Op-Amp Gain Calculator

Calculate

Select the op-amp circuit configuration

Feedback resistor in ohms (e.g. 100000 for 100 kΩ). Ignored in Voltage Follower mode.

Ground (reference) resistor in ohms. Av = 1 + Rf / Rg. Minimum gain = 1 when Rf = 0.

Op-amp GBW in Hz (e.g. 1000000 for 1 MHz). Used to estimate closed-loop bandwidth for inverting, non-inverting, and voltage follower topologies.

Resistor tolerance in percent. Used for rough worst-case gain error screening (approx. 2 × tolerance for simple ratio topologies).

Overview

Op-amp gain follows from the feedback network. Select a topology — inverting, non-inverting, voltage follower, difference, or summing — enter the relevant resistors, and the calculator returns the closed-loop gain as signed Av, magnitude |Av|, and decibels. For inverting topology it also reports noise gain (1 + Rf/Rin), which governs bandwidth and stability independently of signal gain.

If you supply a gain-bandwidth product (GBW), the calculator estimates closed-loop bandwidth as GBW divided by noise gain for inverting, non-inverting, and voltage follower topologies. This helps screen whether the selected op-amp supports the intended signal frequency range. For difference and summing topologies, noise gain requires more detailed circuit analysis and is not shown.

The tool also screens resistor ratios against practical limits: values below 100 Ω increase output loading, values above 10 MΩ amplify bias current errors, and very large ratios flag potential two-stage alternatives. An optional resistor tolerance entry gives a rough worst-case gain error estimate.

A status badge classifies the result from ZERO GAIN through UNITY GAIN, ATTENUATION, LOW GAIN, MID GAIN, HIGH GAIN, and VERY HIGH GAIN, with practical context for each range. For summing topology, the badge reflects the highest per-channel gain. Above roughly 60 dB (1000×) in a single stage, the tool flags the design as impractical and recommends cascaded stages or a dedicated instrumentation amplifier.

How to Use This Calculator

  1. Select the op-amp topology — Inverting, Non-Inverting, Voltage Follower (Buffer), Difference, or Summing (Inverting Summer).

  2. Enter the feedback resistor Rf — in ohms (e.g. 100000 for 100 kΩ). Not used in Voltage Follower mode.

  3. Enter the topology-specific input resistor — Rin for Inverting, Rg for Non-Inverting, R1 for Difference, or R1–R3 channel resistors for Summing.

  4. Optionally enter the op-amp GBW — gain-bandwidth product in Hz (e.g. 1000000 for 1 MHz) to estimate closed-loop bandwidth.

  5. Optionally enter resistor tolerance — in percent (e.g. 1 for 1%) for worst-case gain error screening.

  6. Click Calculate — read Signal Gain Av (signed), magnitude |Av|, gain in dB, noise gain, and closed-loop bandwidth.

This calculator uses ideal op-amp formulas. Real performance depends on finite GBW, input offset voltage, bias current, supply rails, and op-amp datasheet parameters. Use these results as a starting point, then verify against the datasheet.

Inputs & Outputs

Inputs

  • •Op-Amp Topology — Options: Inverting, Non-Inverting, Voltage Follower (Buffer), Difference, Summing (Inverting Summer)
  • •Feedback Resistor Rf (Ω)
  • •Input Resistor Rin (Ω)
  • •Ground Resistor Rg (Ω)
  • •Input Resistor R1 (Ω)
  • •Channel 1 Resistor R1 (Ω)
  • •Channel 2 Resistor R2 (optional) (Ω)
  • •Channel 3 Resistor R3 (optional) (Ω)
  • •Gain-Bandwidth Product GBW (optional) (Hz)
  • •Resistor Tolerance (optional) (%)

Outputs

  • •Signal Gain Av (signed)
  • •|Av| Magnitude
  • •Gain in dB (dB)
  • •Noise Gain
  • •Closed-Loop Bandwidth (if GBW entered) (kHz)

Formula

Calculator Formula

Closed-loop gain is set by external resistors against the op-amp feedback network. The topology determines the sign and exact form.

Inverting Amplifier

Av = −Rf / Rin

Signal gain is negative (inverting). Noise gain — used for bandwidth and stability analysis — differs:

Av_noise = 1 + Rf / Rin

Noise gain is always greater than 1. Bandwidth is determined by noise gain, not signal gain.

Non-Inverting Amplifier

Av = 1 + Rf / Rg

Minimum gain is 1 (when Rf = 0). Signal gain equals noise gain.

Voltage Follower (Unity-Gain Buffer)

Av = 1

No external resistors required. Full GBW is available as closed-loop bandwidth (Av_noise = 1).

Difference Amplifier (Matched-Pair Simplified Model)

Av_diff = Rf / R1

Assumes R1 = R3 and Rf = R2 (matched pairs). Real CMRR depends on resistor matching accuracy, not on the values themselves. Bandwidth estimate not shown for this topology.

Summing Amplifier (Inverting Summer)

Av_n = −Rf / Rn   (per channel)

Each input channel has its own gain. The status badge is based on the highest magnitude channel gain. Bandwidth estimate not shown for this topology.

Derived Quantities

Gain in dB: Gv_dB = 20 × log₁₀(|Av|)     (undefined when Av = 0)
Closed-loop BW: BW = GBW / Av_noise       (inverting, non-inverting, buffer only)

For ZERO GAIN, dB is mathematically undefined (−∞). The calculator outputs 0 in this case — disregard the dB field when the ZERO GAIN badge is shown.

Variables

Symbol Meaning Unit
Av Closed-loop signal gain dimensionless
Av_noise Noise gain (sets BW and stability) dimensionless
Rf Feedback resistor Ω
Rin / Rg / R1 / Rn Input or ground resistor (topology-dependent) Ω
GBW Op-amp gain-bandwidth product Hz
BW Estimated closed-loop bandwidth Hz

Status Classification

The status badge is based on |Av| (or highest per-channel |Av| for summing):

Status |Av| dB Typical Use
ZERO GAIN = 0 — Test state or muted channel
UNITY GAIN = 1 0 dB Buffers, ADC drivers, isolation stages
ATTENUATION 0 – 1 < 0 dB Active dividers, gain trim
LOW GAIN 1 – 10 0 – 20 dB Sensor preamps, microphone front-ends
MID GAIN 10 – 100 20 – 40 dB Audio amps, signal conditioning
HIGH GAIN 100 – 1000 40 – 60 dB Precision instrumentation
VERY HIGH GAIN > 1000 > 60 dB Multi-stage cascade recommended

What is Op-Amp Gain?

An operational amplifier is a high-gain DC-coupled voltage amplifier with differential inputs. Its open-loop gain is enormous — typically 10⁵ to 10⁶ — so practical circuits use external resistors to set a lower, predictable closed-loop gain. The ratio of feedback to input resistance defines that gain, with the topology determining the sign and exact form of the expression.

The classical configurations are inverting (Av = −Rf/Rin), non-inverting (Av = 1 + Rf/Rg), and the unity-gain voltage follower (Av = 1) used for impedance buffering. Difference and summing amplifiers extend the same principle to multiple inputs: the difference amplifier subtracts two signals, and the summing amplifier weights and adds several inputs. Each topology has specific advantages for different signal chain requirements.

Closed-loop bandwidth follows from the gain-bandwidth product: at higher gain, the available bandwidth shrinks proportionally. This trade-off, combined with offset voltage, noise, and supply rail limits, sets the practical ceiling on single-stage gain. Above roughly 60 dB (1000×), most designs split the amplification across multiple stages or use a dedicated instrumentation amplifier IC.

Signal Gain vs Noise Gain

In the inverting topology, signal gain (−Rf/Rin) and noise gain (1 + Rf/Rin) are different quantities. Signal gain is what the desired input signal sees. Noise gain is what the op-amp's own input-referred noise, offset voltage, and bias current see — and it is noise gain that determines closed-loop bandwidth and phase margin.

For an inverting amplifier with Rf = 100 kΩ and Rin = 10 kΩ, the signal gain is −10 but the noise gain is 11. The closed-loop bandwidth is GBW / 11, not GBW / 10. This distinction matters most at higher gains and when interpreting stability: an inverting amplifier with high signal gain still has a noise gain of at least 1, which is why inverting stages can be more stable than their signal gain alone suggests.

For the non-inverting topology, signal gain and noise gain are equal (both 1 + Rf/Rg). For the voltage follower, both are 1, giving the widest possible bandwidth for any gain configuration.

Gain-Bandwidth Product and Closed-Loop Bandwidth

GBW is the frequency at which a voltage-feedback op-amp's open-loop gain drops to 1 (0 dB). For a first-order (dominant-pole) compensated amplifier, the relationship is: closed-loop BW = GBW / noise gain. A 10 MHz GBW op-amp at noise gain 100 has 100 kHz of usable bandwidth.

This relationship holds well for gains well within the bandwidth and breaks down near the op-amp's natural frequency. For practical designs, using 10–20% margin below the calculated bandwidth is advisable. Very high-speed signals or high-gain configurations require selection of op-amps with GBW at least an order of magnitude above the intended closed-loop bandwidth.

Key Facts

  • Op-amp closed-loop gain is set by external resistors, not by the op-amp itself, as long as open-loop gain is much larger than closed-loop gain — a condition that holds in the audio and low-frequency range for most general-purpose op-amps.
  • Inverting topology has signal gain Av = −Rf/Rin but noise gain Av_noise = 1 + Rf/Rin. Bandwidth and stability are determined by noise gain, not signal gain — one of the most common sources of confusion in op-amp design.
  • The minimum gain of a standard non-inverting amplifier is 1. Attenuation (gain below 1) is only possible in inverting and difference configurations.
  • A voltage follower gives the full GBW as closed-loop bandwidth, because noise gain is 1.
  • For matched-pair difference amplifiers, common-mode rejection depends on resistor matching, not on absolute values. Matched 0.1% thin-film networks are common in instrumentation designs.
  • Resistor preferred values follow the IEC 60063 E-series: E12 (10% tolerance), E24 (5%), E48 (2%), E96 (1%), E192 (0.5% / 0.25% / 0.1%).
  • Doubling the closed-loop gain halves the closed-loop bandwidth in voltage-feedback op-amps with dominant-pole compensation.
  • Most general-purpose op-amp stages use 1 kΩ to 100 kΩ resistor values. Below 1 kΩ, output current rises and power dissipation increases. Above 1 MΩ, input bias current and PCB leakage start to affect accuracy.

Applications

  • Audio preamplifiers and microphone front-ends, typically in the LOW to MID GAIN range.
  • Sensor signal conditioning for thermocouples, strain gauges, photodiodes, and accelerometers.
  • ADC driver buffers using voltage followers for impedance matching before analogue-to-digital conversion.
  • Difference amplifiers for differential signal extraction in industrial measurement and instrumentation.
  • Summing amplifiers for analogue mixing, signal averaging, and weighted summation.
  • Verifying whether a gain target is achievable with practical resistor values and a given op-amp GBW during early-stage analogue design.
  • Educational use for teaching feedback theory, gain-bandwidth product, and the practical limits of single-stage amplification.
  • First-pass design verification before SPICE simulation or breadboard prototyping.

Example Calculation

Example 1 — Non-Inverting Audio Preamp

Inputs:

  • Topology: Non-Inverting
  • Rf = 99 kΩ (99000 Ω)
  • Rg = 1 kΩ (1000 Ω)
  • GBW = 10 MHz (10000000 Hz)

Calculation:

Av = 1 + 99000 / 1000 = 100
Gain in dB = 20 × log₁₀(100) = 40 dB
Noise gain = 100
Closed-loop BW = 10,000,000 / 100 = 100,000 Hz (100 kHz)

Result:

  • Signal gain Av = 100, |Av| = 100, 40 dB
  • Noise gain = 100, Bandwidth = 100 kHz
  • Status: MID GAIN
  • 100 kHz bandwidth comfortably exceeds the 20 kHz audio band.

Example 2 — Inverting Amplifier with Attenuation

Inputs:

  • Topology: Inverting
  • Rf = 1 kΩ (1000 Ω)
  • Rin = 10 kΩ (10000 Ω)

Calculation:

Av = −1000 / 10000 = −0.1
|Av| = 0.1
Gain in dB = 20 × log₁₀(0.1) = −20 dB
Noise gain = 1 + 1000 / 10000 = 1.1

Result:

  • Av = −0.1, |Av| = 0.1, −20 dB, signal inversion
  • Noise gain = 1.1
  • Status: ATTENUATION
  • An active divider preserves high input impedance compared to a passive resistive divider.

Example 3 — Summing Amplifier (Three Channels)

Inputs:

  • Topology: Summing (Inverting Summer)
  • Rf = 10 kΩ (10000 Ω)
  • R1 = 10 kΩ (10000 Ω), R2 = 1 kΩ (1000 Ω), R3 = 5 kΩ (5000 Ω)

Per-channel gains:

Av₁ = −10000 / 10000 = −1   (|Av₁| = 1)
Av₂ = −10000 / 1000  = −10  (|Av₂| = 10)
Av₃ = −10000 / 5000  = −2   (|Av₃| = 2)

Result:

  • Highest channel gain: |Av₂| = 10 (channel 2)
  • Status: LOW GAIN (based on highest channel gain)
  • Output voltage = −(V₁ × 1 + V₂ × 10 + V₃ × 2)
  • The badge reflects per-channel amplification, not summed amplitude.

Example 4 — Voltage Follower (Buffer)

Inputs:

  • Topology: Voltage Follower (Buffer)
  • No resistors required

Result:

  • Av = 1, |Av| = 1, 0 dB
  • Noise gain = 1, Bandwidth = GBW (if entered)
  • Status: UNITY GAIN
  • Used for impedance buffering — high input impedance, low output impedance.

Standards & References

  • IEC 60063:2015 — Preferred number series for resistors and capacitors. Defines the E3, E6, E12, E24, E48, E96, and E192 series used for standard resistor values.
  • IEC 60062 — Marking codes for resistors and capacitors. Companion standard to IEC 60063.
  • JEDEC Standards — Semiconductor parameter definitions including op-amp characterisation terminology.
  • Analog Devices Op Amp Applications Handbook — Comprehensive practical op-amp design reference. Freely available from Analog Devices.
  • Horowitz & Hill, "The Art of Electronics" (3rd edition, Cambridge University Press) — Standard textbook reference for practical analogue circuit design including op-amp configurations.
  • Sedra & Smith, "Microelectronic Circuits" — Standard academic textbook reference for op-amp feedback theory and configurations.
  • Full IEC standards are purchased through the IEC webstore. Manufacturer handbooks from Analog Devices and Texas Instruments are freely available online.

Units

This calculator uses SI-derived electrical units that are universal across regions:

  • Resistance — ohms (Ω). Enter values directly in ohms. For common resistor values: 1 kΩ = 1000 Ω, 10 kΩ = 10000 Ω, 100 kΩ = 100000 Ω, 1 MΩ = 1000000 Ω.
  • Frequency — hertz (Hz). For GBW: 1 kHz = 1000 Hz, 1 MHz = 1000000 Hz, 10 MHz = 10000000 Hz.
  • Gain — dimensionless linear ratio and decibels (dB). Voltage gain in dB uses the 20 × log₁₀ convention (distinct from power gain which uses 10 × log₁₀).
  • Tolerance — percent (%).

There is no Imperial alternative for electrical units — they are the same worldwide. A 10 kΩ E96 resistor is the same value on any datasheet regardless of country of manufacture.

Decibels are a logarithmic ratio, not a unit in the SI sense. This calculator always uses the voltage gain convention (20 × log₁₀). For reference: 20 dB = 10×, 40 dB = 100×, 60 dB = 1000×, −20 dB = 0.1×.

Limitations

  • This calculator addresses ideal-model closed-loop gain only. Finite open-loop gain, input bias current, input offset voltage, and slew rate are not modelled and may dominate at high gain or low signal levels.
  • The calculator does not verify whether the required output swing fits within the op-amp supply rails. A mathematically valid gain may still be unusable if the output saturates.
  • It does not check input common-mode range. Many op-amps cannot operate with input voltages close to either supply rail.
  • The difference amplifier model assumes perfect resistor matching (R1 = R3, Rf = R2). Real CMRR depends strongly on matching and is not estimated here.
  • Closed-loop bandwidth is shown only for inverting, non-inverting, and voltage follower topologies, where noise gain is well-defined by the simple model.
  • Stability, phase margin, and compensation are not analysed. The calculator only flags when single-stage gain becomes impractical.
  • Active filter behaviour with capacitors or inductors in the feedback network is out of scope.
  • Temperature coefficient of resistors and op-amp drift are not modelled.
  • The worst-case gain error estimate (2 × tolerance) is a rough screening rule for simple ratio topologies, not a precision guarantee.

Common Mistakes to Avoid

  • Confusing signal gain with noise gain in inverting topology. Av = −Rf/Rin sets signal amplification, but Av_noise = 1 + Rf/Rin sets bandwidth and stability margin.
  • Trying to achieve gain below 1 with a non-inverting amplifier. The minimum non-inverting gain is 1; for attenuation, use an inverting or difference configuration.
  • Picking very small resistors (under 100 Ω). They load the op-amp output and waste current. Most general-purpose stages use 1 kΩ to 100 kΩ values.
  • Picking very large resistors (over 10 MΩ) without considering bias current, PCB leakage, and noise.
  • Specifying gain that exceeds GBW / Av_noise at the signal frequency. Closed-loop bandwidth shrinks as gain rises.
  • Treating the 2 × tolerance rule as a strict bound. It is a rough screening estimate for simple ratio topologies, not a guarantee.
  • Designing single-stage amplifiers above 1000× gain. Cascading two moderate-gain stages typically gives better bandwidth, lower noise, and lower DC offset.
  • Ignoring supply rail limits. A 5 V single-supply circuit cannot deliver a 6 V output regardless of what the gain calculation shows.

Frequently Asked Questions

What is the formula for op-amp gain?
For an inverting amplifier, Av = −Rf / Rin. For a non-inverting amplifier, Av = 1 + Rf / Rg. A voltage follower has Av = 1. A difference amplifier with matched pairs gives Av_diff = Rf / R1. A summing amplifier produces per-channel gain Av_n = −Rf / Rn for each input channel.
How do I convert gain to decibels?
Voltage gain in decibels uses Gv_dB = 20 × log₁₀(|Av|). A gain of 10 equals 20 dB, 100 equals 40 dB, 1000 equals 60 dB. Gain below 1 (attenuation) gives a negative dB value: a gain of 0.1 equals −20 dB. The 20× factor applies to voltage and current ratios; power ratios use 10×.
What is the difference between signal gain and noise gain?
Signal gain describes how the wanted input is amplified at the output. Noise gain describes how input-referred noise and op-amp imperfections propagate to the output, and it sets bandwidth and stability. For inverting topology they differ: signal gain is −Rf/Rin, noise gain is 1 + Rf/Rin. For non-inverting topology they are equal.
How does gain-bandwidth product affect closed-loop bandwidth?
For voltage-feedback op-amps with dominant-pole compensation, closed-loop bandwidth is approximately GBW divided by the noise gain. A 10 MHz GBW op-amp configured for a noise gain of 100 has roughly 100 kHz of closed-loop bandwidth. Doubling the gain halves the bandwidth.
How does the calculator handle summing amplifiers?
For summing topology, the calculator reports the per-channel gain Av_n = −Rf / Rn for each input resistor entered. The status badge is based on the highest channel-gain magnitude. The actual output voltage depends on the inverted sum of all active input signals weighted by their per-channel gains.
Can a non-inverting amplifier produce attenuation?
No. Attenuation is not available in the standard non-inverting topology, where the minimum gain is 1. If you need gain below 1, use an inverting stage, a differential stage with Rf smaller than R1, or a passive divider when high input impedance is not required.
Why is unity-gain stability important for voltage followers?
A voltage follower has noise gain of 1, which is the lowest possible. Op-amps that are not unity-gain compensated may oscillate or peak in this configuration. Datasheets specify whether a part is unity-gain stable; partially compensated op-amps require a minimum noise gain to remain stable.
What resistor values should I use in op-amp circuits?
Most general-purpose stages use values from 1 kΩ to 100 kΩ. Below 1 kΩ the op-amp output current rises and dissipation increases. Above 100 kΩ to 1 MΩ, input bias current starts to matter. Above 10 MΩ, board contamination and humidity can dominate. Use IEC 60063 E-series values — E96 for 1% precision designs, E24 for 5% general use.
How do resistor tolerances affect gain accuracy?
For simple ratio topologies (inverting, non-inverting), worst-case gain error is roughly 2 × the resistor tolerance. With 1% resistors, expect gain accuracy around 2%. For precision applications, use thin-film matched-pair resistor networks rather than discrete components, especially in difference amplifiers where matching directly affects CMRR.

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