Sound intensity calculator
A 1 W source spreads its sound over a sphere, so 1 m away the intensity is 0.079577471546 W/m². Enter the acoustic power and the distance to get the intensity, the sphere area and the level in decibels. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Power
- 1
- Distance
- 1
- Intensity
- 0.0795774715
- Intensity unit
- W/m²
- Sphere area
- 12.5663706144
- Sphere area unit
- m²
A sound intensity calculator turns acoustic power and radial distance into the power per unit area carried by a sound wave. The model is the classic isotropic point source in free field: all power spreads uniformly over a sphere of radius r. Negative power or negative distance are likewise rejected as outside the physical domain of this calculator.
What sound intensity means for a point source
Sound intensity is the average acoustic power flowing through a unit area perpendicular to the direction of propagation. For a compact source that radiates equally in all directions into free space, energy conservation requires that the same total power P cross every sphere centered on the source. The surface area of that sphere is four pi times r squared, so the intensity at distance r is simply I equals P divided by four pi r squared.
Units follow at once: watts of power over square metres of area give watts per square metre. Doubling the distance quarters the intensity because area grows with the square of radius—the inverse-square law familiar from astronomy and radiation problems. Classroom problems usually assume this ideal free-field model; rooms with reflecting walls, baffles, or highly directional loudspeakers need different geometry factors and are outside the scope of this tool.
Intensity is not the same quantity as sound pressure level on a meter, though for plane progressive waves in air the two are related through the characteristic impedance; here the output is the power-based intensity itself, plus an optional level in decibels when I is positive using the conventional reference I-zero of ten to the minus twelve watts per square metre. Teachers care about the zero-distance rejection as much as the arithmetic path, because a student who sets r to zero has left the domain of spherical spreading.
The check path recomputes area and intensity with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets.
Practical tips, limits, and related searches
Keep power and distance inside the published absolute range so four pi r squared and the quotient cannot overflow into non-finite results that the solver must reject. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. Use consistent SI units: power in watts and distance in metres yield intensity in watts per square metre; if your problem states milliwatts or centimetres, convert first.
Prefer this capability when you already have total radiated power and a radial distance under free-field isotropic assumptions; if your source is a word problem, extract those two numbers and convert units first.
What you can do with it
Homework checks for inverse-square intensity
Students enter acoustic power and distance from textbook free-field problems and compare hand-written I and sphere area against a deterministic result before submitting.
Pre-flight before noise-control estimates
Pipelines convert source power and range into free-field intensity first, then branch to dB thresholds or PPE rules only when intensity is finite and positive.
FAQ
What is the formula for sound intensity from a point source?
For an isotropic point source in free field, I = P / (4πr²), where P is acoustic power in watts and r is distance in metres. Intensity is then in W/m².
Can power be zero?
Yes. Zero acoustic power yields zero intensity at every finite distance. Negative power is rejected.
Does this return sound pressure level (SPL)?
No. It returns power-based intensity I in W/m² and, when I > 0, an intensity level in dB relative to I₀ = 10⁻¹² W/m². It is not a pressure-microphone SPL calculator.
Is the sound intensity calculator free?
The browser tool is free and runs locally.
How much does sound intensity drop when the distance doubles?
It drops to a quarter. The same power is spread over a sphere whose area grows with the square of the distance, which is the inverse-square law also used in astronomy and radiation problems.
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 \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"power":1,"distance":1}'const res = await fetch("https://api.kit.forhosting.com/phys/sound-intensity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"power": 1,
"distance": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/sound-intensity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"power": 1,
"distance": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/sound-intensity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"power":1,"distance":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"power":1,"distance":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/sound-intensity", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"power": 1,
"distance": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.sound_intensity",
"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 | 1000000000000 |
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
When distance is zero the formula divides by zero, so the API returns a clear invalid_input error instead of inventing an infinite intensity.
How to call the API and what comes back
Power must be non-negative; distance must be strictly positive. Values of distance whose absolute value is at or below one times ten to the minus fifteen are treated as zero and rejected, matching the product rule that zero range makes intensity undefined. Send a JSON body with two required finite numbers: power (aliases P, acoustic_power, source_power, watts) and distance (aliases r, radius, range, metres, meters). Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded power and distance, sets intensity to I in W/m², intensity_unit to the string W/m², sphere_area to four pi r squared in square metres, sphere_area_unit to m², formula to the classic I equals P over four pi r squared string, model to isotropic_point_source, reference_intensity_I0 to the air reference used for decibels, message to a short English summary, and steps to an ordered array of substitution lines. When intensity is strictly positive the response also includes intensity_level_db equal to ten times log base ten of I over I-zero. Failed validation—missing fields, non-finite numbers, values outside absolute limits, negative power, negative distance, or zero distance—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
When teaching, pair examples: one watt at one metre gives I equals one over four pi watts per square metre; the same power at two metres is four times weaker; zero power yields zero intensity at every finite range; and distance equals zero demonstrates the hard invalid_input path. This landing targets people searching for a sound intensity calculator, acoustic power over area, or I equals P over four pi r squared online; it is not a sound pressure level meter, not a room-acoustics simulator with reverberation time, and not a directional beam pattern tool. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set distance to zero. Round-trip checks are easy: recompute four times pi times r squared by hand, divide power by that area, and confirm it equals the published intensity within the same twelve-decimal rounding, then optionally check ten log ten of I over one picowatt per square metre against intensity_level_db.
Integration use cases
Unit tests for audio and simulation helpers
Generate known-good intensities at one metre, two metres, and zero-power cases plus deliberate zero-distance rejections for coding kata expected values.
Technical questions
What happens when distance is zero?
The spherical-spreading formula divides by zero. This tool returns invalid_input instead of an infinite intensity.