Math
Triangle circumcircle radius
Find the radius of the circle passing through all three triangle vertices.
Calculators / Math / Triangle incircle radius
Triangle incircle radius calculator
Find the radius of the circle touching all three sides inside a triangle.
On this page
Incircle radius1units
Triangle area6units²
Calculator controls
How to calculate
Find the radius of the circle touching all three sides inside a triangle.
Incircle radius =
(sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c)))/((a+b+c)/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
- Incircle radius: 1 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. Degenerate or nearly flat triangles can produce unstable area estimates.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the radius of the circle touching all three sides inside a triangle. Heron’s formula gives area, which is divided by the semiperimeter to obtain the incircle radius.
When this tool is useful
Heron’s formula gives area, which is divided by the semiperimeter to obtain the incircle radius.
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. Degenerate or nearly flat triangles can produce unstable area estimates.
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.