Area Calculator

Area is the amount of two-dimensional space a flat shape occupies, measured in square units such as square metres (m²), square centimetres (cm²) or square feet (ft²). This calculator computes the area — and, where it applies, the perimeter or circumference — for eight of the most common 2D shapes: rectangle and square, circle, triangle, trapezoid, ellipse, circle sector, parallelogram and rhombus. Pick a shape, choose your unit, type the measurements, and it returns the result instantly with a labelled formula, a visual preview, and automatic conversions into other units. It is handy for school and competitive-exam geometry, DIY and home projects, and Indian real-estate work where carpet area, plot size and tiling estimates matter.

Key Formulas

Each shape has its own formula. The eight built into this tool are:

Rectangle / Square: A = l × w (for a square the length and width are equal, so A = side²). Perimeter = 2(l + w).

Circle: A = π r², where r is the radius and π ≈ 3.14159. Circumference (the circle's perimeter) = 2π r.

Triangle: A = ½ × b × h, where b is the base and h is the perpendicular height to that base.

Trapezoid: A = ½ (a + b) × h, where a and b are the two parallel sides and h is the perpendicular distance between them.

Ellipse: A = π × a × b, where a and b are the semi-major and semi-minor axes (half of each full diameter).

Circle sector: A = ½ r² θ, where θ is the central angle in radians. If your angle is in degrees, convert first: θ = degrees × π / 180.

Parallelogram: A = b × h, the base times the perpendicular height (not the slanted side).

Rhombus: A = ½ × d₁ × d₂, using the two diagonals d₁ and d₂.

Worked Example

Suppose you want the area of a circular garden bed with a radius of 7 m. Using A = π r²: A = π × 7² = π × 49 ≈ 153.94 m². Its circumference, if you wanted to edge it with fencing, would be 2π × 7 ≈ 43.98 m. As a second example, a triangular plot with a base of 8 m and a perpendicular height of 6 m has area A = ½ × 8 × 6 = 24 m².

Tips

Always use the same unit for every length before you calculate; mixing metres and centimetres is a frequent source of errors. The height in triangle, parallelogram and trapezoid formulas must be the perpendicular height, measured at a right angle to the chosen base — not the length of a slanted edge. For tiling, flooring or paint, work out the area and then add roughly 10–15% extra for cuts, wastage and pattern matching. Square-unit conversions are the square of the linear conversion: since 1 m = 100 cm, 1 m² = 10,000 cm², and since 1 ft = 12 in, 1 ft² = 144 in². In Indian property contexts, 1 m² ≈ 10.76 sq ft and 1 sq yard (gaj) = 9 sq ft.

Common Mistakes

The most common error is forgetting the ½ factor in the triangle, trapezoid and rhombus formulas, which doubles the answer. Another is using the slant side instead of the perpendicular height for triangles and parallelograms. With circles, people often plug in the diameter where the formula expects the radius — remember r = diameter ÷ 2. For sectors, leaving the angle in degrees instead of converting to radians gives a wildly wrong result. Finally, reporting area in plain (linear) units instead of square units is a small but important slip: area is always in units squared.

Area vs. Perimeter

It helps to keep two different ideas separate. Area measures the space inside a shape and is given in square units (m², ft²). Perimeter measures the distance around its boundary and is given in plain linear units (m, ft). For a circle the perimeter has a special name, the circumference, calculated as 2π r. Two shapes can share the same perimeter yet have very different areas — among all shapes with a fixed perimeter, the circle encloses the most area, a fact known as the isoperimetric property. This calculator shows the perimeter or circumference alongside the area wherever it is meaningful for the chosen shape.

Real-World Uses

Area calculations turn up constantly in everyday life. Buying paint, wallpaper, turf or tiles all start from the area of the surface to be covered, plus an allowance for waste. Property and land dealings in India quote plot and carpet areas in square feet, square metres, square yards (gaj), acres and hectares, so being able to convert cleanly between them avoids costly misunderstandings — recall that 1 hectare = 10,000 m² ≈ 2.47 acres and 1 acre = 43,560 sq ft. Farmers size fields, designers lay out rooms and gardens, and students meet these formulas throughout school geometry. Whenever a real shape is irregular, the practical trick is to split it into the simple shapes above, find each area, and add them together.