Figure 1: An amplifier increases the signal level. Gain is expressed as a linear ratio (Vout/Vin) or in decibels (20 log of the ratio). Gain > 0 dB means amplification; < 0 dB means attenuation.
Table of Contents
What Is Gain?
Gain is the ratio of a circuit’s output to its input. A voltage gain of 10 (20 dB) means the output voltage is ten times the input. A gain less than 1 (negative dB) means attenuation — the output is smaller than the input. Gain can be expressed as a linear ratio (Av), in decibels, or as a percentage change. The Decibel Calculator converts freely between dB and linear ratios if you need to work purely in those units.
The calculator above has three modes. Mode 1 converts bidirectionally between dB, voltage ratio, and Vin/Vout. Mode 2 designs op-amp circuits for three topologies from two resistor values. Mode 3 cascades up to 8 gain/loss stages for multi-stage amplifier chains.
The Formulas
Av = Vout / VinIn decibels:
dB = 20 × log₁₀(Av)Power gain:
Ap = Av² → dB = 10 × log₁₀(Ap) (same number)Reverse:
Av = 10(dB/20)Op-amp inverting:
Av = −Rf/Rin | Non-inverting: Av = 1 + Rf/Rin
Common Gain Values
| dB | Voltage Ratio | Power Ratio | Description |
|---|---|---|---|
| +60 | ×1,000 | ×1,000,000 | High-gain preamp |
| +40 | ×100 | ×10,000 | Microphone preamp |
| +20 | ×10 | ×100 | Standard amplifier stage |
| +6 | ×2 | ×4 | Voltage doubling |
| 0 | ×1 (unity) | ×1 | Buffer / no change |
| −6 | ×0.5 | ×0.25 | Voltage halving |
| −20 | ×0.1 | ×0.01 | 20 dB attenuator |
Mode 1 — Voltage Gain (Bidirectional)
Enter any one of Vin + Vout, gain in dB, or linear ratio. The calculator fills in everything else: voltage gain in dB, linear ratio, power gain (dB and ratio), percentage change, and nepers. A visual signal comparison bar shows input versus output.
Example: 0.1 V In, 5 V Out
Av = 5 / 0.1 = 50×
dB = 20 × log₁₀(50) = 33.98 dB
Power gain Ap = 50² = 2,500× (33.98 dB)
Voltage change: +4,900% | Assessment: amplified
Example: Enter −6 dB → Find Ratio
Av = 10(−6/20) = 0.501× ≈ 0.5
Ap = 0.5² = 0.25×
Voltage halved, power quartered. This is the loss through a simple resistive voltage divider or a 6 dB attenuator pad.
Mode 2 — Op-Amp Gain
Select a topology (inverting, non-inverting, or differential), enter Rf and Rin in Ω, kΩ, or MΩ. The calculator returns gain with sign, gain in dB, phase (0° or 180°), Rf/Rin ratio, input impedance, and the formula used.
Inverting Amplifier: Av = −Rf/Rin
Av = −100k / 10k = −10 | 20 dB
Phase: 180° (inverted) | Input Z: 10 kΩ
A +0.5 V input produces −5 V output. The input impedance equals Rin. For higher input impedance, scale both resistors up proportionally — 1 MΩ / 100 kΩ gives the same gain with 100 kΩ input impedance.
Non-Inverting Amplifier: Av = 1 + Rf/Rin
Av = 1 + 100k/10k = +11 | 20.83 dB
Phase: 0° (in-phase) | Input Z: Very high (op-amp input)
Same resistors as the inverting example but gain is +11 instead of −10, and there is no phase inversion. The very high input impedance makes it ideal for buffering high-impedance sources like sensors and piezo transducers.
Voltage Follower (Unity Gain Buffer)
Av = 1 + 0/∞ = 1 (0 dB)
Output equals input. No voltage gain, but massive impedance transformation. Essential for driving low-impedance loads from high-impedance sources without signal loss.
Differential Amplifier: Av = Rf/Rin
Av = 100k / 10k = 10 | 20 dB
Amplifies only the difference between the two inputs (Vout = Av × (V+ − V−)), rejecting any signal common to both. Used for sensor bridges, current-sense amplifiers, and differential signal conditioning. The Noise Figure Calculator can then analyse how the amplifier’s noise contribution affects the overall signal-to-noise ratio.
Mode 3 — Cascaded Gain
Enter up to 8 stages with positive (gain) or negative (loss) dB values. The calculator shows a running total at each stage in both dB and voltage ratio, plus the final totals.
Example: Two Amplifiers + Cable Loss
Stage 1: Preamp +20 dB → running: +20 dB (10×)
Stage 2: Power amp +20 dB → running: +40 dB (100×)
Stage 3: Cable loss −6 dB → running: +34 dB (50.1×)
Total: +34 dB = 50.1× voltage, 2,512× power
Example: 5-Stage Receiver
Stage 1: RF amp +15 dB → +15
Stage 2: Filter loss −10 dB → +5
Stage 3: IF amp +25 dB → +30
Stage 4: Cable −6 dB → +24
Stage 5: Baseband amp +30 dB → +54 dB
Total: +54 dB = 501× voltage, 251,189× power
The running total at each stage tells you where the signal is strongest and weakest. If any stage drives the signal above the next stage’s maximum input, you get clipping. If any stage drops the signal below the noise floor, you lose it. The Signal Attenuation Calculator extends this with a link budget mode that includes named stages for real system design.
Voltage Gain vs Power Gain
Voltage gain (Av) is Vout/Vin. Power gain (Ap) is Pout/Pin. For the same load impedance, Ap = Av². In decibels, both give the same number: 20 × log(Av) = 10 × log(Ap). A voltage gain of 10× (20 dB) corresponds to a power gain of 100× (also 20 dB). When people say “20 dB gain,” it means 10× voltage and 100× power simultaneously.
Gain-Bandwidth Product
Every op-amp has a gain-bandwidth product (GBW): the product of gain and bandwidth is constant. An op-amp with GBW = 1 MHz can provide a gain of 100 (40 dB) up to 10 kHz, or a gain of 10 (20 dB) up to 100 kHz, or unity gain up to 1 MHz. Higher gain means lower bandwidth. The calculator shows the DC gain from your resistor values — check the op-amp data sheet to confirm the GBW supports your gain at your signal frequency. The Bandwidth Calculator computes the −3 dB bandwidth from cutoff frequencies or Q factor.
Inverting vs Non-Inverting — When to Use Which
Non-inverting when you need high input impedance (sensor buffering, high-impedance sources) or when phase inversion is unacceptable. The input sees the op-amp’s own input impedance (typically megaohms or higher), not Rin.
Inverting when you need precise gain set purely by the Rf/Rin ratio, or when the 180° phase inversion does not matter (AC-coupled signals, differential pairs). Input impedance equals Rin, which can load the source.
Differential when you need to amplify the difference between two signals while rejecting common-mode noise. Used in sensor bridges, current-sense circuits, and balanced audio inputs.
Frequently Asked Questions
What is gain?
What is the difference between voltage gain and power gain?
20 × log(Av) = 10 × log(Av²). When someone says “20 dB gain” it means 10× voltage and 100× power.Why does the inverting op-amp have negative gain?
What is gain-bandwidth product?
How do cascaded gains combine?
When should I use inverting vs non-inverting?
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