Area of a Sector Calculator
Calculate a circle sector's area, arc length, perimeter, chord length and segment area. Enter any two of radius, central angle, arc length or sector area, in degrees or radians, and get a labeled diagram.
Input
Provide any TWO of radius, central angle, arc length and sector area — the rest are solved.
Output
The sector diagram will appear here.
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/area-of-a-sector-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"radius": "10",
"angle": "60",
"angleUnit": "degrees"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `area-of-a-sector-calculator` tool (Area of a Sector Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/area-of-a-sector-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Area of a Sector Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
Guides
Find the area, arc length, perimeter, chord length and segment area of a circle sector. Enter any two of radius, central angle, arc length or sector area — the others are solved for you — and get a labeled diagram.
The formulas
With the central angle θ in radians and radius r:
arc length = r × θ
sector area = ½ × r² × θ
perimeter = r × θ + 2r
chord = 2r × sin(θ / 2)
segment area = ½ × r² × (θ − sin θ)In degrees, θ = degrees × π / 180, so the sector area is (degrees / 360) × π r².
Solving from other pairs
- Radius + arc length →
θ = arc / r - Radius + sector area →
θ = 2 × area / r² - Arc length + angle →
r = arc / θ - Sector area + angle →
r = √(2 × area / θ) - Arc length + sector area →
r = 2 × area / arc
How to use it
- Enter two known values, picking degrees or radians for the angle.
- Read the results and the diagram, or copy the SVG source.
The segment is the region between the chord and the arc; the triangle area is the part of the sector inside the chord. All calculations run in your browser.