Area Calculator for Common Shapes

Area formulas for seven common two-dimensional shapes

Area measures the amount of two-dimensional space enclosed within a boundary. It is expressed in square units: square centimetres, square metres, square feet, square inches, or any other squared unit of length. Whether you are tiling a floor, planning a garden, sizing a canvas, or completing a geometry exercise, knowing how to calculate area quickly and accurately is a fundamental skill.

This calculator supports seven shapes: rectangle, square, triangle, circle, trapezoid, parallelogram, and ellipse. Each shape has a distinct formula, and the calculator shows you which formula it applied alongside the numerical result. That transparency makes it easy to verify the answer and to understand the underlying mathematics rather than just accepting a number.

To use the calculator, select your shape from the dropdown menu, enter the relevant dimensions in the corresponding input fields, and click Calculate area. Only the fields relevant to the selected shape will be used. For example, if you choose Circle, only the Radius field matters. Other fields can be left blank or ignored.

The rectangle formula is Length times Width. This is the most fundamental area formula: it counts how many unit squares fit inside the rectangle. A square is a special case of a rectangle where all sides are equal, so its formula is simply Side squared. The triangle formula is one half times Base times Height, where height is the perpendicular height from the base to the opposite vertex, not the length of a slanted side.

The circle formula is pi times the radius squared, where pi is approximately 3.14159. The radius is the distance from the centre of the circle to its edge. If you know the diameter instead, divide it by two to get the radius before entering it. The trapezoid formula is one half times the sum of the two parallel sides times the height. The parallelogram formula is simply Base times Height, where again the height is perpendicular to the base. The ellipse formula is pi times the semi-major axis times the semi-minor axis.

Practical uses for area calculations

Area calculations come up in many real-world contexts beyond formal geometry. In home improvement, you calculate the floor area of a room to know how much flooring to buy. In landscaping, you calculate the area of a lawn to know how much fertilizer or seed to apply. In construction, you calculate the surface area of walls to know how much paint to buy. In fabric and textiles, you calculate the area of material needed to cut a garment piece. In agriculture, field area directly determines how much seed, water, and fertilizer a crop requires.

In the classroom, area problems appear from primary school through advanced geometry and calculus. The basic formulas for rectangles and triangles are introduced early, and more complex shapes like trapezoids and ellipses appear in secondary school. This calculator is useful for checking homework, confirming test prep answers, and building intuition about how dimensions relate to area.

One important distinction is the difference between area and perimeter. Area measures the space inside a shape, while perimeter measures the total length of its boundary. They are related but independent: two shapes with the same perimeter can have very different areas, and vice versa. If you need perimeter calculations, use the separate perimeter calculator available on this site.

Notes on units and precision

The calculator works with whatever unit you enter. If you enter dimensions in metres, the area result is in square metres. If you enter dimensions in feet, the result is in square feet. The calculator does not convert between units, so make sure all your inputs use the same unit before entering them. Mixing metres with feet will give a result that is numerically incorrect for either unit system.

Results are rounded to two decimal places for readability. For very large or very small dimensions, the displayed result may appear to be zero due to rounding, but the underlying calculation is still performed with full floating-point precision. If you need more decimal places for a precision application, the underlying formulas shown in the result let you verify the calculation manually.