Math
Square pyramid
Find volume, slant height and surface area of a right square pyramid.
Calculators / Math / Triangle circumcircle radius
Triangle circumcircle radius calculator
Find the radius of the circle passing through all three triangle vertices.
On this page
Circumcircle radius2.5units
Circumcircle diameter5units
Calculator controls
How to calculate
Find the radius of the circle passing through all three triangle vertices.
Circumcircle radius = a*b*c/(4*sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c))) units; Circumcircle diameter = a*b*c/(2*sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c))) units
Worked example
Triangle side a: 3; Triangle side b: 4; Triangle side c: 5.
Circumcircle radius: 2.5 units; Circumcircle diameter: 5 units.
Assumptions and limits
All three side lengths must form a nondegenerate triangle. The circumcircle passes through the three vertices; its radius differs from the incircle radius.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the radius of the circle passing through all three triangle vertices.
When this tool is useful
Circumcircle radius = a*b*c/(4*sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c))) units; Circumcircle diameter = a*b*c/(2*sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c))) units
Understanding your inputs
| Input | What to enter |
|---|---|
| Triangle side a | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Triangle side b | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Triangle side c | Enter a number of at least 1e-12 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
All three side lengths must form a nondegenerate triangle. The circumcircle passes through the three vertices; its radius differs from the incircle radius.
How is the result calculated?
Circumcircle radius = a*b*c/(4*sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c))) units; Circumcircle diameter = a*b*c/(2*sqrt((a+b+c)/2*((a+b+c)/2-a)*((a+b+c)/2-b)*((a+b+c)/2-c))) units