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Op-Amp Gain Calculator

Calculate inverting and non-inverting op-amp voltage gain from feedback and input resistors, with gain in decibels and an optional output voltage

Frequently Asked Questions

What is the difference between inverting and non-inverting gain?

Non-inverting gain is one plus Rf over Rin and keeps the signal in phase, never below unity. Inverting gain is the negative ratio of Rf to Rin, flips the signal, and can be below unity.

Why does my real circuit not reach the calculated gain?

Actual gain is limited by the op-amp open-loop gain, gain-bandwidth product, and supply rails. At high frequencies the bandwidth caps achievable gain, and output cannot exceed the supply voltages.

How do I convert the gain to decibels?

Voltage gain in decibels is 20 times the base-10 logarithm of the gain magnitude: dB = 20 x log10(|gain|). A gain of 10 is 20 dB, a gain of 100 is 40 dB, and a gain of 2 is about 6 dB. The decibel value uses the absolute value of the gain, so an inverting amplifier with a gain of -10 has the same 20 dB magnitude as a non-inverting amplifier with a gain of +10; the minus sign only indicates the 180 degree phase inversion. This calculator reports both the linear gain (in volts per volt) and the gain in decibels.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

An operational amplifier sets its closed-loop voltage gain through two resistors: the feedback resistor Rf and the input resistor Rin. In the non-inverting configuration the gain is one plus the ratio of Rf to Rin, so the output is always at least unity and in phase with the input. In the inverting configuration the gain is the negative ratio of Rf to Rin, flipping the signal and allowing gains below one.

This tool computes the voltage gain, converts it to decibels, and, if you provide an input voltage, gives the resulting output voltage.

Worked Example

Take a non-inverting amplifier with a feedback resistor Rf = 100 kΩ and an input resistor Rin = 10 kΩ, driven by an input of 0.5 V. The non-inverting gain is:

Gain = 1 + Rf ÷ Rin = 1 + 100 ÷ 10 = 1 + 10 = 11 V/V.

In decibels that is 20 × log₁₀(11) ≈ 20.8 dB. With a 0.5 V input the output is 11 × 0.5 = 5.5 V.

Wired instead as an inverting amplifier with the same resistors, the gain would be −Rf ÷ Rin = −100 ÷ 10 = −10 V/V, and the 0.5 V input would give −5 V at the output (same 20 dB magnitude, opposite phase).

How To Use It

Choose the configuration, enter the feedback and input resistor values in kilohms, and optionally enter an input voltage. The result shows gain in volts per volt, gain in decibels, and output voltage when an input is given.

Inverting Versus Non-Inverting

Non-inverting amplifiers have very high input impedance and never attenuate, making them ideal as buffers and sensor front ends. Inverting amplifiers are handy when you need to subtract, mix, or scale signals below unity and a 180 degree phase shift is acceptable.

Real-World Limits

Actual gain is bounded by the op-amp's open-loop gain, bandwidth, and supply rails. At high frequencies the gain-bandwidth product caps how much gain you can realize, and the output cannot swing beyond the supply voltages.

Tips

Keep resistor values moderate to balance noise and bias-current error.
Watch the gain-bandwidth product when designing for high frequency.
Verify the output stays within the supply rails at maximum input.

Inverting vs. Non-Inverting Configurations

In the inverting configuration, the input signal drives the inverting terminal through Rin, and Rf connects from the output back to the inverting terminal. The non-inverting terminal is tied to ground (or a reference). The closed-loop gain is -Rf/Rin, negative because the output is 180° out of phase with the input. The input impedance equals Rin, which can be a limitation when Rin must be low to achieve high gain while keeping Rf at a reasonable value. One major advantage is that the inverting input is held at a virtual ground - the op-amp actively drives the inverting input to match the non-inverting input, which in this case is at zero volts. Virtual ground makes it straightforward to build summing amplifiers: multiple input resistors can connect to the same inverting node and their currents add algebraically.

In the non-inverting configuration, the signal drives the non-inverting terminal directly, and the feedback network (Rf + R1 from output to ground) sets the gain as 1 + Rf/R1. Because the signal drives the non-inverting input directly, the input impedance is the extremely high open-loop input impedance of the op-amp - typically hundreds of megaohms for a JFET or CMOS input op-amp. This makes non-inverting stages ideal for reading from high-impedance sensors. The minimum gain is unity (with Rf = 0, R1 = open), so the non-inverting configuration cannot attenuate.

A difference amplifier uses matched resistors on both inputs to amplify the difference between two signals and reject the common-mode voltage. Good common-mode rejection ratio (CMRR) requires careful resistor matching; 0.1% tolerance metal-film resistors are typical for demanding applications. An instrumentation amplifier (INA) uses three op-amps and a single gain-setting resistor to achieve very high CMRR without the matching requirement, making it the standard front end for bridge sensors, thermocouples, and ECG inputs.

Unity-Gain Buffer (Voltage Follower)

The voltage follower is the simplest op-amp circuit: the output is connected directly back to the inverting input, and the input signal drives the non-inverting terminal. Gain is exactly 1 and no phase inversion occurs. The circuit transforms a high-impedance signal source into a low-impedance driver capable of sourcing or sinking the op-amp's full output current (typically 10 to 25 mA) without loading the source. Voltage followers appear between sensor networks and ADC inputs, after DAC outputs before filtering, and at the output of reference voltage circuits.

Gain-Bandwidth Product and Frequency Limits

For voltage-feedback op-amps, the gain-bandwidth product (GBW) is a constant equal to the product of closed-loop gain and the bandwidth at that gain. An op-amp with GBW = 1 MHz set to a gain of 10 has a -3 dB bandwidth of only 100 kHz. Set to a gain of 100, the bandwidth drops to 10 kHz. This means that increasing gain always sacrifices bandwidth. When designing amplifier chains, it is often better to cascade two stages of moderate gain than one stage of high gain, because each stage retains more bandwidth.

The slew rate (V/µs) limits how fast the output can change for large signals. If a sine wave's maximum rate of change exceeds the slew rate, the output clips into a triangle wave - this is slew-rate distortion and occurs even if the signal frequency is within the small-signal bandwidth. For an output swing of ±10 V at 100 kHz, the required slew rate is at least 2π × 100,000 × 10 = 6.28 V/µs. Phase margin is the amount of phase shift at the frequency where the open-loop gain equals 1; if phase shift reaches -180° before gain falls to 1, the feedback becomes positive and the circuit oscillates. Most stable op-amp designs target at least 45° of phase margin.

Choosing Op-Amp Speed

For audio applications (20 Hz to 20 kHz), op-amps like the NE5532 or OPA2134 with GBW of 10 MHz are more than adequate and offer excellent noise performance. Video signals (DC to 6 MHz composite, or DC to 50 MHz for component) require op-amps with GBW of 50 to 500 MHz and high slew rates. For RF signal chain applications above 100 MHz, dedicated RF amplifier ICs designed with transmission-line matching are the right tool; standard op-amps have too much phase shift and insufficient speed at those frequencies.

Input and Output Characteristics

Input offset voltage is the differential voltage that must be applied between the inputs to force the output to zero. General-purpose op-amps have offset voltages in the millivolt range. Precision op-amps (such as the OPA277 or ADA4528) reduce this to microvolts. Auto-zero and chopper-stabilized op-amps continuously null the offset, achieving nanovolt-level effective offset at the cost of some noise and bandwidth.

Input bias current flows into or out of both input terminals and creates an error voltage when multiplied by the source impedance. Bipolar input op-amps have bias currents in the microamp range, which limits them to low-impedance sources unless careful compensation is used. JFET and CMOS input op-amps have bias currents below 100 pA and even sub-picoamp levels, making them essential for charge amplifiers, electrometer inputs, and pH electrode interfaces.

Output swing is limited by the supply rails. Standard op-amps cannot swing fully to either rail; rail-to-rail output op-amps approach within a few millivolts of each supply, which is critical in single-supply designs where the signal range may use nearly the full supply voltage. Output current is typically limited to 10 to 25 mA by internal circuitry. Exceeding this causes output voltage clamping and potential damage.

Noise

Op-amp noise has two components: voltage noise density (nV/√Hz), which is amplified by the closed-loop gain, and current noise density (pA/√Hz), which creates voltage noise when multiplied by source impedance. At low frequencies, both noise sources rise as 1/f (flicker noise or pink noise), above the 1/f corner frequency the noise is approximately flat (white noise). For precision measurement, choose an op-amp whose 1/f corner is below the signal frequency band and whose noise density matches the source impedance. Low-noise bipolar op-amps (like the LT1028) have excellent voltage noise but high current noise; JFET op-amps have higher voltage noise but negligible current noise, making them better for high-impedance sensors.