Area Calculator — Circle, Rectangle, Triangle & More

Shape

A = πr²

Radius (r)

units

0.1200

Circle — Area

—sq units

Formula: A = πr²

Area Formulas

CircleA = πr²

RectangleA = l × w

SquareA = s²

TriangleA = ½ × b × h

TrapezoidA = ½(a+b) × h

ParallelogramA = b × h

What is a Area?

The Area Calculator computes the enclosed two-dimensional space — and, where applicable, the perimeter or circumference — of six common geometric shapes: circle, rectangle, square, triangle, trapezoid, and parallelogram. Switch between shapes using the shape selector, enter the relevant dimensions, and the result updates instantly with the applicable formula shown.

Area is one of the most practical mathematical concepts in everyday life. Whether you are estimating how many floor tiles are needed for a room, calculating the amount of paint for a wall, determining the size of a plot of land, or solving a school geometry problem, the same fundamental area formulae apply. In Indian construction and real estate, area is typically measured in square metres (sq m), square feet (sq ft), or square yards, and accurate calculation is essential for both pricing and compliance with RERA carpet-area disclosure norms.

This calculator is also a natural companion to the Pythagorean Theorem Calculator when working with right triangles — you can use Pythagoras to determine a missing side and then feed those dimensions directly into the area calculation. For triangles where three sides are known (rather than base and height), the Triangle Calculator computes area via Heron's formula and additionally gives all angles and the perimeter.

How to use this Area calculator

Select your Shape — click the shape that matches what you need to measure: Circle, Rectangle, Square, Triangle, Trapezoid, or Parallelogram. The input fields update immediately to show only the dimensions relevant to that shape.
Enter the dimensions — use the sliders or type values directly. For a Circle: enter the radius (not the diameter). For a Rectangle: enter length and width. For a Square: enter one side length. For a Triangle: enter the base and the perpendicular height (not the slant height). For a Trapezoid: enter both parallel bases and the perpendicular height. For a Parallelogram: enter the base and the perpendicular height.
Read the Area result — the primary result card displays the area in square units of your input. If you entered metres, the result is in sq m.
Check the Perimeter / Circumference — for circle, rectangle, and square, the boundary length is shown below the area. Use this to calculate fencing, skirting, or framing material needs.
Switch shapes for comparison — if you are deciding between a circular and rectangular garden of similar dimensions, toggle between shapes and compare areas to see which uses more space.

Formula & Methodology

CircleArea = πr²Circumference = 2πr- r = radius; π ≈ 3.14159265

RectangleArea = l × wPerimeter = 2(l + w)- l = length; w = width

SquareArea = s²Perimeter = 4s- s = side length

TriangleArea = ½ × b × h- b = base; h = perpendicular height

TrapezoidArea = ½ × (b₁ + b₂) × h- b₁ = parallel base 1; b₂ = parallel base 2; h = perpendicular height

ParallelogramArea = b × h- b = base; h = perpendicular height (not slant height)

Worked example — tiling a living room:

A rectangular living room in a Mumbai apartment is 5.5 m long and 4.2 m wide. The owner wants to tile the floor using 60 cm × 60 cm tiles.

Step 1 — Room area:Area = 5.5 × 4.2 = 23.1 sq m

Step 2 — Tile area:Each tile = 0.6 × 0.6 = 0.36 sq m

Step 3 — Number of tiles:23.1 / 0.36 = 64.17 → round up to 65 tiles (plus 10% wastage allowance ≈ 72 tiles total)

Step 4 — Perimeter (for skirting):P = 2(5.5 + 4.2) = 2 × 9.7 = 19.4 m of skirting required

Assumption: All formulas assume Euclidean (flat) geometry. For extremely large land parcels, the curvature of the Earth introduces a small error, but for any plot up to a few square kilometres this is negligible. The triangle formula assumes the height is the true perpendicular height to the base — using the slant side instead of the true height is the most common mistake.

Frequently Asked Questions

What is an area calculator and what shapes does it support?

An area calculator computes the two-dimensional space enclosed by a geometric shape given its key dimensions. Our Area Calculator supports six common shapes: circle, rectangle, square, triangle, trapezoid, and parallelogram — covering the shapes most frequently encountered in school mathematics, construction, land measurement, and interior design.

What is the formula for the area of a circle?

The area of a circle is A = πr², where r is the radius and π ≈ 3.14159. The circumference (perimeter) is C = 2πr. For a circular plot with radius 7 metres, area = π × 7² ≈ 153.94 sq m. In Indian land measurement contexts, this is often converted to square yards or bigha depending on the state.

How do I calculate the area of a rectangle?

The area of a rectangle is A = length × width, and the perimeter is P = 2(length + width). A rectangular room 12 m long and 9 m wide has an area of 108 sq m and a perimeter of 42 m. This is the most common area calculation in construction, flooring, and room painting estimates in India.

What is the formula for the area of a triangle?

The area of a triangle using base and height is A = ½ × base × height. For a triangular plot of land with a base of 20 m and perpendicular height of 15 m, the area is ½ × 20 × 15 = 150 sq m. If you know all three sides instead of the height, Heron's formula applies — use the [Triangle Calculator](/triangle-calculator/) for that case.

What is the difference between area and perimeter?

Area is the total two-dimensional space enclosed within a shape, measured in square units (sq m, sq cm, sq ft). Perimeter is the total length of the boundary surrounding the shape, measured in linear units (m, cm, ft). For a 10 m × 5 m rectangle, the area is 50 sq m but the perimeter is 30 m — they measure entirely different things and are used in different calculations.

What is the area formula for a trapezoid?

The area of a trapezoid is A = ½ × (base₁ + base₂) × height, where base₁ and base₂ are the two parallel sides and height is the perpendicular distance between them. A trapezoid with parallel sides of 8 m and 5 m and a height of 4 m has area = ½ × (8 + 5) × 4 = 26 sq m. Trapezoid-shaped land parcels are common in Indian cities where roads cut diagonally across rectangular blocks.

How is area calculation useful in real estate and construction in India?

Area calculation is fundamental to real estate in India for estimating plot sizes, built-up areas, and carpet areas. Builders and buyers use area calculations to price property, plan flooring and tiling, estimate paint required per room, and design layouts. RERA regulations require carpet area to be disclosed separately, making accurate area calculation important for both developers and homebuyers.

How do I calculate the area of a parallelogram?

The area of a parallelogram is A = base × height, where height is the perpendicular distance between the two parallel bases (not the slant side length). A parallelogram with base 12 m and perpendicular height 7 m has area = 12 × 7 = 84 sq m. Note that the perimeter requires knowing the slant side length in addition to the base, which is why our calculator does not compute perimeter for parallelograms.

Can I use this calculator to find dimensions if I know the area?

The Area Calculator computes area from given dimensions, not the reverse. To find dimensions from a known area, you typically need to set up an algebraic equation — for example, if a rectangle has area 60 sq m and length exceeds width by 4 m, you write w(w+4) = 60, which gives the quadratic w² + 4w − 60 = 0. Use the [Quadratic Formula Calculator](/quadratic-formula-calculator/) to solve for w in such cases.

What is the difference between a square and a rectangle?

A square is a special case of rectangle where all four sides are equal in length. For a rectangle, area = length × width; for a square, area = side² (since both dimensions are the same). A square with side 10 m has area 100 sq m and perimeter 40 m. Both shapes have right angles at all four corners — the only distinction is whether opposite sides are equal (rectangle) or all four sides are equal (square).

How do I convert square metres to square feet for construction purposes?

1 square metre = 10.764 square feet. Multiply the area in square metres by 10.764 to get square feet. A 100 sq m flat is approximately 1,076 sq ft — a conversion frequently needed when comparing Indian property listings, since some builders quote in sq ft and others in sq m. For land, 1 square yard = 9 sq ft = 0.836 sq m.

How to calculate the area of an irregular or composite shape?

Break the irregular shape into regular sub-shapes (rectangles, triangles, circles), calculate the area of each using the appropriate formula, then add them together. For example, an L-shaped room can be divided into two rectangles whose areas are summed. Subtract any cut-out sections (e.g., a circular fountain in a rectangular garden). This approach works for any composite shape, however complex.