{ "id": "op-amp-gain", "slug": "op-amp-gain-calculator", "url": "https://electronics.tools/tools/op-amp-gain-calculator/", "name": "Op-Amp Voltage and Gain Calculator", "group": "amp-timing", "summary": "Vout = V2·R4/(R3+R4)·(1+R2/R1) − V1·R2/R1. Equal 10 kΩ, 1 V and 1.5 V is 0.5 V.", "formulas": [ { "id": "vout", "label": "Ideal closed-loop Vout", "plain": "Vout = V2 · R4/(R3+R4) · (1 + R2/R1) − V1 · R2/R1", "mathml": "

V_{out} = V_{2} \cdot \frac{R_{4}}{R_{3} + R_{4}} \cdot (1 + \frac{R_{2}}{R_{1}}) - V_{1} \cdot \frac{R_{2}}{R_{1}}

", "symbols": [ "Vout", "V2", "R4", "R3", "R2", "R1", "V1" ], "sources": [ "sedra" ] }, { "id": "clip", "label": "Rail clip", "plain": "Clip to [V−, V+]", "mathml": "

V_{clip} = min (V_{+}, max (V_{-}, V_{out}))

", "symbols": [ "Vp", "Vn", "Vout" ], "sources": [ "sedra" ] }, { "id": "sat", "label": "Saturation", "plain": "Saturated when ideal is beyond the rails", "mathml": "

sat = (V_{out} < V_{-}) \lor (V_{out} > V_{+})

", "symbols": [ "Vout", "Vn", "Vp" ], "sources": [ "sedra" ] } ], "variables": [ { "symbol": "preset", "name": "Preset", "unit": "1", "role": "input", "precision": { "sig": 1 }, "default": "differential", "urlParam": "preset" }, { "symbol": "V1", "name": "Inverting input", "unit": "V", "role": "input", "precision": { "sig": 4 }, "default": 1, "urlParam": "v1" }, { "symbol": "V2", "name": "Non-inverting input", "unit": "V", "role": "input", "precision": { "sig": 4 }, "default": 1.5, "urlParam": "v2" }, { "symbol": "R1", "name": "Inverting gain resistor", "unit": "Ω", "role": "input", "precision": { "sig": 4 }, "range": { "min": 0, "note": "R1 must be > 0" }, "default": 10000, "urlParam": "r1" }, { "symbol": "R2", "name": "Feedback", "unit": "Ω", "role": "input", "precision": { "sig": 4 }, "range": { "min": 0 }, "default": 10000, "urlParam": "r2" }, { "symbol": "R3", "name": "+input series", "unit": "Ω", "role": "input", "precision": { "sig": 4 }, "range": { "min": 0 }, "default": 10000, "urlParam": "r3" }, { "symbol": "R4", "name": "+input to ground", "unit": "Ω", "role": "input", "precision": { "sig": 4 }, "range": { "min": 0 }, "default": 10000, "urlParam": "r4" }, { "symbol": "Vp", "name": "Positive rail", "unit": "V", "role": "input", "precision": { "sig": 4 }, "default": 15, "urlParam": "vp" }, { "symbol": "Vn", "name": "Negative rail", "unit": "V", "role": "input", "precision": { "sig": 4 }, "default": -15, "urlParam": "vn" }, { "symbol": "Vout", "name": "Ideal output", "unit": "V", "role": "output", "precision": { "sig": 4 } }, { "symbol": "Vclip", "name": "Clipped output", "unit": "V", "role": "output", "precision": { "sig": 4 } }, { "symbol": "sat", "name": "Saturated", "unit": "1", "role": "output", "precision": { "sig": 1 } }, { "symbol": "G", "name": "R2/R1", "unit": "1", "role": "output", "precision": { "sig": 4 } }, { "symbol": "div", "name": "Non-inverting divider", "unit": "1", "role": "output", "precision": { "sig": 4 } } ], "examples": [ { "id": "diff-10k", "title": "Differential 10 kΩ × 4", "input": [ { "symbol": "preset", "value": "differential", "unit": "1", "display": "differential" }, { "symbol": "V1", "value": 1, "unit": "V", "display": "1 V" }, { "symbol": "V2", "value": 1.5, "unit": "V", "display": "1.5 V" }, { "symbol": "R1", "value": 10000, "unit": "Ω", "display": "10 kΩ" }, { "symbol": "R2", "value": 10000, "unit": "Ω", "display": "10 kΩ" }, { "symbol": "R3", "value": 10000, "unit": "Ω", "display": "10 kΩ" }, { "symbol": "R4", "value": 10000, "unit": "Ω", "display": "10 kΩ" }, { "symbol": "Vp", "value": 15, "unit": "V", "display": "15 V" }, { "symbol": "Vn", "value": -15, "unit": "V", "display": "-15 V" } ], "output": [ { "symbol": "Vout", "value": 0.5, "unit": "V", "display": "0.5 V" }, { "symbol": "Vclip", "value": 0.5, "unit": "V", "display": "0.5 V" }, { "symbol": "sat", "value": "no", "unit": "1", "display": "no" }, { "symbol": "G", "value": 1, "unit": "1", "display": "1" } ], "computedBy": "opAmpGain" }, { "id": "inv-clip", "title": "Inverting 1 kΩ / 47 kΩ clips", "input": [ { "symbol": "preset", "value": "inverting", "unit": "1", "display": "inverting" }, { "symbol": "V1", "value": 0.5, "unit": "V", "display": "0.5 V" }, { "symbol": "V2", "value": 0, "unit": "V", "display": "0 V" }, { "symbol": "R1", "value": 1000, "unit": "Ω", "display": "1 kΩ" }, { "symbol": "R2", "value": 47000, "unit": "Ω", "display": "47 kΩ" }, { "symbol": "R3", "value": 1000, "unit": "Ω", "display": "1 kΩ" }, { "symbol": "R4", "value": 1000000000, "unit": "Ω", "display": "1000 MΩ" }, { "symbol": "Vp", "value": 15, "unit": "V", "display": "15 V" }, { "symbol": "Vn", "value": -15, "unit": "V", "display": "-15 V" } ], "output": [ { "symbol": "Vout", "value": -23.5, "unit": "V", "display": "-23.5 V" }, { "symbol": "Vclip", "value": -15, "unit": "V", "display": "-15 V" } ], "computedBy": "opAmpGain" } ], "sources": [ { "title": "Sedra/Smith, Microelectronic Circuits — ideal op-amp superposition", "url": "https://global.oup.com/academic/product/microelectronic-circuits-9780190853464", "retrieved": "2026-11-02" } ], "datePublished": "2026-11-02T00:00:00+08:00", "dateModified": "2026-11-02T00:00:00+08:00", "author": { "name": "Jasper", "url": "https://electronics.tools/about/#jasper" }, "relatedTools": [ "https://electronics.tools/tools/inverting-op-amp-calculator/", "https://electronics.tools/tools/555-timer-calculator/", "https://electronics.tools/tools/voltage-divider-calculator/" ] }