How do you calculate op-amp gain for an inverting amplifier?

For an inverting amplifier, the voltage gain is Av = −Rf / R1, where Rf is the feedback resistor and R1 is the input resistor. The negative sign indicates that the output is 180° out of phase with the input.

How do you calculate op-amp gain for a non-inverting amplifier?

For a non-inverting amplifier, the voltage gain is Av = 1 + Rf / R1. The minimum gain is 1 (unity), which occurs when Rf = 0 or R1 is infinite (voltage follower configuration).

How do you convert op-amp gain to decibels?

To convert voltage gain to dB: Gain(dB) = 20 × log₁₀(|Av|). For example, a gain of 10 V/V equals 20 dB, and a gain of 100 V/V equals 40 dB.

What is the difference between inverting and non-inverting op-amp?

An inverting op-amp has the input at the − terminal (gain = −Rf/R1, output is phase-inverted, input impedance ≈ R1). A non-inverting op-amp has the input at the + terminal (gain = 1+Rf/R1, output is in-phase, input impedance is very high).

Op-Amp Gain Calculator

Calculate inverting and non-inverting amplifier gain, output voltage, and gain in decibels.

Component Values

R1 (input resistor)

Rf (feedback resistor)

Input Voltage (Vin) (optional)

Results

Voltage Gain (Av)-10.00 V/V

Gain in dB20.00 dB

Output Voltage (Vout)-10.00 V

Input Impedance10.00 kΩ

Av = −Rf / R1

VOUT VS VIN — TRANSFER FUNCTION

Vout vs Vin — Av = -10.0 (±15V rails)

How does op-amp gain work?

An operational amplifier with negative feedback forms a stable amplifier whose gain depends only on external resistors, not on the op-amp's internal gain. This is what makes op-amp circuits so practical: the gain formula is simple, predictable, and set by components you choose.

In the inverting configuration, the input signal connects through R1 to the inverting (−) input, and Rf provides feedback from the output to the same node. Gain = −Rf/R1. The negative sign means the output is phase-inverted. The input impedance is approximately R1, since the inverting input is a virtual ground.

In the non-inverting configuration, the input connects directly to the non-inverting (+) input, and the voltage divider R1/Rf sets the feedback. Gain = 1 + Rf/R1. The output is in phase with the input. Input impedance is very high (MΩ range), limited only by the op-amp itself.

Inverting

Av = −Rf / R1

Non-Inverting

Av = 1 + Rf / R1

Key Points

Inverting: Gain = −Rf/R1, output is phase-inverted
Non-inverting: Gain = 1 + Rf/R1, minimum gain is 1 (unity)
Gain in dB = 20 × log₁₀(|Av|)
Bandwidth decreases as gain increases (gain-bandwidth product)

Applications

Signal amplification and conditioning
Active filters (combined with capacitors)
Audio preamplifiers
Instrumentation and sensor interfaces

Formula Reference

Op-amp gain configurations:

Inverting amplifier:
Av = –Rf / Rin    (negative = phase inversion)
Rin_in = Rin (input resistance)

Non-inverting amplifier:
Av = 1 + Rf / R1   (always ≥ 1, in-phase)
Rin_in = very high (MΩ–GΩ)

Voltage follower (buffer):
Av = 1   Rin_in = very high   Rout ≈ 0Ω

Differential amplifier:
Vout = (Rf/Rin) × (V+ – V–)   (requires matched resistors)

Quick Resistor Selection for Common Gains

Config	Gain	Rin	Rf	Notes
Non-inverting	2×	10kΩ	10kΩ	Av = 1+Rf/R1
Non-inverting	10×	10kΩ	90kΩ	Use 100kΩ – 10kΩ
Non-inverting	100×	1kΩ	99kΩ	Use 100kΩ – 1kΩ
Inverting	–1×	10kΩ	10kΩ	Unity inverter
Inverting	–10×	1kΩ	10kΩ	Audio preamp stage
Inverting	–100×	1kΩ	100kΩ	Sensor amplifier
Voltage follower	1×	—	short	Buffer, impedance match

Worked Examples

Example A — Microphone preamp, Av=100 (non-inverting)

R1=1kΩ, Rf=99kΩ (use 100kΩ in practice, Av=101).

With NE5532 (GBW=10MHz): f₋₃dB = 10MHz/101 = 99kHz → covers audio band ✓

Example B — Sensor signal conditioning, ±5V → 0–3.3V

Shift –5V–+5V to 0–3.3V for MCU ADC.

Use inverting summing amplifier: Vout = –(Vs×Rf/Rin + Vref×Rf/R2)
Rf=10kΩ, Rin=20kΩ, R2=20kΩ, Vref=3.3V → Vout = –Vs/2 + 1.65V ✓

Design Tips

Keep resistor values between 1kΩ–100kΩ for best noise/bandwidth trade-off. Too low (< 1kΩ): op-amp output current limited, distortion increases. Too high (> 1MΩ): noise, stray capacitance, and bias current errors dominate. Always decouple op-amp supply pins with 100nF ceramic cap as close as possible.

Did you know? The first operational amplifier was a vacuum tube design built in the 1940s for analog computers. The μA741, introduced by Fairchild in 1968 and designed by Dave Fullagar, became the iconic 8-pin DIP op-amp that is still sold today.