Triangle Circumradius
The circumcircle passes through every vertex. Divide the product of the three sides by four times the area. In a right triangle the hypotenuse is the diameter, so the radius is half of it.
Your numbers
Circumradius
6.037cm
Area
31.305cm²
Circumference
37.93cm
Formula
Circumradius = Side a × Side b × Side c ÷ (4 × Area)
The closer the three points come to a straight line, the larger the circumcircle grows. Perfectly collinear points have no circle at all.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Side a (cm)The length of the first side. | 7 | 0 and up |
| Side b (cm)The length of the second side. | 9 | 0 and up |
| Side c (cm)The third side; it must be shorter than the other two combined. | 12 | 0 and up |
Step by step
Quick reference table
Results when only Side a (cm) changes and everything else stays put.
| Side a (cm) | Circumradius (cm) | Area (cm²) | Circumference (cm) |
|---|---|---|---|
| 3.5 | 10.126 | 9.332 | 63.63 |
| 5.25 | 6.472 | 21.901 | 40.67 |
| 7 | 6.037 | 31.305 | 37.93 |
| 10.5 | 6.197 | 45.75 | 38.94 |
| 14 | 7.064 | 53.511 | 44.38 |
What each result means
| Result | At default values |
|---|---|
| Circumradius (cm)Radius of the circle through every vertex, wrapping the shape. | 6.037 |
| Area (cm²)The space a shape covers — length squared. | 31.305 |
| Circumference (cm)The distance once around a circle. | 37.93 |
Common mistakes
The closer the three points come to a straight line, the larger the circumcircle grows. Perfectly collinear points have no circle at all.
Glossary
- Side a
- The length of the first side.
- Side b
- The length of the second side.
- Side c
- The third side; it must be shorter than the other two combined.
- Circumradius
- Radius of the circle through every vertex, wrapping the shape.
- Area
- The space a shape covers — length squared.
- Circumference
- The distance once around a circle.
Frequently asked questions
Q. How is Triangle Circumradius calculated?
Circumradius = Side a × Side b × Side c ÷ (4 × Area) — The circumcircle passes through every vertex. Divide the product of the three sides by four times the area. In a right triangle the hypotenuse is the diameter, so the radius is half of it.
Q. Can you walk through an example?
With Side a 7cm, Side b 9cm, Side c 12cm, the answer is Circumradius 6.037cm.
Q. What do I need to enter?
Enter Side a, Side b, Side c. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Side a (cm) moves the answer to Side a (cm) 3.5 → Circumradius (cm) 10.126 and Side a (cm) 14 → Circumradius (cm) 7.064. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
The closer the three points come to a straight line, the larger the circumcircle grows. Perfectly collinear points have no circle at all.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.