Area Calculator
Calculate 2D surface area for common geometric shapes.
Area = Length × Width
Every formula is a rectangle in disguise
Area measures surface in square units, and most plane formulas descend from the rectangle'slength × width. A parallelogram is a rectangle with a slice moved from one end to the other, so it is base × height. A triangle is half a parallelogram, hence½ × base × height. A trapezoid averages its two parallel sides and multiplies by the height.
The word height means perpendicular height throughout, and this is where most errors originate. For a slanted parallelogram or a non-right triangle, the height is the straight-line distance between the base and the opposite vertex or side — not the length of a sloping side. Using the slant length always overstates the area.
Units are the other trap. Area scales with the square of length, so converting requires squaring the factor: 1 m² is 10,000 cm², not 100, because the conversion applies in both directions at once. For an irregular shape, decompose it into rectangles and triangles, compute each, and add — or subtract, where the shape has a hole in it.
Frequently Asked Questions
What is the formula for area of a rectangle?
Area = Length × Width.
What is the area formula for a trapezoid?
Area = ((a + b) / 2) × h, where a and b are parallel base lengths and h is height.
What are the area formulas for common shapes?
Rectangle l x w; triangle 1/2 x base x height; circle pi x r^2; trapezoid 1/2 x (a+b) x h; ellipse pi x a x b using the semi-axes; parallelogram base x perpendicular height. The height in a triangle or parallelogram is the perpendicular distance, not the slanted side.
How do I find the area of an irregular shape?
Divide it into shapes you can measure - rectangles, triangles and circle segments - calculate each, then add them. For a shape with a hole, calculate the outer area and subtract the inner. For genuinely curved outlines, approximating with many thin trapezoids converges quickly on the true area.