Area Calculator
Calculate the area and perimeter of common 2D shapes: square, rectangle, triangle, circle, trapezoid, parallelogram, and ellipse.
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How to use this calculator
Square: A=s². Rectangle: A=lw. Triangle: A=½bh. Circle: A=πr². Trapezoid: A=½(a+b)h. Parallelogram: A=bh. Ellipse: A=πab.
- 1
Select the shape from the dropdown menu.
- 2
Enter the required dimensions (length, width, radius, base, height, etc.).
- 3
The area and perimeter (or circumference) are calculated immediately.
- 4
For trapezoids and parallelograms, the third field is the height — enter it too.
Frequently asked questions
Which input boxes does each shape use?
Square and circle use only the first box (side or radius). Rectangle, triangle and ellipse use the first two (length and width, base and height, or the two semi-axes). Trapezoid and parallelogram use all three. Boxes a shape does not use are ignored, so a leftover value in them does not affect the result.
What do the three boxes mean for a trapezoid and a parallelogram?
For a trapezoid, a and b are the two parallel sides and the third box is the perpendicular height between them. For a parallelogram, a is the base, b is the slanted side and the third box is the perpendicular height onto the base. Area uses a and the height only, while the slanted side matters just for the perimeter.
Why is no perimeter shown for a triangle?
A base and a height do not fix the other two sides, so the perimeter cannot be found from them. The triangle option returns area = ½ × base × height and a note instead. For all three sides, with perimeter, angles and area, use the separate Triangle Calculator.
Is the trapezoid perimeter exact?
Only for an isosceles trapezoid, whose two non-parallel sides are equal. The calculator assumes that, finding each leg from the height and half the difference between the bases, and labels the result accordingly. For a trapezoid with unequal legs the area is still correct, but you must add the actual leg lengths yourself for the perimeter.
Is the ellipse perimeter exact?
No, it is an approximation and is labelled so. An ellipse has no simple closed-form perimeter; the tool uses Ramanujan’s first approximation, π[3(a+b) − √((3a+b)(a+3b))]. When a equals b it reduces to the circle’s 2πr exactly. The area πab is exact, and a and b are the semi-axes, meaning half the full width and height.
Does it convert units?
No. Enter every length in the same unit, and the area comes out in that unit squared while perimeter stays in the plain unit. Mixing metres and centimetres gives a meaningless result. Results are rounded to six decimal places with trailing zeros dropped.
What inputs are rejected?
Zero or negative dimensions give a “must be positive” error, and non-numeric entries do too. A parallelogram is also rejected when the slanted side is shorter than the height, since that shape cannot exist.
Area and perimeter of common 2D shapes
Formulas and what to enter
Pick a shape and fill in the boxes it needs. The calculator returns area and, where it can be found from the inputs, perimeter or circumference. Square area is s², rectangle lw, triangle ½bh, circle πr², trapezoid ½(a+b)h, parallelogram bh and ellipse πab. The parallelogram’s third box is its perpendicular height, not the slanted side, and mixing the two up is the commonest error.
| Shape | Boxes used | Area | Second output |
|---|---|---|---|
| Square | a | a² | 4a |
| Rectangle | a, b | a × b | 2(a + b) |
| Triangle | a = base, b = height | ½ × a × b | not available |
| Circle | a = radius | πa² | 2πa |
| Trapezoid | a, b, height | ½(a + b) × h | perimeter, equal legs assumed |
| Parallelogram | a, b, height | a × h | 2(a + b) |
| Ellipse | a, b = semi-axes | πab | approximate perimeter |
Worked example: a trapezoidal garden bed
A bed has parallel sides of 8 and 5 and is 4 high. The calculator gives an area of 26 square units, which is the average of the parallel sides, 6.5, times 4. The perimeter shows 21.544004, found by treating the two legs as equal: each leg is √(1.5² + 4²). If the bed is lopsided, keep the 26 for soil and measure the actual legs for the edging.
Worked example: circle versus ellipse
A circle of radius 3 has an area of 28.274334 and a circumference of 18.849556. An ellipse with semi-axes 5 and 3 has an area of 47.12389 and an approximate perimeter of 25.526986. A parallelogram with base 10, slanted side 6 and height 5 gives area 50 and perimeter 32, and the same base and height with a different slant angle would keep the area at 50 while changing the perimeter.
Choosing the right height
Height always means the perpendicular distance between the base and the opposite side, never a slanted edge. A rectangle’s width happens to be its height, which is why it needs only two boxes. For a triangle that sits on a sloped side, drop a perpendicular to the base line even if it falls outside the triangle. If you know the three sides instead, use the triangle calculator.
Rounding and units
Output is rounded to six decimal places, and trailing zeros are stripped, so 24.000000 shows as 24. Keep every dimension in one unit and read the area as that unit squared. Convert to square metres, acres or similar elsewhere, because this calculator does not change units.
Learn more from an authoritative source:
WikipediaSurface Area Calculator
Calculate the total surface area and lateral surface area of common 3D shapes: cube, rectangular box, sphere, cylinder, cone, and square pyramid.
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Cone Calculator
Calculate the volume, slant height, lateral surface area, and total surface area of a cone from its base radius and height.
Sphere Calculator
Calculate radius, diameter, surface area, and volume of a sphere from any one known measurement.
Cylinder Calculator
Calculate the volume, lateral surface area, total surface area, and base area of a cylinder from its radius and height.
Percentage Difference Calculator
Calculate the symmetric percentage difference between two values — useful when neither value is a reference baseline.
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →