What is the formula for Differential op-amp calculator?

Core formula: Vout = V2·R4/(R3+R4)·(1+R2/R1) − V1·R2/R1 | when matched, Vout = Ad·(V2−V1), Ad = R2/R1. The tool returns results instantly using this formula and the selected parameters.

What engineering notes should I keep in mind when using Differential op-amp calculator?

Difference (subtractor) amplifier: V1 drives the − input through R1 with R2 feeding back from the output to −; V2 drives the + input through R3 with R4 from + to ground. Only when R2/R1 = R4/R3 does Vout = Ad·(V2−V1) with Ad = R2/R1. CMRR is set by how well the four resistors match, not by the op amp itself: 1% resistors give only about 34 dB at Ad = 1, while 0.1% reaches 54 dB or more. For demanding cases use an integrated difference amplifier, an instrumentation amplifier…

Differential op-amp calculator

Favorite

Four-resistor difference (subtractor) amplifier: compute the output, differential gain, common-mode gain and CMRR from R1–R4 and two inputs, bound the gain / output error and worst-case CMRR with the resistor tolerance, or match standard resistors to a target gain, and check input impedance, bandwidth and slew rate.

Key points

A differential (difference / subtractor) amplifier uses four resistors and one op amp: V1 drives the − input through R1 with R2 feeding back from the output to −, while V2 drives the + input through R3 with R4 from + to ground. The output is Vout = V2·[R4/(R3+R4)]·(1+R2/R1) − V1·(R2/R1); when R2/R1 = R4/R3 = Ad it reduces to Vout = Ad·(V2 − V1) with zero common-mode gain. CMRR is dominated by how precisely the four resistors match (about 34 dB for 1% resistors at Ad = 1), and the closed-loop bandwidth uses the noise gain 1+Ad: BW = GBW/(1+Ad). The tool solves output / gain / CMRR from the resistors, or standard matched resistors for a target gain, together with differential and common-mode input impedance, required slew rate and full-power bandwidth.

Inputs

Vout = V2·R4/(R3+R4)·(1+R2/R1) − V1·R2/R1 | when matched, Vout = Ad·(V2−V1), Ad = R2/R1

DirectionInput resistor R1kΩV1 → inverting input (−)Feedback resistor R2kΩOutput → inverting input (−)Input resistor R3kΩV2 → non-inverting input (+)Divider resistor R4kΩNon-inverting input (+) → groundInput voltage V1 (inverting side)VInput voltage V2 (non-inverting side)VResistor tolerance%Used for the worst-case CMRR estimate (1% common; 0.1% / 0.01% for high common-mode rejection)Gain-bandwidth product GBWMHzClosed-loop BW = GBW / (1 + Ad), i.e. based on the noise gainSlew rate SRV/µsAbout 0.5 for the LM358 and 13 for the TL072Differential test amplitude (peak)VSine differential peak; output peak = Ad × this valueSignal frequency fHzUsed for the bandwidth and slew-rate checksPositive supply V+VNegative supply V−VSingle supply / ground: 0

Calculation model (updates with parameters)

Bode plot (magnitude / phase, updates with parameters)

Differential gain Ad = R2 / R1	1.0000V/V	≈ 0.00 dB
Differential gain range (resistor tolerance)	0.9802 ~ 1.0202V/V	±1.00% resistor worst case (R2/R1)
Output range (resistor tolerance)	179.8 mV ~ 219.8 mV	V1 / V2 unchanged; nominal 200 mV
Maximum resistor-mismatch error	-20.2 mV ~ 19.8 mV	relative to ideal 200 mV: max ±20.2 mV; gain error -1.98% ~ +2.02%; Vcm common-mode error ±22.22 mV
Matching ratio R4 / R3	1.0000	Perfectly matched to Ad: common-mode gain is 0
Resistor set R1 / R2 / R3 / R4	10 kΩ / 10 kΩ / 10 kΩ / 10 kΩ
Common-mode Vcm / differential Vd	1.1000 / 0.2000 V	Vcm = (V1+V2)/2, Vd = V2 − V1
Ideal output (matched formula)	200 mV	Ad · (V2 − V1)
Actual output Vout	200 mV	With resistor mismatch: V2·R4/(R3+R4)·(1+R2/R1) − V1·R2/R1
Common-mode gain Acm	0.00000	Output factor for V1 = V2; closer to 0 is better
CMRR (actual resistors)	ideal ∞	the four resistor ratios are exactly equal
CMRR (±1.00% worst case)	33.9 dB	Worst case over the resistor corners; sets the real common-mode rejection
Differential input impedance R1 + R3	20 kΩ	Total series resistance seen by the differential source
Common-mode input impedance R1∥R2	5 kΩ	Take R1∥R2 (symmetric with R3∥R4 when matched)
Noise gain 1 + Ad	2.0000	Amplification of the op-amp offset / noise
Closed-loop bandwidth BW = GBW/(1+Ad)	500 kHz	GBW 1 MHz; a difference amp uses the noise gain
Output amplitude (peak)	100 mV	differential peak 100 mV × Ad
Required slew rate SR_req	6.28 mV/µs	2π · f · Vpk @ 10 kHz
Device SR / margin	×79.58	Device 500 mV/µs \| required 6.28 mV/µs
Full-power bandwidth FPBW	795.8 kHz	Highest sine frequency the slew rate allows
Small-signal rise time tr	700 ns	≈ 0.35 / BW (10–90%)

⚠ tolerance ±1.00% gives a worst-case CMRR of only 33.9 dB: for high common-mode rejection use 0.1% resistors, a resistor network (matched within the package) or an instrumentation amplifier (INA).

Engineering notes

Difference (subtractor) amplifier: V1 drives the − input through R1 with R2 feeding back from the output to −; V2 drives the + input through R3 with R4 from + to ground. Only when R2/R1 = R4/R3 does Vout = Ad·(V2−V1) with Ad = R2/R1.
CMRR is set by how well the four resistors match, not by the op amp itself: 1% resistors give only about 34 dB at Ad = 1, while 0.1% reaches 54 dB or more. For demanding cases use an integrated difference amplifier, an instrumentation amplifier or a resistor network.
For gain ≥ 1 the differential input impedance is R1 + R3; gain < 1 (R2 < R1) costs common-mode rejection and input impedance, so weigh the trade-off.
The closed-loop bandwidth uses the noise gain 1 + R2/R1 (not the signal gain Ad): BW = GBW/(1+Ad), narrower than a non-inverting stage of the same gain.
The + input common-mode level is V2·R4/(R3+R4) and must stay within the input common-mode range; keep the source impedances equal, otherwise unequal division further degrades CMRR.

FAQ

What is Differential op-amp calculator for?: Four-resistor difference (subtractor) amplifier: compute the output, differential gain, common-mode gain and CMRR from R1–R4 and two inputs, bound the gain / output error and worst-case CMRR with the resistor tolerance, or match standard resistors to a target gain, and check input impedance, bandwidth and slew rate.
What is the formula for Differential op-amp calculator?: Core formula: Vout = V2·R4/(R3+R4)·(1+R2/R1) − V1·R2/R1 | when matched, Vout = Ad·(V2−V1), Ad = R2/R1. The tool returns results instantly using this formula and the selected parameters.
What engineering notes should I keep in mind when using Differential op-amp calculator?: Difference (subtractor) amplifier: V1 drives the − input through R1 with R2 feeding back from the output to −; V2 drives the + input through R3 with R4 from + to ground. Only when R2/R1 = R4/R3 does Vout = Ad·(V2−V1) with Ad = R2/R1. CMRR is set by how well the four resistors match, not by the op amp itself: 1% resistors give only about 34 dB at Ad = 1, while 0.1% reaches 54 dB or more. For demanding cases use an integrated difference amplifier, an instrumentation amplifier…