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Area is the amount of surface a shape covers, and every shape has its own formula — a square's area is its side squared, a circle's is π times the radius squared. Painting a room, laying sod in a garden, estimating tiles, or solving a geometry problem: all of it comes down to applying the right formula to the right measurements.
Pick a shape, enter the dimensions, and the area is calculated instantly in the square of your unit (cm², m²…).
Area Calculator: step-by-step worked example
A trapezoid-shaped garden with parallel sides of 12 m and 8 m, 5 m apart
- Shape
- Trapezoid
- Lower base
- 12
- Upper base
- 8
- Height
- 5
- 1
Sum of the parallel sides
a + b
12 + 8 = 20 m
- 2
Average base
Mid-base = (a + b) ÷ 2
20 ÷ 2 = 10 m
- 3
Trapezoid area
Area = (a + b) ÷ 2 × h
10 × 5 = 50 m²
- 4
Check: rectangle + triangles
Area = short base × h + (long − short base) × h ÷ 2
8 × 5 + 4 × 5 ÷ 2 = 50 m²
- Rectangle (short base × h)40 m²80%
- Triangles10 m²20%
Good to know: The height is the PERPENDICULAR distance between the parallel sides, not the slanted side. Enter all sides in the same unit — the result is that unit squared (m → m²).
Area Calculator — how it works
Basic shapes and their formulas
| Shape | Area formula |
|---|---|
| Square | side × side |
| Rectangle | length × width |
| Triangle | (base × height) ÷ 2 |
| Circle | π × radius² |
| Trapezoid | (base₁ + base₂) ÷ 2 × height |
| Parallelogram | base × height |
Watch out for
- Unit consistency: all measurements must be in the same unit. Enter metres and the area is m²; enter centimetres and it's cm². Don't mix (one side in metres, another in centimetres).
- Height ≠ slant side: in a triangle or trapezoid, "height" is the perpendicular distance to the base, not the slanted edge. This is the most common mistake.
- Radius ≠ diameter: the circle formula uses the radius; if you have the diameter, halve it.
Practical uses
- Paint/plaster: find the wall area, multiply by the coverage per square metre (subtract doors and windows).
- Flooring: multiply the room area by the tile/laminate price per square metre and add about 10% for waste.
- Land/plots: split an irregular plot into triangles and trapezoids, then add the areas.
For a solid's capacity use a volume calculator; for the boundary length use a perimeter calculator.
Worked example
A circular pool with a radius of 5 m has a floor area of π × 5² = 3.14159 × 25 = 78.54 m². For comparison, a rectangular terrace 8 m by 5 m is 40 m², and a triangular garden corner with a 10 m base and 6 m height is 30 m². Note that in the triangle the height is the perpendicular distance to the base, not the slanted edge — the 6 m here is the perpendicular height; using the slanted side would give a wrong (larger) area.
Frequently asked questions
How do I calculate area?+
It depends on the shape: square is side², rectangle is length × width, triangle is (base × height) ÷ 2, circle is π × radius². Pick the shape in the tool and enter the dimensions.
What is the formula for the area of a circle?+
π × radius² (πr²). A circle with radius 5 has an area of 3.14159 × 25 = 78.54 square units. If you have the diameter, halve it first to get the radius.
Which height do I use for a triangle?+
The height perpendicular to the base you chose — not the length of the slanted side. This is the most common error. Multiply base by perpendicular height and divide by two.
What unit does the area come out in?+
The square of the length unit you enter: metres give m², centimetres give cm². All measurements must be in the same unit.
How do I find the square footage of a room?+
For a rectangular room, length × width. For irregular rooms, split into rectangles and add. For flooring, adding about 10% for waste is a good idea.
How is the area of a trapezoid calculated?+
Add the two parallel sides (bases), halve, and multiply by the height: (a + b) ÷ 2 × h. A trapezoid with bases 10 and 6 and height 4 has an area of 32 square units.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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