Circumcenter Calculator
With the circumcenter calculator you'll discover how to use the coordinates of a triangle's vertices to get the coordinates of the circumcenter.
Circumradius R4.131182circle through all three vertices
Circumcircle area53.616515
Circumcircle circumference25.956984
Inradius r1.936492largest circle that fits inside
Incircle area11.780972
Euler distance1.032796between the two centres, √(R² − 2Rr)
Triangle area20.333163
Working
| Semi-perimeter s | 10.5 |
| Area (Heron) | √(s(s−a)(s−b)(s−c)) = 20.333163 |
| Height on side a | 2 × area ÷ a = 6.777721 |
| Inradius | area ÷ s = 1.936492 |
| Circumradius | abc ÷ 4·area = 4.131182 |
| Angle sum | 180° (always 180°) |
The formula
R = abc ÷ 4A, r = A ÷ s
What always holds
- The three angles add to 180°, without exception.
- Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
- The longest side always faces the largest angle.
Area = ½ × base × heightfor any triangle, with the height measured perpendicular to that base.
Which formula to reach for
With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.