Angle Bisector Calculator
Find the three angle-bisector lengths of a triangle from its side lengths, plus the segments each bisector cuts, the angles, area and inradius, with a labeled diagram.
Input
Output
The triangle diagram will appear here.
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/angle-bisector-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"sideA": "7",
"sideB": "8",
"sideC": "9"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `angle-bisector-calculator` tool (Angle Bisector 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/angle-bisector-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Angle Bisector 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
Enter a triangle's three side lengths and get the length of each internal angle bisector, the two pieces each bisector cuts the opposite side into, the angles, area and inradius — with a labeled diagram.
The formulas
The bisector from the vertex opposite side a (adjacent sides b and c) has length:
t_a = √( b·c · (1 − a² / (b + c)²) )By the angle bisector theorem, it splits side a into pieces proportional to the adjacent sides: a·b / (b + c) and a·c / (b + c).
The angles come from the law of cosines, the area from Heron's formula, and the inradius is area / semi-perimeter. The incenter (where the three bisectors meet) lies r / sin(A/2) from vertex A along its bisector.
How to use it
- Enter sides a, b and c.
- Read each bisector length and the segments it creates, plus the triangle's angles, area and inradius.
If the sides don't satisfy the triangle inequality, you'll get an explanation instead. All calculations run in your browser.