Choose a circle or a triangle. For a circle, start from the radius, diameter or circumference. For a triangle, use base and height, all three sides, or two sides and the angle between them.
Results are estimates for planning. Check the figures before you make a financial or health decision.
How the Triangle and circle area works
Circle: the calculator first finds the radius, from the diameter (half of it) or the circumference (divided by 2π). Then area = πr², circumference = 2πr and diameter = 2r.
Triangle, by method:
- Base and height: area = ½ × base × height. The height must be measured at a right angle to the base. The perimeter needs all three sides, so it is not shown.
- Three sides (Heron’s formula): with s as half the perimeter, area = √(s(s − a)(s − b)(s − c)). The tool checks that the sides can form a triangle, meaning each is shorter than the other two combined, and also gives the three angles.
- Two sides and the included angle: area = ½ × a × b × sin(angle). The third side comes from the cosine rule, giving the perimeter too.
Use any unit you like, but use the same one for every length. The area is in that unit squared. Results are rounded to six decimal places, and angles are entered in degrees.
Worked example
Using the default values in the calculator above:
| Input | Value |
|---|---|
| Shape | Circle |
| You know the circle's | Radius |
| Length | 5 |
Area: 78.539816 square units
| Radius | 5 |
|---|---|
| Diameter | 10 |
| Circumference | 31.415927 |
| Formulas | area = πr², circumference = 2πr |
Tips and common mistakes
Mixing units is the usual cause of wrong answers, so convert everything to one unit first. Do not use a slanting side as the height in the base-and-height method; the height is the straight-line distance from the base to the opposite corner.
For the angle method, make sure the angle sits between the two sides you entered. A circle’s diameter is twice its radius, so check which one you have measured. For other shapes such as rectangles or trapeziums, use the area calculator.
Frequently asked questions
How do I find the area of a triangle with three sides?
Use Heron’s formula. Work out s, half the sum of the sides, then take the square root of s(s − a)(s − b)(s − c). The calculator does this for you.
Can I find a circle's area from its circumference?
Yes. Divide the circumference by 2π to get the radius, then use area = πr². Choose circumference in the calculator and it does both steps.
Why does it say my sides cannot form a triangle?
Each side of a triangle must be shorter than the other two added together. If one side is as long as or longer than the other two combined, the sides cannot close up into a triangle.