Op-Amp Gain Calculator

Inverting Configuration

Typical range: 1kΩ to 100kΩ for stability
Maintain Rf/Rin ratio for desired gain
V
Ensure |Vin × Gain| < Supply voltage

Results

Gain (Av):

-10

Output Voltage (Vout):

-10 V

Formula:

Av = -Rf/Rin

Vout = Av × Vin

The negative sign indicates 180° phase inversion. Gain magnitude is determined solely by resistor ratio under ideal op-amp assumptions.

Circuit Diagram

Circuit Analysis: The inverting configuration applies negative feedback through Rf. The virtual ground at the inverting input (maintained by high open-loop gain) forces the input current Iin = Vin/Rin to flow through Rf, establishing Vout = -Iin × Rf.

Non-Inverting Configuration

Ground-referenced resistor sets gain with Rf
Feedback establishes closed-loop gain
V
Applied directly to non-inverting (+) input

Results

Gain (Av):

11

Output Voltage (Vout):

11 V

Formula:

Av = 1 + (Rf/R1)

Vout = Av × Vin

Minimum gain is 1 (voltage follower when Rf=0). The non-inverting input exhibits high input impedance (typically >1MΩ for BJT op-amps, >1012Ω for FET-input types).

Circuit Diagram

Circuit Analysis: Negative feedback forces the voltage at the inverting input to equal Vin (virtual short concept). The voltage divider formed by R1 and Rf sets Vout = Vin × (1 + Rf/R1).

Voltage Calculator

V
V
This calculator solves the fundamental gain equation Vout = Av × Vin for any variable. Remember that actual op-amp outputs saturate near supply rails (±(VCC-1.5V) typical for 741-type).

Results

Gain (Av):

10

Input Voltage (Vin):

1 V

Output Voltage (Vout):

10 V

Formula:

Vout = Av × Vin

Av = Vout / Vin

Vin = Vout / Av

Gain (Av) is dimensionless but often expressed in V/V or dB (20log10|Av|). Negative gain indicates phase inversion.

Bandwidth Estimation

Hz
Typically 1MHz for common op-amps like 741. Check datasheet for specific device.
DC or low-frequency voltage gain magnitude (absolute value)
GBP Definition: For a voltage-feedback op-amp, the product of closed-loop gain and -3dB bandwidth is approximately constant. This relationship holds for frequencies above the dominant pole.

Results

Bandwidth:

100 kHz

Gain-Bandwidth Product:

1 MHz

Formula:

Bandwidth = GBP / |Av|

Where GBP is the Gain-Bandwidth Product

Example: LM741 with GBP = 1 MHz: At Av = 100, bandwidth ≈ 10 kHz. At Av = 1 (unity gain), bandwidth ≈ 1 MHz.

Information

The gain-bandwidth product (GBP) is a key parameter of voltage-feedback operational amplifiers that remains approximately constant for frequencies above the dominant pole. As you increase the closed-loop gain, the bandwidth decreases proportionally.

Common GBP values (typical):

  • LM741: 1 MHz (classic general-purpose)
  • TL081: 3 MHz (JFET-input, higher speed)
  • OP27: 8 MHz (low-noise precision)
  • LM318: 15 MHz (high-speed)
  • OPA627: 16 MHz (precision FET-input)
  • ADA4817: 400 MHz (ultra-high speed)
Note: Current-feedback op-amps (CFA) do not follow the constant GBP relationship. Their bandwidth is primarily set by feedback resistor value, not gain.

Reverse Calculation

For inverting: negative value produces positive Rf. Magnitude used in calculation.
This will be Rin for inverting or R1 for non-inverting
Practical values: 1kΩ to 100kΩ. Avoid values below 1kΩ (excessive current) or above 1MΩ (noise, bias current errors).

Results

Input Resistor (Rin):

1 kΩ

Feedback Resistor (Rf):

10 kΩ

Actual Gain:

10

Formulas:

For inverting: Rf = |Av| × Rin

For non-inverting: Rf = (Av - 1) × R1

Design Tip: For best DC accuracy, choose resistors so that parallel combination Rin||Rf (inverting) or R1||Rf (non-inverting) equals the source impedance seen by non-inverting input. This minimizes offset voltage due to input bias currents.

Op-Amp Gain Guide

Inverting Amplifier

An inverting amplifier produces an output that is the inverted and amplified version of the input signal. The gain is determined by the ratio of the feedback resistor (Rf) to the input resistor (Rin).

Key characteristics:

  • Gain: Av = -Rf/Rin
  • Input impedance is approximately Rin
  • Output is inverted (180° phase shift)
  • Virtual ground at inverting input simplifies analysis
Non-Inverting Amplifier

A non-inverting amplifier produces an output that is in phase with the input signal. The gain is always greater than or equal to 1.

Key characteristics:

  • Gain: Av = 1 + (Rf/R1)
  • High input impedance (theoretically infinite, practically >1MΩ)
  • Output is in phase with input
  • Minimum gain = 1 (voltage follower configuration)
Practical Considerations

Resistor Selection: Choose resistor values in the range of 1kΩ to 100kΩ for best results. Very low values may overload the op-amp output stage, while very high values increase Johnson noise and sensitivity to parasitic capacitance.

Bandwidth: All op-amps have a finite bandwidth. The gain-bandwidth product (GBP) determines how much gain you can achieve at a given frequency. For AC applications, consider both DC gain and bandwidth requirements.

Power Supply: Ensure your power supply voltages are sufficient for the desired output swing. Most op-amps can't output voltages equal to their supply rails (typical output swing is within 1-2V of rails).

Important Safety & Practical Notes
  • This calculator assumes ideal op-amp behavior (infinite gain, infinite input impedance, zero output impedance)
  • Real op-amps have limitations: finite gain, input offset voltage, bias currents, slew rate, and output current limits
  • Always consult device datasheet for absolute maximum ratings and thermal considerations
  • For high-precision applications, consider offset voltage, bias current, and temperature effects
  • Include decoupling capacitors near power pins in actual circuits
  • This tool is for educational and design assistance only - verify calculations with actual measurements
Example Calculations
Inverting Example

Given:

  • Rin = 1kΩ
  • Rf = 10kΩ
  • Vin = 0.5V

Gain = -10kΩ/1kΩ = -10

Vout = -10 × 0.5V = -5V

Input impedance = 1kΩ. For ±15V supplies, output is within linear range.
Non-Inverting Example

Given:

  • R1 = 1kΩ
  • Rf = 9kΩ
  • Vin = 0.5V

Gain = 1 + (9kΩ/1kΩ) = 10

Vout = 10 × 0.5V = 5V

Input impedance ≈ op-amp input impedance (>1MΩ). Bandwidth = GBP/10.

Technical Reference & Engineering Context

Operational Amplifier Fundamentals

Operational amplifiers are differential-input, high-gain voltage amplifiers with external feedback components determining their function. The calculations in this tool are based on the ideal op-amp model:

Infinite open-loop gain (AOL → ∞)
Forces differential input voltage (V+ - V-) → 0 via negative feedback
Infinite input impedance (Zin → ∞)
No current flows into input terminals (I+ = I- = 0)
Zero output impedance (Zout → 0)
Output voltage unaffected by load within current limits
Infinite bandwidth
No frequency limitations (addressed separately via GBP calculation)
Zero offset voltage (VOS = 0)
Output is zero when inputs are equal
Practical Applications

Inverting Configuration Uses:

  • Audio preamplifiers with controlled gain
  • Current-to-voltage converters (transimpedance amplifiers). For more on current division principles, you might find the current divider calculator helpful.
  • Summing amplifiers (audio mixers, DACs)
  • Integrators and differentiators (with capacitors)
  • Low-impedance microphone/instrument inputs

Non-Inverting Configuration Uses:

  • Voltage followers/buffers (impedance matching)
  • High-input-impedance measurement circuits
  • Signal conditioning for sensors
  • Distribution amplifiers (one input to multiple outputs)
  • Active filters with gain. You can explore related frequency response with our filter calculator tool.
Unit Conventions & Standards

SI Units Used:

  • Resistance: Ω (ohm), kΩ (10³ Ω), MΩ (10⁶ Ω)
  • Voltage: V (volt), mV (10⁻³ V)
  • Frequency: Hz (hertz), kHz (10³ Hz), MHz (10⁶ Hz)
  • Gain: Dimensionless (V/V) or dB: 20·log₁₀(|Av|). For conversions, the dB converter can be a useful companion tool.

Symbol Standards (IEC 60617):

Triangle symbol for op-amp, resistors shown as rectangles, ground symbol as IEC 5017.

Common Design Mistakes & Solutions

Avoid These Common Errors:

  1. Missing power supply decoupling: Always use 0.1µF ceramic capacitors close to supply pins
  2. Ignoring input bias currents: For DC accuracy, add compensation resistor equal to Rin||Rf (inverting) or R1||Rf (non-inverting) in series with non-inverting input
  3. Exceeding output swing capabilities: Ensure Vout < (VCC+ - Vsat) and Vout > (VCC- + Vsat)
  4. Unbalanced impedances: Causes offset voltage errors; balance resistances seen by both inputs
  5. Ignoring bandwidth requirements: Check GBP at required frequency: fmax = GBP / |Av|
  6. Forgetting slew rate limitations: SR limits maximum dV/dt: fmax = SR / (2π × Vp)
Accuracy Notes & Limitations

This Calculator's Assumptions:

  • Ideal op-amp model applies (see above)
  • Linear operation (output not saturated)
  • Negative feedback is properly applied and stable
  • Resistors are perfect (no tolerance, no temperature coefficient)
  • No parasitic capacitances or inductances
  • DC analysis (bandwidth calculated separately)

Rounding Behavior:

Gain and voltage calculations show 2 decimal places. Resistance formatting: values <1000 show as Ω, 1000-999999 as kΩ, ≥1,000,000 as MΩ.

Applicable Range:

Valid for typical op-amp circuits with gains from 0.001 to 10,000, resistor values 100Ω to 10MΩ, and frequencies where GBP model applies.

Frequently Asked Questions (FAQ)

Real op-amps have finite open-loop gain (typically 100,000 to 1,000,000 V/V). The actual closed-loop gain is Av(actual) = Av(ideal) / (1 + Av(ideal)/AOL). For gains < 100, error is usually <1%. Also check resistor tolerances (1% typical).

Yes, for frequencies well below the op-amp's bandwidth limit. The gain formulas apply to both DC and AC. However, at higher frequencies, consider: 1) Bandwidth limitations (use GBP tab), 2) Slew rate limitations, 3) Phase shift/stability, 4) Capacitive loading effects.

Recommended ranges:
  • General purpose: 1kΩ to 100kΩ
  • Low noise: 10kΩ to 100kΩ (lower values reduce Johnson noise)
  • High speed: 100Ω to 1kΩ (lower values reduce RC time constants)
  • Low power: 100kΩ to 1MΩ (higher values reduce current)
  • Avoid: <100Ω (excessive current), >10MΩ (noise, bias current errors)
Use standard E24 or E96 resistor values where possible.

Temperature affects:
  1. Resistor values: Typical tempco ±100 ppm/°C for metal film
  2. Op-amp parameters: Offset voltage (3-10 µV/°C), bias current, GBP
  3. Output swing: May decrease at temperature extremes
For precision applications, use low-tempco resistors (<25 ppm/°C) and low-drift op-amps (OPA277, LT1012).

Choose inverting when:
  • You need phase inversion
  • Low input impedance is acceptable/desired
  • Building summing amplifiers
  • Implementing integrators/differentiators
Choose non-inverting when:
  • High input impedance is required
  • Phase must be preserved
  • Gain ≥ 1 is needed
  • Buffering high-impedance sources
Related Calculations & Next Steps

After determining basic gain parameters:

  1. Slew Rate Check: Ensure SR > 2πfmaxVp for full output swing
  2. Noise Analysis: Calculate total output noise considering resistor Johnson noise and op-amp voltage/current noise
  3. Power Dissipation: Pdiss = (VCC+ - VCC-) × IQ + (Vout × Iload)
  4. Stability Analysis: Check phase margin, consider compensation if needed
  5. PCB Layout: Minimize parasitic capacitances, use ground planes, keep feedback paths short

Trust & Transparency Note: This tool performs all calculations locally in your browser using JavaScript. No data is transmitted to servers. Formulas are based on standard electrical engineering textbooks and IEEE standards. Calculations assume ideal conditions; real-world implementations require consideration of device-specific parameters from datasheets.

Last Engineering Review: September 2025 - Formulas verified against "Op-Amps for Everyone" (Texas Instruments) and "The Art of Electronics" (Horowitz & Hill).