurement accuracy.
Planned Engineering Guide
Bridge Sensor Signal Conditioning
Planned guide covering strain gauges, bridge sensors, excitation, offset, and instrumentation amplifier front ends.
Planned Engineering Guide
Precision Analog Measurement
Planned guide covering offset, drift, noise, filtering, grounding, and ADC interface considerations.
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Engineering Disclaimer
This calculator uses an ideal three-op-amp instrumentation amplifier equation for estimation and education. Real designs must verify supply rails, output swing, input common-mode range, gain bandwidth, offset, drift, noise, resistor tolerance, load current, stability, and device-specific datasheet limits before hardware release.