Decibel calculator
An intensity of 0.000001 W/m² is a million times the hearing threshold, which is a level of 60 dB. Enter a measured intensity, and your own reference if you need one, to get the level in decibels and the ratio. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Intensity
- 0.000001
- Reference
- 0
- Ratio
- 1,000,000
- Level db
- 60
- Intensity unit
- W/m²
Sound intensity level expresses how many decibels a measured acoustic intensity sits above a chosen reference threshold. In SI units intensity I is power per unit area in watts per square metre, and the conventional reference I0 for air is one times ten to the minus twelve watts per square metre—the approximate threshold of human hearing at one kilohertz. The level is then L equals ten times the base-ten logarithm of the ratio I over I0, so every factor-of-ten change in intensity is a ten-decibel step and a doubling of intensity is about three decibels. This calculator accepts a positive intensity, optionally a custom positive reference, and returns the level in decibels, the intensity ratio, and the formula strings used on worksheets. Non-positive intensity is rejected with a clear validation error because the real logarithm is undefined at zero and negative arguments.
How decibels measure sound intensity
Acoustic intensity I measures the average power carried by a sound wave through a unit area perpendicular to the direction of propagation, so its SI unit is the watt per square metre. Human hearing spans many orders of magnitude of intensity, from about one times ten to the minus twelve watts per square metre near the threshold of hearing up to roughly one watt per square metre near the threshold of pain.
A linear scale is awkward for that dynamic range, so acoustics uses a logarithmic sound intensity level L equals ten times log base ten of I divided by a reference intensity I0.
With the conventional air reference I0 equal to one times ten to the minus twelve watts per square metre, a quiet library near one times ten to the minus eight watts per square metre sits near forty decibels, conversational speech near one times ten to the minus six is about sixty decibels, and one times ten to the minus two is about one hundred decibels.
Because the factor ten multiplies a common logarithm, multiplying intensity by ten raises the level by exactly ten decibels, and multiplying intensity by two raises the level by about three point zero one decibels. The map is model-independent for pure intensity ratios: it does not assume free-field spherical spreading, A-weighting filters, or any particular frequency spectrum.
Where intensity-to-decibel conversion shows up in real work
Secondary-school and introductory college physics constantly assign table drills that convert measured intensities into decibel levels and back using L equals ten log ten of I over I0; a single trusted oracle speeds grading and demo setup without spreadsheet formula drift. Environmental and occupational noise programs document source intensities from equipment datasheets and need honest rejection of non-positive values rather than silent negative infinity from an unchecked logarithm.
Audio and acoustic consultants translate intensity estimates from free-field models into level language that stakeholders already understand, while keeping pressure-level workflows on a separate twenty-log path when microphones report pascals instead of watts per square metre. Firmware authors calibrating acoustic sensors or smart-home monitors convert linear intensity estimates into decibel readouts for UI and alarm thresholds.
If you later need sound pressure level with twenty log ten of p over p0, A-weighted equivalent continuous levels, octave-band summation, or waveform loudness metrics, treat those as separate search intents and landings rather than overloading this elementary intensity-to-decibel calculator page.
What you can do with it
Environmental noise estimates
Map intensity predictions from source models into dB labels for reports, rejecting zero or negative intensity instead of producing -Infinity.
FAQ
Can I set a custom reference I0?
Yes. Send reference (or I0 / I_ref) as a positive number in W/m².
Is this sound pressure level or intensity level?
Intensity level: ten times log10 of an intensity ratio. Sound pressure level uses twenty times log10 of a pressure ratio and is a different calculation.
What does it cost?
The browser tool is free and runs locally.
How many decibels does doubling the intensity add?
About 3 dB. Every tenfold increase in intensity adds exactly 10 dB, because the level is ten times the common logarithm of the ratio, and doubling sits at roughly three tenths of that step.
Why can't the intensity be zero or negative?
Because the logarithm of zero or of a negative number does not exist. The calculator turns such values away with a clear message instead of showing a level that has no physical meaning.
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/phys/sound-intensity-db \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"intensity":0.000001}'const res = await fetch("https://api.kit.forhosting.com/phys/sound-intensity-db", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"intensity": 0.000001
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/sound-intensity-db",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"intensity": 0.000001
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/sound-intensity-db", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"intensity":0.000001}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"intensity":0.000001}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/sound-intensity-db", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"intensity": 0.000001
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.sound_intensity_db",
"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
How sound intensity level is defined (L = 10 log10(I/I0))
This capability evaluates the closed form with deterministic floating-point arithmetic—no random seeds, no wall-clock timestamps, no network calls, and no model drift—so identical inputs always produce identical JSON. Validation still matters: the payload must be an object, intensity must be present and finite, and both intensity and any supplied reference must be strictly positive so the logarithm never receives a non-positive argument.
What you send and what you get back
Send intensity as a finite positive number in watts per square metre under the field intensity. A zero or negative custom reference likewise fails, because dividing by a non-positive I0 is not a physical level. Classic checks include intensity equal to the default reference giving zero decibels, intensity one times ten to the minus six giving sixty decibels against the default I0, and intensity equal to ten times a custom reference giving exactly ten decibels. Wire the free browser form for homework and quick sanity checks, then call the identical contract from scripts when you need bulk conversion of lab tables or firmware sensor calibrations. Aliases I, intensity_wm2, and i are accepted for convenience in scripts. Optionally send reference as a finite positive custom I0 in the same units; aliases include I0, I_ref, reference_intensity, and i0. When reference is omitted the conventional hearing threshold one times ten to the minus twelve watts per square metre is used and the response flag reference_is_default is true. Omitting intensity, sending NaN or Infinity, or providing zero or negative intensity fails with invalid_input and is not charged. On success the response echoes cleaned intensity and reference, reference_is_default, the dimensionless ratio I over I0, level_db as the sound intensity level in decibels, unit labels intensity_unit and reference_unit as W/m² plus level_unit as dB, and short formula and relation strings including the inverse I equals I0 times ten to the power of L over ten. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where intensity-to-decibel conversion shows 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
Homework and lab tables
Convert measured sound intensities (W/m²) to decibel levels with the standard I0 = 1e-12 reference so teachers and students share one ground-truth logarithm.
Sensor calibration and UI readouts
Turn linear intensity estimates from acoustic sensors into decibel displays and alarm thresholds using the same formula in browser demos and API pipelines.
Technical questions
What formula does this decibel calculator use?
Sound intensity level L = 10·log10(I/I0), where I is intensity in W/m² and I0 is the reference threshold (default 1×10⁻¹² W/m²).
What happens if intensity is zero or negative?
The request fails with invalid_input. The real logarithm is undefined for non-positive intensity, so the API rejects those values instead of returning -Infinity.