Op-amp full-power bandwidth calculator
An op-amp with a 6.283 V/µs slew rate can swing 10 V peak up to 100 kHz before the sine turns into a triangle. Enter the slew rate and the peak output to get that full-power bandwidth in hertz. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Slew rate
- 6,283,185.30718
- Amplitude
- 10
- V peak
- 10
- V pp
- 20
- Slew rate v per s
- 6,283,185.30718
- Slew rate v per us
- 6.2831853072
Op-amp full-power bandwidth is the highest frequency at which an amplifier can still deliver a stated peak sinusoidal output without the large-signal edge becoming a triangle wave. Datasheets often list slew rate in volts per microsecond and leave the designer to rearrange the classical identity: the steepest slope of a sine is two pi times frequency times peak voltage, so the maximum undistorted frequency is slew rate divided by two pi times Vpeak. Audio power stages, video line drivers, ADC front ends, and instrumentation outputs all need that number when the part is already chosen and the question is how high a full-swing tone can go before slew limiting. Students check homework against the FPBW footnote next to the published SR; design reviews ask whether a five-volt-per-microsecond rail-to-rail amp can still swing ten volts peak at one hundred kilohertz; test teams convert bench SR and amplitude settings into a frequency ceiling for pass-fail limits. This op-amp full-power bandwidth calculator accepts a positive slew rate in volts per second or volts per microsecond and a positive peak output amplitude in volts, divides by two pi times Vpeak, and returns full-power bandwidth in hertz plus cleaned inputs and a printable expression. Zero or negative slew rate or amplitude fails with a clear validation error because the sinusoid model is undefined for non-positive magnitudes.
How full-power bandwidth follows from slew rate
A pure sinusoid of peak amplitude Vpeak and frequency f has instantaneous voltage Vpeak times sine of two pi f t. Differentiating with respect to time shows that the steepest slope occurs at the zero crossings and equals two pi f Vpeak volts per second. When that required slope exceeds the op-amp’s slew rate, the large-signal edge clips into a triangle, distortion rises, and the intended peak is no longer reached at that frequency.
Full-power bandwidth is therefore defined as the highest frequency where the amplifier can still deliver the specified peak or peak-to-peak swing without slew limiting, which rearranges to f approximately equal to SR over two pi Vpeak. Using peak voltage keeps the formula aligned with the derivative; if you only know peak-to-peak swing, Vpeak is half of Vpp, and SR over two pi Vpeak is the same as SR over pi Vpp.
Classic classroom checks include six point two eight volts per microsecond at ten volts peak, which yields about one hundred kilohertz, and the same slew rate at one volt peak, which yields about one megahertz. Real amplifiers also have small-signal bandwidth, output current limits, thermal derating, and capacitive load effects that can starve slew rate in the lab, but the first closed-form ceiling from the data sheet is still this quotient.
Gain-bandwidth product, settling time to a step, and the inverse problem of required slew rate from a target frequency are different search intents and belong on separate landings so this page stays focused on the SR-and-Vpeak-to-FPBW question.
Where full-power bandwidth calculators show up in real work
Analog design reviews size the usable large-signal band of an already shortlisted op-amp by locking the published slew rate and the intended peak swing, then converting that pair into a maximum full-power sine frequency before signing off audio, video, or industrial drive stages. Students in signals and electronics courses verify that the FPBW footnote on a data sheet matches SR over two pi Vpeak for the stated amplitude, then compare the result with the highest tone they plan to run in the lab.
ADC driver and sample-and-hold selection uses the same quotient when a multiplexed front end must deliver a large swing within a fixed bandwidth window still bounded by large-signal slope. Keep the inverse slew-rate-from-FPBW landing, gain-bandwidth, and RC time-constant pages separate so each search intent has one clear page rather than an overloaded multi-formula tool that confuses both students and search engines.
What you can do with it
Datasheet FPBW from published SR
Convert a data-sheet slew rate (V/µs or V/s) and your target peak swing into the maximum undistorted sine frequency before locking audio, video, or industrial drive stages.
Homework and lab checks
Verify that full-power bandwidth matches f = SR/(2π·Vpeak) for the amplitude stated on the sheet, and flag zero or negative SR or Vpeak as invalid.
FAQ
What formula does this full-power bandwidth calculator use?
f = SR / (2 · π · Vpeak) in hertz, where SR is slew rate in volts per second and Vpeak is peak output amplitude in volts. If you supply SR in V/µs, it is converted as SR_V/s = SR_V/µs × 1e6 before the quotient.
What happens if slew rate or amplitude is zero or negative?
Both slew rate and peak amplitude must be strictly greater than zero for f = SR/(2π·Vpeak) to be a physical full-power bandwidth.
What does it cost?
The browser tool is free and runs locally.
What if I only know the peak-to-peak swing?
Halve it to get the peak voltage. Dividing the slew rate by two pi times the peak gives the same result as dividing it by pi times the peak-to-peak swing, so a 20 V swing means 10 V peak.
What happens above the full-power bandwidth?
The sine needs a steeper slope at its zero crossings than the amplifier can slew, so its edges turn into a triangle, distortion rises and the intended peak is no longer reached at that frequency.
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/opamp-full-power-bw \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"amplitude":10,"slew_rate":6283185.30718}'const res = await fetch("https://api.kit.forhosting.com/elec/opamp-full-power-bw", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"amplitude": 10,
"slew_rate": 6283185.30718
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/opamp-full-power-bw",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"amplitude": 10,
"slew_rate": 6283185.30718
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/opamp-full-power-bw", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"amplitude":10,"slew_rate":6283185.30718}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"amplitude":10,"slew_rate":6283185.30718}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/opamp-full-power-bw", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"amplitude": 10,
"slew_rate": 6283185.30718
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.opamp_full_power_bw",
"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.
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
What you send and what you get back
Send a finite positive slew rate and a finite positive peak output amplitude. Numeric values and numeric strings are both accepted so form widgets and spreadsheet paste stay convenient; SI prefix strings such as six volts per microsecond written as text are not parsed, so pass six point two eight three for V/µs or six million two hundred eighty-three thousand for V/s. If you need required slew rate from a target frequency, small-signal GBW, or filter corner frequencies, treat those as separate tools rather than extending this pure FPBW quotient. Slew rate may arrive under slew_rate, sr, slew_rate_v_per_s, or SR in volts per second, or under slew_rate_v_per_us, sr_us, slew_us, or slew_rate_us in volts per microsecond; provide exactly one unit family, never both V/s and V/µs keys in the same request. Peak amplitude arrives under amplitude, or the aliases v_peak, vpeak, Vpeak, peak, output_amplitude, or v_out, with only one key present. Slew rate and amplitude must both be strictly greater than zero; zero, negative, NaN, and Infinity fail with invalid_input and are not charged. On success the response includes cleaned amplitude and v_peak, v_pp as twice the peak, slew_rate and slew_rate_v_per_s in volts per second, slew_rate_v_per_us as that value divided by one million, bandwidth, full_power_bandwidth, fpbw, frequency, and f_max as the same full-power bandwidth in hertz, unit labels for volt, volt per second, volt per microsecond, and hertz, a short expression string showing the quotient, method opamp_full_power_bw, and the formula string. Classic checks include slew_rate six million two hundred eighty-three thousand one hundred eighty-five point three zero seven one eight with amplitude ten yielding about one hundred thousand hertz, and slew_rate_v_per_us equal to six point two eight three one eight five three zero seven one eight with amplitude one yielding about one megahertz. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where full-power bandwidth calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
CI fixtures and answer keys
Script the same f = SR/(2π·Vpeak) quotient used in the browser so automated graders and bench frequency ceilings share one ground truth.
Technical questions
How is this different from the slew rate calculator?
The sibling slew-rate tool answers SR = 2π·f·Vpeak when you already know frequency and amplitude. This page is the inverse design question: given SR and Vpeak, what is the maximum undistorted sine frequency (full-power bandwidth)?
Is amplitude peak or peak-to-peak?
Peak (Vpeak). If you only know peak-to-peak swing, divide by two before calling, or use the returned v_pp field after a successful call (v_pp = 2 · Vpeak).