Circumscribed Circle Calculator
The circumscribed circle calculator will help you study the circumradius as well as other properties of the circle circumscribed about a triangle.
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.