Math
Triangle incircle radius
Find the radius of the circle touching all three sides inside a triangle.
Calculators / Math / Triangle excircle radius
Triangle excircle radius calculator
Find the radius of the excircle opposite a selected triangle side.
On this page
Excircle radius opposite side a2units
Triangle area6units²
Calculator controls
How to calculate
Find the radius of the excircle opposite a selected triangle side.
Excircle radius opposite side a =
(sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c)))/((b+c-a)/2) unitsTriangle area =
sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c)) units²Worked example
- Triangle side a: 3
- Triangle side b: 4
- Triangle side c: 5
- Excircle radius opposite side a: 2 units
- Triangle area: 6 units²
Assumptions and limits
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. Side a identifies the excircle being calculated; it is not the incircle.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the radius of the excircle opposite a selected triangle side. An excircle touches one side and the extensions of the other two. Select side a deliberately when comparing results.
When this tool is useful
An excircle touches one side and the extensions of the other two. Select side a deliberately when comparing results.
Understanding your inputs
| Input | Example |
|---|---|
Triangle side a a | 3 |
Triangle side b b | 4 |
Triangle side c c | 5 |
Frequently asked questions
Which assumptions matter for this result?
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. Side a identifies the excircle being calculated; it is not the incircle.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.