Semicircle area and perimeter calculator
Enter a radius and get both measures of a half disk: a radius of 1 gives an area of half π and a perimeter of π plus 2, because the flat diameter is part of the outline. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Radius
- 5
- Area
- 39.2699081699
- Perimeter
- 25.7079632679
- Arc length
- 15.7079632679
- Diameter
- 10
A semicircle is half of a full disk cut along a diameter, leaving a curved arc and a straight base. Given a single non-negative radius, this calculator returns the enclosed area and the full perimeter that adds the arc length to the diameter. Zero is allowed and yields zero area and perimeter for a degenerate bound.
How semicircle area and perimeter are computed from radius
Label the distance from the center of the full circle to any point on the curved edge as the radius r. The area of a solid semicircle is exactly half the classic disk area: area equals one-half pi times r squared, written A = (1/2) π r². That measures the planar region inside the arc and down to the flat diameter.
The curved arc alone has length π r, which is half the full circumference 2 π r. The flat base is the diameter of length 2 r. The perimeter of the closed semicircular region is therefore the sum of arc and diameter: P = π r + 2 r, or equivalently P = r(π + 2).
Classic checks include radius one, which yields area about 1.570796326795 and perimeter about 5.14159265359; radius two, which yields area about 6.28318530718 and perimeter about 10.28318530718; and radius five, a common textbook case with area about 39.269908169872 and perimeter about 25.708. Because the path uses only multiplication, addition, a fixed half factor, and Math.PI, it is deterministic, O(1), and free of iterative solvers.
What you send and what you get back
Provide one required finite number: radius is the radius of the semicircle and must be non-negative. Zero is accepted and produces area zero and perimeter zero. Example checks: radius one yields area half pi and perimeter pi plus two; radius five scales area by r squared and perimeter linearly with r; a radius of minus three fails naming the field and the non-negative rule.
Wire the free browser tool for quick sanity checks, then call the identical contract from scripts for bulk evaluation without reimplementing the semicircle formulas in every language. Invalid input is not charged, so exploratory validation in CI stays cheap while production calls remain predictable.
Where semicircle calculations show up in real work
Secondary-school and college plane-geometry courses constantly ask students for the area and perimeter of a semicircle given only the radius, and often distinguish the arc length from the full perimeter that includes the diameter on the same problem set; a trusted calculator with a strict non-negative radius gate speeds homework grading and removes spreadsheet mistakes where someone uses the full-disk area or forgets the diameter in the perimeter.
Architecture, window fabrication, and metalwork size half-round arches, rose windows, and decorative half-circles from outer or design radius; area feeds glass and fill estimates while perimeter informs trim, gasket, and railing lengths. Landscape and civil plans place half-circle beds, turnarounds, and paved aprons; area drives planting or paving takeoffs and perimeter drives edging. Game, graphics, and CAD libraries store half-disk colliders and primitives; deterministic area and perimeter support debug readouts and material estimates without a full mesh library.
If you later need a full circle, a circular sector of arbitrary angle, a circular segment, or a solid hemisphere in 3D, treat those as separate search intents rather than overloading this semicircle landing.
What you can do with it
Homework and exam checks
Compute semicircle area and perimeter from radius, and reject a negative radius with a clear error.
Arches, half-round windows, and trim
From design radius, recover fill area and total edge length including the flat diameter base.
Half-disk metrics in games and CAD
Turn a single radius into area and perimeter for layout, material estimates, and property panels.
FAQ
What formulas does this calculator use?
area = (1/2) π r²; perimeter = π r + 2 r (arc length plus diameter).
What happens if the radius is negative?
The radius must be a finite non-negative number; the error message names the field and states that the radius must not be negative.
Is zero allowed?
Yes. A zero radius yields area zero and perimeter zero (a degenerate semicircle). Only strictly negative values are rejected.
What does it cost?
The browser tool is free and runs locally.
Does the perimeter include the diameter?
Yes. The perimeter is the arc, π times the radius, plus the straight diameter, twice the radius. For a radius of 5 that makes about 25.708 in total.
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/geom/semicircle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"radius":5}'const res = await fetch("https://api.kit.forhosting.com/geom/semicircle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"radius": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/semicircle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"radius": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/semicircle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"radius":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"radius":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/semicircle", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"radius": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.semicircle",
"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
A missing, non-finite, or negative radius is rejected with a clear invalid_input error instead of a silent nonsense area. No network calls, no random sampling, and no floating-point surprises beyond ordinary IEEE-754 arithmetic on the radius you provide.
How semicircle area and perimeter are computed from radius
Huge magnitudes can still overflow IEEE-754 double range; when intermediates are non-finite the request fails with a clear overflow message instead of returning Infinity in JSON. That closed form matches elementary geometry textbooks and keeps automated graders aligned with hand computation on the same radius.
What you send and what you get back
Missing fields, empty strings, non-numeric text, NaN, Infinity, and any negative radius are rejected with invalid_input and are not charged. On success the JSON response returns radius, area, perimeter, arc_length, diameter, formula set to the half-disk identities, and method set to semicircle_half_pi_r2_perimeter_pi_r_plus_2r so logs and teaching UIs can document the algorithm. API pricing is the published base of $0.002 per successful item.
Where semicircle calculations show up in real work
Because this capability is a pure parse engine, failed validation does not consume balance and successful runs stay at $0.002 per item.
Technical questions
Does the perimeter include the diameter?
Yes. arc_length is the curved half alone (π r); perimeter adds the flat diameter (2 r) for π r + 2 r overall. That is the closed boundary of the semicircular region.