Math
Area Calculator
Pick a shape, type its dimensions, and the area calculator returns the area in square units with the formula it used, the substituted numbers, and a labeled diagram.
It covers rectangles, squares, triangles (including Heron's formula and two-sides-plus-angle), circles, trapezoids, parallelograms, rhombuses, ellipses, regular polygons, sectors, and kites.
Pick the shape; the fields below change to match its formula.
Lengths use this unit; area is reported in square units of it.
The longer side of the rectangle.
The shorter side of the rectangle.
Try an example
Result
Area
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- Area with units
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- Perimeter
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- Formula
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Area formulas for every shape on this page
| Shape | Formula | What the letters mean |
|---|---|---|
| Rectangle | A = l × w | length and width |
| Square | A = s² | side |
| Triangle (base, height) | A = ½ b h | base and perpendicular height |
| Triangle (three sides) | A = sqrt(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 | Heron's formula |
| Triangle (SAS) | A = ½ a b sin C | two sides and the included angle |
| Circle | A = πr² | radius |
| Trapezoid | A = ½ (a + b) h | the two parallel bases and the height |
| Parallelogram | A = b h | base and perpendicular height |
| Rhombus / kite | A = ½ p q | the two diagonals |
| Ellipse | A = π a b | semi-major and semi-minor axes |
| Regular polygon | A = n s² / (4 tan(180°/n)) | number of sides and side length |
| Sector | A = (θ/360) πr² | central angle in degrees and radius |
Why area uses square units
Area counts how many unit squares cover a shape. If the sides are measured in centimeters, the area is in square centimeters (cm²). The calculator labels every area with the square unit and every length (perimeter, diagonal) with the plain unit so they never get mixed up.
How to use it
- Choose the shape from the list. For a triangle, also choose what you know: base and height, all three sides, or two sides and the angle between them.
- Enter the dimensions in the same unit; pick that unit so the result is labeled correctly.
- Read the area, then check the substitution line to see exactly which numbers went into the formula.
- Use the perimeter and extra values (diagonal, apothem, arc length) when the next question asks for them.
How to read the answer
Circle, ellipse, and sector areas show an The answer kept as a fraction or radical instead of a rounded decimal. in terms of π (for example 25π) next to the decimal. Heron's-formula and regular-polygon areas show a simplified A root expression written with the √ symbol, such as a square root. when one exists (a hexagon with side 6 has area 54√3). Everything else is a plain decimal rounded to four places.
Common mistakes and edge cases
- Using a slanted side as the height. Height is always the perpendicular distance to the base.
- Forgetting the ½ in the triangle formula — a triangle is half of the parallelogram with the same The number being raised to a power, or the side a shape's height is measured from. and height.
- Averaging the trapezoid bases and then forgetting to multiply by the height.
- Entering the full axes of an ellipse instead of the semi-axes (halves). A 12 by 8 ellipse has a = 6 and b = 4.
- Three sides that break the triangle inequality (like 1, 2, 3) do not form a triangle; the calculator says so instead of returning 0.
- A zero or negative dimension is rejected — a real shape has positive size.
Worked examples
Rectangle 12 by 8
Area
96
Triangle with base 10 and height 6
Area
30
Triangle with sides 7, 8, 9 (Heron)
Area
26.8328
Triangle from two sides and 60° angle
Area
24.2487
Circle radius 5 (25π)
Area
78.5398
Trapezoid bases 8 and 14, height 5
Area
55
Regular hexagon side 6 (54√3)
Area
93.5307
Ellipse with semi-axes 6 and 4 (24π)
Area
75.3982
Sector of 60° in a radius-5 circle
Area
13.09
Decimal rhombus diagonals 7.5 and 4.2
Area
15.75
Impossible triangle 1, 2, 3
Area
—
Zero width rectangle
Area
—
Frequently asked questions
What is the difference between area and perimeter?+
Area is the amount of surface inside a shape, measured in square units. Perimeter is the distance around the outside, measured in plain length units. A 12 by 8 rectangle has area 96 square units and perimeter 40 units.
How do I find the area of a triangle without the height?+
If you know all three sides, use Heron's formula: find s = (a + b + c)/2, then A = sqrt(s(s−a)(s−b)(s−c)). If you know two sides and the angle between them, use A = ½ab·sin(C). Both modes are on this page.
Why is the area of a triangle half the base times height?+
Two copies of any triangle fit together into a parallelogram with the same base and height. The parallelogram's area is base × height, so each triangle is half of that.
What are the bases of a trapezoid?+
The two parallel sides. It does not matter which is on top; the formula averages them and multiplies by the perpendicular height between them.
How is the area of an ellipse calculated?+
A = πab, where a and b are the semi-axes (half the full width and half the full height). When a = b the ellipse is a circle and the formula becomes πr².
How do I find the area of a regular hexagon?+
Use A = (3√3/2)s² for a hexagon with side s, or the general regular-polygon formula A = ns²/(4·tan(180°/n)) with n = 6. Side 6 gives 54√3 ≈ 93.53.
Can I convert the area to a different unit?+
Convert the lengths first, then compute — or remember that square units scale by the square of the length factor: 1 m² = 10,000 cm² because 1 m = 100 cm and 100² = 10,000.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026