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Op-Amp Gain Calculator

Closed-loop gain for non-inverting (1+Rf/Rg) and inverting (−Rf/Rg) op-amp circuits. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 3/3 declared partitions (noninverting, inverting, invalid-domain) · Matrix
Known limitations
  • Ideal infinite open-loop gain; no bandwidth limits
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Closed-loop op-amp gain from Rf and Rg.
Scope
Ideal op-amp; resistors only
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
1/1 property · digest ea412a169d5d
Legacy regression
6/6 tests · Production surface contract 4/4
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
2/2 golden · 2/2 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • Sedra/Smith — Microelectronic Circuits — Ideal closed-loop gain
  • Horowitz & Hill — The Art of Electronics — Op-amp circuits
Sources
Evidence
3 legacy golden · 2 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Non-invertingG = 1 + Rf/Rg
InvertingG = −Rf/Rg
iIdeal op-amp; DC/low-frequency. Not for open-loop Aol or GBW-limited AC gain.

How to use

1

Choose non-inverting or inverting

Non-inverting: G = 1 + Rf/Rg. Inverting: G = −Rf/Rg.

2

Enter Rf and Rg

Both resistances must be greater than zero.

3

Read closed-loop gain

Result is the ideal DC gain (no bandwidth or finite Aol effects).

Example calculations

Common configurations with formula and result.

ϟ

Non-inv 10k/1k

Rf=10k · Rg=1k

1+10
G=11 (20.83 dB)

Op-Amp Gain calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-08

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
Closed-loop voltage gain is set by feedback resistors. Non-inverting: G = 1 + Rf/Rg. Inverting: G = −Rf/Rg.
What it calculates
Closed-loop op-amp gain from Rf and Rg.
Inputs
  • mode noninverting|inverting
  • Rf_ohm>0
  • Rg_ohm>0
Outputs
  • G
  • G_abs
  • G_dB
Formula
G_noninv=1+Rf/Rg; G_inv=−Rf/Rg
Assumptions
  • Ideal op-amp; resistors only
Units
  • Ω → V/V, dB
Boundary conditions
  • Rf or Rg ≤0 → VALUE_MUST_BE_POSITIVE
  • Bad mode → INVALID_MODE
Example
Rf=10k, Rg=1k noninv → G=11
Validation cases

2 published on this page · 6/6 tests · Production surface contract 4/4 · View evidence

  • noninv Rf=10000 Rg=1000 → G=11
  • inv Rf=10000 Rg=1000 → G=-10
Sources
  • Sedra/Smith — Microelectronic Circuits — Ideal closed-loop gain
    Supports: Non-inverting and inverting gain formulas
  • Horowitz & Hill — The Art of Electronics — Op-amp circuits
    Supports: Ideal non-inverting / inverting closed-loop gain
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute closed-loop op-amp gain.

Default: non-inverting Rf=10 kΩ · Rg=1 kΩ → G = 11.

Supported and not supported

Supported — Ideal DC closed-loop gain · API electrical.opamp_gain

Not supported — Open-loop Aol, GBW roll-off, complex feedback

Agent / API notes

Capability id: electrical.opamp_gain · tool id: opamp-gain · pin 1.0.0.

Errors: MISSING_REQUIRED_INPUT, VALUE_MUST_BE_POSITIVE, INVALID_MODE.

Other calculators in this family: ADC Error Budget Calculator, ADC SNR / Quantization Calculator, Op-amp Error Budget Calculator, Op-amp Noise Calculator . Explore all Analog & Data Conversion.

→ ADC Error Budget Calculator Combine ADC gain, offset, INL, and DNL errors (RSS or worst-case) into total LSB, volts, and %FS. Runs locally in your browser. › → ADC SNR / Quantization Calculator Ideal quantization SNR ≈ 6.02·N + 1.76 dB for a full-scale sine; reverse measured SINAD to ENOB. Runs locally in your browser. › → Op-amp Error Budget Calculator Estimate DC output-referred error from Vos, Ib, Ios and feedback resistors (RSS or worst-case). › → Op-amp Noise Calculator Estimate flat-band output noise from en, optional in, gain, and bandwidth. Runs locally in your browser. ›
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Frequently asked questions

Key distinctions behind the calculation.

Why is inverting gain negative?

The signal is applied to the inverting input; the magnitude is Rf/Rg.