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Op-Amp Gain Logic Engine

Calculate the voltage gain and final output voltage for both inverting and non-inverting operational amplifier circuits using the Rf/Rin resistor ratio formula.

Op-Amp Gain Calculator

Calculate the voltage gain and final output voltage for both inverting and non-inverting operational amplifier circuits.

Non-Inverting Op-Amp (Gain = 1 + Rf/Rin)
Vin ──────────── (+) ┐
│ ─────── Vout
┌──── Rf ───┘ (-) ┘
│
Rin
│
GND
01 — Circuit Parameters

= 10,000 Ω

= 1,000 Ω

Gain = 1 + (Rf / Rin) = 1 + (10,000 / 1,000) = 11.0000
Voltage Gain
11.00
non-inverting · |G| = 11.00
Output Voltage — Vout
5.500 V
⟶ In-phase
02 — Full Analysis
Rf / Rin
10.0000
Gain
11.000
Vin
0.5 V
Vout
5.500 V
ConfigurationNon-Inverting (+)
Feedback Resistor (Rf)10,000 Ω
Input Resistor (Rin)1,000 Ω
Rf / Rin10.000000
Gain = 1 + Rf/Rin11.0000
Vin0.5 V
Vout = Gain × Vin11.0000 × 0.5 = 5.500 V
Phase0° (in-phase)
Summary: Using a Non-Inverting configuration with Rf=10kΩ and Rin=1kΩ, your op-amp provides a gain of 11.00, boosting your 0.5V input signal to 5.500V.
Practical Example

Non-Inverting audio preamp: Rf = 10kΩ, Rin = 1kΩ. Gain = 1 + 10,000/1,000 = 11. A 0.5V mic signal → Vout = 11 × 0.5 = 5.5V (in-phase, boosted).
Inverting signal conditioner: Rf = 47kΩ, Rin = 10kΩ. Gain = −(47,000/10,000) = −4.7. A 1V input → Vout = −4.7V (phase inverted — used commonly in signal subtraction circuits).
Rule: For a non-inverting buffer (unity gain), set Rf = 0 (short) and Rin = ∞ (open) → Gain = 1. This is the classic voltage follower used for impedance isolation.

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What is Operational Amplifiers: Inverting vs Non-Inverting Gain and Virtual Ground?

Calculate op-amp voltage gain and understand the virtual ground concept, input/output phase relationships, and how to select Rf and Rin to achieve any target gain in inverting or non-inverting configurations.

Mathematical Foundation

Non-Inverting Gain
GNI=1+RfRinG_{NI} = 1 + \frac{R_f}{R_{in}}
1+1 += The '+1' means the minimum gain in non-inverting mode is 1 (unity). Setting Rf=0 and Rin=∞ makes G=1 — this is the voltage follower/buffer topology.
Rf/RinR_f / R_{in}= The feedback network. The op-amp adjusts its output until V− = V+. Since V+ = Vin, V− is driven to Vin through the Rf/Rin voltage divider, producing a gain greater than 1.
Inverting Gain
GINV=−RfRinG_{INV} = -\frac{R_f}{R_{in}}
−−= The output is 180° out of phase with the input. A positive Vin produces a negative Vout.
VirtualGroundVirtual Ground= In inverting mode, V− is held at 0V by negative feedback (virtual ground). This means Vin/Rin current flows through Rf, producing Vout = −Vin × Rf/Rin.

Laws & Principles

  • The 'ideal' op-amp assumptions used in these calculations: infinite open-loop gain, infinite input impedance, zero output impedance, and infinite bandwidth. Real op-amps (LM741, TL072, OPA2134) deviate from these, especially at high frequencies.
  • Gain-Bandwidth Product (GBW): for a given op-amp, gain × bandwidth = constant. An LM741 (GBW = 1 MHz) at G=10 has only 100 kHz of usable bandwidth. At G=100, only 10 kHz. Choose op-amps with GBW >> gain × signal frequency.
  • Supply rails limit Vout: the output cannot exceed ±(Vsupply − 1.5V) for standard op-amps, or almost ±Vsupply for rail-to-rail types. If the calculated Vout exceeds the supply, the output saturates at the rail.
  • The inverting amplifier has a fixed, low input impedance of Rin (typically kΩ). This can load the source. The non-inverting amplifier has essentially infinite input impedance, making it ideal for high-impedance source buffering.
  • Summing amplifier: the inverting topology extends to a summing amplifier by adding N input resistors all to V−. Vout = −Rf × (V1/R1 + V2/R2 + … Vn/Rn). This is the foundation of analog mixing consoles.

Step-by-Step Example Walkthrough

" Designing a microphone preamplifier: mic output = 5mV peak, need output = 500mV peak for ADC input. "

  1. Target gain: 500mV / 5mV = 100.
  2. Choose non-inverting (no phase inversion needed for audio).
  3. Formula: G = 1 + Rf/Rin = 100 → Rf/Rin = 99.
  4. Choose Rin = 1kΩ, Rf = 100kΩ (standard E24 values, ratio = 100, giving G = 101 — close enough).
  5. Verify GBW: using NE5532 (GBW = 10 MHz), max audio bandwidth = 10 MHz / 101 ≈ 99 kHz. Well above 20 kHz audio range. ✓
  6. Check supply: Vout_peak = 500mV. With ±5V supply, output has ±3.5V headroom. No saturation. ✓
Final Result: NE5532, Rf=100kΩ, Rin=1kΩ. Gain = 101. 5mV mic signal → ~505mV output. This is a textbook low-noise audio preamp design used in professional recording equipment.

Quick Answer: How does the Op-Amp Gain Calculator work?

Select your op-amp topology (inverting or non-inverting), enter the feedback resistor Rf and input resistor Rin, and optionally provide an input voltage. The calculator applies the Rf/Rin ratio formulas to determine voltage gain and output voltage for your circuit configuration.

Mathematical Formulas

Non-Inv: G = 1 + Rf/Rin | Inv: G = -Rf/Rin

Where Rf is the feedback resistor, Rin is the input resistor, and the negative sign in inverting mode indicates 180° phase inversion.

Common Op-Amp ICs (Reference)

Popular operational amplifier ICs and their key specifications for gain calculations.

Op-Amp IC GBW Product Slew Rate Typical Use
LM7411 MHz0.5 V/µsEducational / DC
TL0723 MHz13 V/µsAudio / General
NE553210 MHz9 V/µsPro Audio
OPA21348 MHz20 V/µsHi-Fi / Precision

Circuit Design Use Cases

Sensor Signal Conditioning

Sensors like thermocouples and strain gauges output millivolt-level signals. A non-inverting op-amp stage amplifies these tiny signals to the 0-5V range required by ADC inputs, with the high input impedance preventing sensor loading.

Audio Mixing Console

Inverting summing amplifiers combine multiple audio inputs into a single output. Each input channel feeds through its own input resistor to the virtual ground at V-, with Rf controlling the overall mix gain. This is how analog mixing desks blend microphone channels.

Op-Amp Design Best Practices (Pro Tips)

Do This

  • ✓Always verify GBW headroom. Your op-amp's Gain-Bandwidth Product must exceed your gain multiplied by your maximum signal frequency. An amplifier running near its GBW limit shows gain rolloff and phase distortion.

Avoid This

  • ✗Don't forget rail saturation. If your calculated Vout exceeds the supply voltage minus the op-amp's output voltage swing limit (typically 1-2V from each rail), the output clips flat and gain formulas no longer apply.

Frequently Asked Questions

What is a virtual ground in an inverting op-amp?

In an inverting configuration, the non-inverting input (V+) is connected to ground. Negative feedback forces the inverting input (V-) to match V+, holding it at 0V even though it is not physically connected to ground. This virtual ground allows current to flow from Vin through Rin and then through Rf to the output.

Why does non-inverting gain always start at 1?

The formula G = 1 + Rf/Rin means that even with Rf = 0 (a direct wire from output to inverting input), the gain is still 1. This is the voltage follower or buffer topology — it passes the input signal through with unity gain and very high input impedance, useful for impedance matching.

How do I choose between inverting and non-inverting?

Use non-inverting when you need high input impedance (won't load the source), gain of 1 or greater, and no phase inversion. Use inverting when you need gain less than 1 (attenuator), need to sum multiple inputs, or the 180° phase flip doesn't matter for your application.

What is gain-bandwidth product and why does it matter?

GBW is a constant for each op-amp: gain multiplied by bandwidth always equals the same number. An op-amp with 10 MHz GBW delivers full gain of 100 only up to 100 kHz. Above that frequency, the gain rolls off at 20 dB/decade. For high-frequency applications, you need an op-amp with a proportionally higher GBW.

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