Area of a Circle
The area of a circle is π times the radius squared: S = πr². If you know the diameter, just halve it.
Solution
Where the formulas come from. All area formulas grow out of the rectangle's a · b. A parallelogram rearranges into a rectangle, a triangle is half a parallelogram, a trapezoid is its “average width” times the height. The circle's πr² comes from slicing the circle into thin sectors. The calculator shows the formula and the substitution for every shape — ready to copy into a notebook.
FAQ
How do you find a triangle's area from the sides alone?
With Heron's formula: compute the semi-perimeter p = (a + b + c) / 2, then the area is the square root of p(p−a)(p−b)(p−c). No height needed. The calculator has a switch for this method.
What value of π should I use?
π ≈ 3.14159… School problems usually take 3.14; the calculator uses higher precision. If the problem says “take π = 3.14”, the answer may differ slightly from the calculator's — that is normal.
What units does the area come in?
Square units: dimensions in centimeters give cm², in meters — m². Just make sure all dimensions of one shape use the same unit.
Why isn't a parallelogram's area the product of its sides?
Because it leans: the height is shorter than the slanted side. The product of the sides would be the area of a rectangle with those sides, and a parallelogram with the same sides is always “lower”. Hence the height in the formula: S = a · h.
Free online area calculator for geometric shapes with formulas and explanations: circle, triangle, square, rectangle, trapezoid, and parallelogram. Every shape gets its formula, your dimensions substituted, and the answer.
The triangle is computed two ways: via base and height or from three sides with Heron's formula, including the semi-perimeter step. The circle additionally gets its circumference, the square and rectangle their perimeter.
Everything is computed in the browser. Handy for geometry classes, for home projects — the area of a room or material — and anywhere you need a shape's area with the working shown.