Inverting amplifier calculator
Matched resistors give a gain of −1 and a ten-to-one feedback ratio gives −10: enter Rin and Rf and get the ideal closed-loop gain of an inverting amplifier, plus its decibel value, rounded as you choose. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Rin
- 10,000
- Rf
- 100,000
- Gain
- -10
- Gain db
- 20
- Precision
- 10
- Unit resistance
- ohm
This inverting amplifier calculator returns the ideal closed-loop voltage gain of an operational-amplifier stage wired as an inverter. You provide the input resistor Rin from the signal source to the inverting terminal and the feedback resistor Rf from the output back to that same node; the engine evaluates Av equals negative Rf over Rin under the usual virtual-ground idealization. The sign is always inverted for positive resistor values, so a ten-to-one feedback ratio yields a gain of negative ten, and matched resistors yield negative one. Classic textbook checks include ten kilohms with one hundred kilohms, one kilohm with ten kilohms, and any pair where Rf equals Rin. The arithmetic is pure and deterministic: no network calls, no sampling, and no date-dependent shortcuts.
What an inverting amplifier does and what you get
An inverting operational-amplifier stage places the input signal through Rin into the inverting (−) input, routes feedback from the output through Rf to that same node, and ties the non-inverting (+) input to signal ground (or a reference). Ideal analysis treats the differential input voltage as zero and the input currents as zero, so the inverting node sits at a virtual ground and the current through Rin must equal the current through Rf with opposite sense at the summing node.
That balance produces the closed-loop voltage gain Av equals Vout over Vin equals negative Rf over Rin. There is no SPICE netlist, no open-loop A0 model, and no random Monte Carlo on resistor tolerance: the engine either evaluates the closed form inside the supported numeric range or rejects the input.
Where inverting gain checks fit in study, design, and software
Students meet the inverting amplifier when a circuits course introduces operational amplifiers, when a lab asks for a closed-loop gain before measuring Vout over Vin on a breadboard, or when a contest problem gives two resistor values and asks for Av without a full SPICE run. Teachers can pre-generate answer keys for modest Rin and Rf pairs without trusting opaque calculator apps that silently mix kilo-ohms with ohms or drop the minus sign.
Developers call the same contract from scripts to seed deterministic test vectors for audio preamps and sensor front-ends, to normalize user-entered resistor pairs before a bill-of-materials sketch, or to satisfy programming-challenge statements that demand the ideal inverting gain rather than a hand-waved estimate. Field technicians and makers use it for quick checks on microphone preamps, photodiode transimpedance approximations with a large Rf, and simple signal conditioners when only discrete resistor values are known.
What you can do with it
Homework and lab checks
Compute ideal inverting gain Av = −Rf/Rin before grading op-amp worksheets or DC amplifier lab write-ups.
Design and education software
Normalize user-entered Rin and Rf into Av and optional dB for planners, tutors, and interactive analog lessons.
FAQ
What does the inverting amplifier calculator cost?
It is free in your browser on this page.
What formula is used for the gain?
For an ideal inverting op-amp, Av = Vout/Vin = −Rf/Rin. Positive resistor values always produce a negative (inverting) gain.
What happens if the input resistor is zero?
Zero Rin makes Av = −Rf/Rin undefined (division by zero).
Why are results rounded to a precision?
Default precision is 10 decimal places; you can set precision from 0 to 15.
What happens if the feedback resistor is zero?
It is accepted. The gain comes out as zero and the decibel value is left empty, because the decibels of zero gain would be minus infinity. Only a zero input resistor is rejected, since the gain divides by it.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/elec/op-amp-inverting \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"rin":10000,"rf":100000}'const res = await fetch("https://api.kit.forhosting.com/elec/op-amp-inverting", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"rin": 10000,
"rf": 100000
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/op-amp-inverting",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"rin": 10000,
"rf": 100000
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/op-amp-inverting", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"rin":10000,"rf":100000}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"rin":10000,"rf":100000}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/op-amp-inverting", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"rin": 10000,
"rf": 100000
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.op_amp_inverting",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs_ohm | 1000000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Zero input resistance is rejected with invalid_input because the ratio is undefined.
What an inverting op-amp stage is and what the response contains
This calculator accepts those two resistances and returns the normalized rin and rf values, the linear gain Av, an optional magnitude gain in decibels as twenty times log base ten of the absolute value of Av when that magnitude is positive, a boolean inverted flag set true for this topology, a short formula string, the method tag inverting_op_amp, the precision used, and a unit hint of ohm for SI-consistent inputs. Zero Rin fails with invalid_input and a message that names the division-by-zero problem.
How Rin and Rf are read and how the gain stays reproducible
Each value must be a finite decimal within the documented magnitude ceiling; optional leading plus signs and scientific notation are allowed when they parse cleanly. Embedded spaces inside a token, hex prefixes, and non-numeric junk are rejected with a clear message so a bad cell does not become a wrong gain. Zero and near-zero rin fail explicitly because Av divides by Rin. Feedback of zero is mathematically allowed and yields a linear gain of zero with a null dB field rather than a silent infinity. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for resistances, gain, and gain_db, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the inverting formula yourself.
Where inverting gain checks fit in study, design, and software
Product and education tools use the endpoint when a learner types two resistances and the UI must show Av and optionally the dB magnitude. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with parallel-resistance or power helpers when you need related electrical steps, and with other math endpoints when you are building a small lab of free, deterministic circuit calculators for study and software tests.
Integration use cases
Deterministic test fixtures
Generate reproducible closed-loop gains for unit tests, breadboard demos, and CI assertions on the virtual-ground formula.
Technical questions
Does this tool also compute non-inverting gain?
No. It only evaluates the inverting topology. A non-inverting stage uses Av = 1 + Rf/Rg with a different resistor arrangement.