Area of shapes
Math & numbersHow big is the area of this shape?
Area and perimeter of rectangles, circles, triangles and eight more shapes, drawn to scale.
What you enter stays on your device while you use this tool. Opening a shared link sends the settings in its address to HowToolbox to prepare the page.
Area
12 m²
Perimeter 14 m
Formula and units
- Formula
- A = w × h, P = 2 × (w + h)
- Area in other units
- 129.167 ft²
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Area and perimeter of rectangles, circles, triangles and eight more shapes, drawn to scale.
How to use
- Pick the shape.
- Enter its measurements and choose the unit beside any field: every length follows it.
- Read the area and the perimeter; the drawing shows the shape to scale with its measurements.
How it works
Area is how much flat surface a shape covers, counted in squares of the length unit: a 4 m × 3 m floor holds twelve 1 m × 1 m squares, so its area is 12 m². The perimeter is the distance around the edge, here 4 + 3 + 4 + 3 = 14 m.
Each shape has its own formula. A rectangle is width × height, a circle π × r², and a triangle from its three sides uses Heron's formula: with p half the perimeter, the area is √(p × (p − a) × (p − b) × (p − c)). For sides 3, 4 and 5, p = 6 and the area is √(6 × 3 × 2 × 1) = 6. A ring is the big circle minus the hole, and a sector is the share θ / 2π of a whole circle. Source: CRC Standard Mathematical Tables and Formulae.
Every formula here is exact except an ellipse's perimeter, which has no simple closed form: Ramanujan's approximation is used, accurate to a few parts in a hundred thousand. The trapezoid has two legs of equal length. For an irregular area, split it into these shapes and add them up.
Worked example
What is the area of a rectangle 4 m long and 3 m wide?
- A = 4 × 3 = 12 m².
The area is 12 m².
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Frequently asked questions
How do I find the area of an L-shaped room?
Split it into two rectangles, work out each one and add them together. The perimeter of the whole room is not the sum of the two perimeters, so measure that around the walls.
Why does the area grow four times when I double the sides?
Area is two-dimensional: doubling the width and the height doubles both factors, so the area grows 2 × 2 = 4 times. The perimeter only doubles.
How do I convert square feet to square metres?
Change the unit beside any field: the lengths and the area follow, and the other-units row shows the area in the other system. One square metre is about 10.76 square feet.
What is the difference between a radius and a diameter?
The radius goes from the centre to the edge; the diameter goes right across, so it is twice the radius. Halve a measured diameter before entering it as the radius.
Does this include extra material for cuts and waste?
No. The result is the geometric area. Allow separately for cuts, overlaps and waste when buying flooring or other materials.
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