Octave band frequency converter
See a frequency on every log scale at once: 1000 Hz above a 1 Hz reference is exactly 3 decades, about 9.965784284662 octaves and 119.589411415945 semitones, with cents and third-octaves alongside. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Value
- 1,000 hz
- Value in
- 1,000
- Unit in
- hz
- Ref hz
- 1
- Hz
- 1,000
Acoustic and RF work constantly moves between absolute frequency in hertz and logarithmic interval measures such as octaves and decades. An octave is a frequency ratio of two to one; a decade is a ratio of ten to one; musical cents and semitones subdivide the octave; a linear ratio is simply f over a reference. This octave-band frequency converter accepts one value, names the unit you already hold, and optionally a positive reference frequency, then returns every equivalent form with exact log base two and log base ten factors.
Why octave and decade scales sit next to hertz
People search for an octave band frequency converter when a spectrum plot, filter datasheet, or ISO preferred-frequency table is stated in octaves or decades and they need the matching hertz value, or when two frequencies are known and they must report how many octaves or decades separate them. Absolute frequency in hertz is the SI unit of cyclic rate, but human hearing, vibration standards, and proportional bandwidth filters are almost always specified on a logarithmic frequency axis.
One octave means the upper frequency is twice the lower; one decade means a factor of ten. Those ratios compound: three octaves is a factor of eight, two decades is a factor of one hundred. Music further splits the octave into twelve equal-tempered semitones and twelve hundred cents, which are still pure powers of two on the frequency ratio.
Mixing the scales without a converter doubles or halves reported bandwidth and breaks third-octave band maps, link budgets, and A-weighting sanity checks. This capability forces an explicit unit on the input value and always returns the full set of equivalents relative to a reference frequency so clients can display hertz next to octaves without a second call.
The math is pure and local: ratio equals frequency over reference, octaves equal log base two of that ratio, decades equal log base ten of the same ratio, cents equal twelve hundred times octaves, and semitones equal twelve times octaves. No network lookup, no locale-dependent constants, and no silent clamp of non-positive frequencies into a fake infinity.
Where teams use it and what it costs
Acousticians convert centre frequencies of octave and one-third-octave bands between hertz tables and log axes when building noise maps and compliance reports. Audio engineers express filter slopes and crossover spacing in octaves while the DSP still needs absolute cutoffs in hertz. RF and vibration teams talk in decades per decade of frequency and must reconcile those statements with measured spectra in hertz before dashboards accept the data.
Music-tech products map cents and semitones onto hertz offsets from a tuning reference such as A four at four hundred forty hertz. Product and support teams embed the same conversion in lab tools so customers never apply log two and log ten by hand under deadline pressure. Map your UI labels to the allowed unit names, treat unknown-unit errors as user-fixable feedback, and keep the system of record in whichever form your domain prefers while still exposing every field in the response.
What you can do with it
Acoustic octave-band tables
Convert ISO preferred centre frequencies between hertz and octave or decade offsets from a one-kilohertz reference when building noise-band reports.
Audio filter and crossover design
Express proportional bandwidth and slope spacing in octaves while computing absolute cutoff frequencies in hertz for DSP coefficients.
FAQ
What is the difference between an octave and a decade?
An octave is a frequency ratio of 2:1 (log2). A decade is a ratio of 10:1 (log10). One decade equals log2(10) ≈ 3.321928 octaves; one octave equals log10(2) ≈ 0.301030 decades.
Can I enter a negative octave value?
Yes. Negative log intervals mean below the reference (ratio less than one). Only hz and ratio inputs must be strictly positive.
What does it cost?
The interactive page runs free in your browser.
How many octaves is 1000 Hz above 1 Hz?
About 9.965784284662 octaves, which is exactly 3 decades. The same interval is 119.589411415945 semitones and 29.897352853986 third-octaves, and all of these appear together.
Which reference frequency should I use?
The default is 1 hertz, which makes hertz and the ratio the same number. Use 1000 hertz around the standard acoustic band centres near one kilohertz, or 440 hertz to count musical octaves above A4.
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/conv/octave-band \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":1000,"unit":"hz"}'const res = await fetch("https://api.kit.forhosting.com/conv/octave-band", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 1000,
"unit": "hz"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/conv/octave-band",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 1000,
"unit": "hz"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/conv/octave-band", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":1000,"unit":"hz"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":1000,"unit":"hz"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/conv/octave-band", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"value": 1000,
"unit": "hz"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "conv.octave_band",
"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
Unknown unit names fail with a clear invalid_input error instead of a silent wrong scale. Use the tool free on this page, or call the same deterministic logic by API at $0.002 per request for scripts, noise-band tables, and filter design notebooks that must never invent a decade factor by hand.
How to call the converter and read the response
The default reference is one hertz, which makes absolute frequency and the linear ratio numerically equal and is ideal for pure interval conversions. When unit is a log interval such as octaves or decades, any finite number is accepted, including negatives that mean below the reference. Send value as a finite number, unit naming what that number already is, and optionally ref_hz as a positive reference in hertz. Set ref_hz to one thousand when you work around ISO acoustic centre frequencies near one kilohertz, or to four hundred forty when you reason in musical octaves above A four. Allowed units are hz (aliases hertz, cps), octaves (octave, oct), decades (decade, dec), ratio (linear, lin), cents (cent), and semitones (semitone, st, halfstep). When unit is hz or ratio the value must be strictly positive; zero and negatives raise invalid_input because real logarithms of non-positive arguments are undefined. The engine reduces the input to a positive ratio, then emits hz, ratio, octaves, decades, cents, semitones, and third_octaves (three times the octave count, useful for one-third-octave band spacing), plus unit_in, value_in, ref_hz, and a short formula string for audit trails. Missing fields, non-finite numbers, non-positive ref_hz, and unknown unit names all fail with invalid_input naming what was wrong, so form validation and API error handling stay aligned.
Where teams use it and what it costs
Prefer this endpoint when search intent is specifically octave-band or decade frequency conversion; use general frequency unit converters for megahertz versus kilohertz prefixes alone, and use musical note calculators when the question is note name rather than interval measure.
Integration use cases
Music and tuning offsets
Map cents or semitones above a reference such as A4 = 440 Hz into absolute frequency and linear ratio for tuners and sample-rate tools.
Technical questions
Why do I need ref_hz?
Octaves, decades, cents and semitones measure intervals relative to a reference. Absolute hertz equals ref_hz times the linear ratio. Default ref_hz is 1, so hz and ratio match numerically until you set another reference.
What happens if I send an unknown unit?
The API returns invalid_input with a message listing allowed units: hz, octaves, decades, ratio, cents, and semitones (plus documented aliases).