Op-Amp Gain Calculator
Two resistors decide how loud an op-amp speaks. Choose the topology, enter the feedback and input resistors, and this calculator returns the voltage gain — as a ratio and in decibels — with the sign that tells you whether the output keeps the input’s phase or flips it, and the bandwidth the gain will cost you.
Feedback: The Amplifier That Corrects Itself, Exactly
The op-amp's open-loop gain is enormous (a hundred thousand or more) and nearly useless — imprecise, drifting, nonlinear. The two topologies here spend that surplus on obedience: a resistor divider feeds a fraction of the output back to the input, and the amplifier, forever correcting the difference toward zero, ends up amplifying by exactly the divider's inverse. Non-inverting, the divider is R1 and Rf from output to ground, and the gain settles at 1 + Rf ÷ R1; inverting, the input resistor Rin joins the accounting and the gain is −Rf ÷ Rin, the sign recording the phase flip. The miracle of the arrangement is that the gain depends on two passive components' ratio — stable, cheap, precise — and not on the wild device inside the loop. This is arguably the most successful idea in analogue electronics, and its entire user-facing surface is the two fractions the calculator evaluates.
Worked Example: Ninety Over Ten
The defaults run the textbook pair: Rf = 90 kΩ, R = 10 kΩ. Non-inverting: 1 + 90 ÷ 10 = 10.00×, which is 20.0 dB — the decibel conversion (20 × log₁₀ of the ratio) turning the multiplication into the addition engineers think in. Inverting with the same pair: −9.00× (19.1 dB) — note the asymmetry, the "+1" that the non-inverting topology keeps and the inverting does not, which at low gains dominates the design (a non-inverting stage cannot go below unity at all; an inverting stage attenuates happily). The note's gain-bandwidth line prices the hidden tax: the amplifier's gain-bandwidth product is (roughly) conserved, so a gain of 10 from a 1 MHz part leaves about 100 kHz of bandwidth — plenty for audio, a wall for video — and gain is revealed as bandwidth spent, a trade no resistor value can repeal.
Why Decibels Run the Building
The dB column is not a courtesy translation: cascaded stages add in decibels while they multiply in ratios, so a three-stage chain of 10×, 5× and 2× is "20 + 14 + 6 = 40 dB" (a gain of 100) in the units engineers actually carry in their heads. Doubling voltage is +6 dB; tenfold is +20; halving is −6 — a logarithmic folk arithmetic that turns system budgets into sums. The calculator prints both because design fluency is bilingual: ratios for the single stage in front of you, decibels for the system it joins. And the sign discipline matters in both languages — the inverting stage's minus has no decibel representation (logarithms of negative numbers being unavailable), which is why the answer prints the signed ratio beside the unsigned dB: phase is information the magnitude politely declines to carry.
The 741 and the Democratisation of Gain
Before 1968, feedback amplifiers were designed per-application by specialists; the µA741 put a compensated, forgiving op-amp in an eight-pin can for pennies, and the two formulas on this page became the most-computed fractions in hobbyist and professional electronics alike. Guitar pedals, mixing consoles, medical sensors and a generation of synthesisers are 741s (and their descendants) evaluating 1 + Rf ÷ R1 by the billion. The calculator's ordinariness is the historical point: a computation that once justified an engineer's week now justifies a web form, and the expertise migrated from performing the arithmetic to knowing its limits — bandwidth, slew, impedance, noise, the fine print this page's FAQs carry. Tools that finish a calculation should always smuggle its boundaries in with the answer; that is the entire editorial policy of this hub, stated once, here, where the example is oldest and the readership widest.
When the Formula Lies: Saturation and the Rails
The calculator's promise holds only while the output can physically swing: an op-amp on ±12 V rails cannot deliver a gain of 10 from a 2 V input — the output would need 20 V and will instead clip flat against the rail, manufacturing harmonics from arithmetic. Saturation is the commonest real-world "wrong gain" after the bandwidth tax, and its diagnostic is the same multiplication run in advance: input peak × gain must stay inside the rails with headroom to spare. Design therefore flows backwards — choose the output swing the next stage wants, divide by the input, and that is the gain the resistors must implement. The formula never lies; it merely answers the linear question it was asked, and this section exists so the reader asks it with the rails in view — gain chosen against the supply, the signal and the next stage's appetite, rather than as the largest number the resistors can be persuaded to form.
Related Tools
More from the Other Calculators hub: the Duty Cycle Calculator for the square waves this amplifier will meet, and the Delay and Reverb Calculator for the effects this stage will feed.
Frequently Asked Questions
Why can't a non-inverting amplifier have gain below 1, ever?
Because its formula is 1 plus a positive ratio: the divider can return at most the whole output (Rf = 0, a wire — the famous voltage follower, gain exactly 1) and any resistance in the feedback path only raises the gain above unity. Attenuation on the non-inverting side is done before the stage (a divider at the input) or not at all, and the follower's unity is itself a prized configuration — enormous input impedance, tiny output impedance, gain of one — proving that an amplifier's value is not always its gain. The calculator enforces the physics silently: no resistor values in this topology will ever print a gain under 1.00×.
What resistor values should I actually use, then?
Ratios set the gain; absolute values set the side effects, and the working band for general-purpose parts is roughly 1 kΩ to 1 MΩ. Too small and the output stage must drive heavy currents into its own feedback (distortion, heat, wasted power); too large and bias currents across the resistors become offset voltages, thermal (Johnson) noise rises, and stray capacitance turns your gain stage into a low-pass filter with opinions. The 10 kΩ neighbourhood of the worked example is the profession's compromise, and designs scale both resistors together — 9 kΩ over 1 kΩ, 900 kΩ over 100 kΩ — when current or noise budgets demand, holding the ratio (and the calculator's answer) constant.
What is input impedance in each topology?
Non-inverting: the op-amp's own input faces the source — gigohms in modern parts, effectively infinite for most sources, which is why sensors with weak outputs love this topology. Inverting: the input resistor Rin is the input impedance (the summing node sits at virtual ground), so a 10 kΩ Rin loads the source with 10 kΩ — usually fine, occasionally a design constraint, always a known one. The choice between topologies is therefore seldom about the gain formula — both are one line — and mostly about impedance, phase and the unity floor: the three properties the formulas wear openly.
My real circuit's gain is lower than calculated, at high frequencies. Why?
The gain-bandwidth product collecting its tax (the note's check), possibly joined by slew rate: the output can only swing so many volts per microsecond, so large fast signals distort below their calculated amplitude even inside the bandwidth. Both limits live in the op-amp's datasheet, not in the resistors — the calculator's figures are the low-frequency truth the device approximates until physics files its objection. The diagnostic order is: verify the ratio (this page), then the GBW at your frequency, then the slew rate at your amplitude — three multiplications that between them explain nearly every "the gain is wrong" bench mystery.
What does "virtual ground" mean in the inverting topology?
The feedback drives the inverting input to sit at the same voltage as the non-inverting input — ground, in the standard circuit — without any actual connection: the node is a ground maintained by correction, a "virtual" earth. Input current through Rin therefore flows entirely through Rf (the op-amp's input draws ~none), and the voltage divider logic inverts into the −Rf ÷ Rin formula. It is one of electronics' great fictions-that-work, and the summing amplifier (many Rins into one node, outputs adding) and the mixer stages of every console are built directly on it — this calculator's minus sign is the virtual ground's signature.
Can I cascade stages for more gain?
Freely — gains multiply, decibels add, and two stages of 10× make 100× (40 dB) with better bandwidth than one stage of 100× from the same parts (each stage keeps its own GBW share: two 1 MHz parts at 10× each hold ~100 kHz; one at 100× holds ~10 kHz). Cascading is the standard answer to the bandwidth tax, priced in extra components and extra chances for noise and offset to accumulate — the eternal trade. The calculator prices each stage; the system arithmetic (multiply the ratios, add the decibels) is the reader's new party trick, courtesy of the dB column — and the working designer's daily bread, three stages deep, before breakfast.