Area calculator

What is area?

Area is the measure of the surface enclosed within the boundaries of a two-dimensional figure. It tells you how much flat space a shape covers and is always expressed in square units, such as square centimeters or square feet. Area is one of the most fundamental quantities in geometry and appears throughout architecture, construction, agriculture, design, and the sciences. Knowing how to compute the area of common shapes lets you estimate materials, plan layouts, and compare surfaces quickly.

Why area matters in everyday life

Area calculations show up far more often than most people realize. When buying paint, flooring, turf, or wallpaper, the quantity you need depends directly on the surface area to be covered. Gardeners use area to work out how much soil or fertilizer to spread, while farmers rely on it to plan planting and irrigation. In interior design, the area of a room determines carpet, tiling, and heating requirements. Understanding area also builds the spatial reasoning that underpins much of practical mathematics.

How the area calculator works

This calculator lets you pick a shape and then enter only the dimensions that shape requires. As soon as the necessary measurements are filled in, the area is computed instantly and shown in the unit you choose. Because each unit is convertible, you can enter lengths in centimeters and read the result in square meters or square feet without any manual conversion. The supported shapes are the square, rectangle, triangle, circle, trapezoid, parallelogram, and ellipse.

Formulas

Square

A square has four equal sides, so its area depends only on the side length: $A = a^2$ where $a$ is the length of a side.

Rectangle

The area of a rectangle is the product of its two side lengths: $A = a \times b$ where $a$ is the length and $b$ is the width.

For other ways to describe a rectangle, such as a side and the diagonal, use the Rectangle calculator.

Triangle

The area of a triangle is half the product of a base and the height drawn to that base: $A = \frac{1}{2} b h$ where $b$ is the base and $h$ is the height.

Circle

The area enclosed by a circle is proportional to the square of its radius: $A = \pi r^2$ where $r$ is the radius and $\pi$ is the mathematical constant, approximately 3.14159.

Trapezoid

The area of a trapezoid is the average of its two parallel sides multiplied by the height between them: $A = \frac{1}{2} (a + b) h$ where $a$ and $b$ are the parallel bases and $h$ is the height.

Parallelogram

The area of a parallelogram equals its base times its height: $A = b h$ where $b$ is the base and $h$ is the perpendicular height.

Ellipse

The area of an ellipse generalizes the circle formula using its two semi-axes: $A = \pi a b$ where $a$ is the semi-major axis and $b$ is the semi-minor axis.

Calculation examples

Square

A square with a side of 5 cm has an area of: $A = 5^2 = 25 \text{ cm}^2$

Rectangle

A rectangle with a length of 10 cm and a width of 7 cm has an area of: $A = 10 \times 7 = 70 \text{ cm}^2$

Triangle

A triangle with a base of 8 cm and a height of 6 cm has an area of: $A = \frac{1}{2} \times 8 \times 6 = 24 \text{ cm}^2$

Circle

A circle with a radius of 4 cm has an area of: $A = \pi \times 4^2 \approx 50.27 \text{ cm}^2$

Trapezoid

A trapezoid with bases of 6 cm and 4 cm and a height of 5 cm has an area of: $A = \frac{1}{2} (6 + 4) \times 5 = 25 \text{ cm}^2$

Parallelogram

A parallelogram with a base of 9 cm and a height of 5 cm has an area of: $A = 9 \times 5 = 45 \text{ cm}^2$

Ellipse

An ellipse with a semi-major axis of 6 cm and a semi-minor axis of 4 cm has an area of: $A = \pi \times 6 \times 4 \approx 75.40 \text{ cm}^2$

Notes

• Always enter every dimension in the same unit so the result is consistent.
• Make sure the height you use is the perpendicular distance to the chosen base, not a slanted side.
• The calculator can switch the result between metric and imperial square units automatically.
• To estimate flooring or land in square feet, the Square footage calculator is a convenient companion.

FAQs

What units is area measured in?

Area is measured in square units, such as square millimeters, square centimeters, square meters, square inches, square feet, and square yards. The unit you pick should match the scale of the object you are measuring.

How is area different from perimeter?

Area measures the surface enclosed by a shape, while perimeter measures the total length of its boundary. Two shapes can have the same perimeter but very different areas, and vice versa.

How do I find the area of a triangle without the height?

If you only know the three side lengths, you can use Heron’s formula instead. This calculator uses the base-and-height form, so you would first need to determine the height that corresponds to your chosen base.

Can a shape have zero area?

A genuine two-dimensional shape always has a positive area. An area of zero would mean the figure has collapsed into a line or a point and no longer encloses any surface.

Why is the area of a circle based on π?

The constant $\pi$ expresses the fixed ratio between a circle’s circumference and its diameter. It naturally appears when summing the infinitely many thin rings that make up a circle, which leads to the formula $A = \pi r^2$.