📐Area Calculator

An area calculator makes short work of one of geometry's most frequently needed measurements. Knowing how to calculate the area of common shapes is essential for home improvement, land measurement, construction, and design. Whether you are laying tile in a bathroom, seeding a lawn, planning a garden bed, or pricing paint for a room, this calculator covers nine 2D shapes and automatically converts results into square feet and square meters so you can work in any unit system.

Area of Rectangle, Triangle, and Circle Calculator

Three shapes handle the majority of real-world area problems: the rectangle, the triangle, and the circle. Their formulas are the foundation of geometry:

• Rectangle area: A = length x width. A room measuring 12 ft by 10 ft has area = 120 square feet. Add all rectangular sections together to handle L-shaped rooms.
• Triangle area: A = (1/2) x base x height. The height must be the perpendicular distance from the base to the opposite vertex, not the slant side. For a triangle with base 8 ft and height 5 ft, area = 20 square feet.
• Circle area: A = pi x r2. A circular fountain with radius 4 ft has area = approximately 50.3 square feet. Because area grows with the square of the radius, doubling the radius produces four times the area, not twice.

This calculator supports all three shapes plus trapezoids, parallelograms, ellipses, sectors, and regular polygons, each with its own precise formula.

How to Calculate Area in Square Feet

Square footage is the standard unit for rooms, lots, and building materials in the United States. Here is the step-by-step process for the most common situations:

• Rectangular rooms: Measure length and width in feet, then multiply. Add separate sections for L-shaped or irregular layouts.
• Triangular spaces: Measure the base and perpendicular height in feet, multiply, and divide by 2.
• Circular areas: Measure the radius in feet and apply pi x r2. For a diameter measurement, divide by 2 first.
• Irregular lots: Divide the lot into rectangles and triangles, calculate each piece, and sum the results.

This calculator outputs every result in square feet and square meters simultaneously, so no manual conversion is necessary when switching between unit systems.

Area Calculator for Different 2D Shapes

Square

A square with side length a has area = a2 and perimeter = 4a. Squares are a special case of rectangles where all four sides are equal. Square footage of a square room is simply the side length in feet, squared.

Trapezoid

A trapezoid has one pair of parallel sides called the bases (a and b) and a perpendicular height (h) between them. Area = (1/2) x (a + b) x h. The formula averages the two bases and multiplies by the height, treating the shape as a rectangle with the average width. Trapezoidal cross-sections appear in irrigation channels, road embankments, and certain architectural profiles.

Parallelogram

A parallelogram has two pairs of parallel sides. Area = base x height, where the height is the perpendicular distance between the parallel sides, not the slant side. A common mistake is using the slant side as the height, which overstates the area. Parallelograms appear in structural design, tile patterns, and crystallography.

Ellipse

An ellipse is a stretched circle with two axes: the semi-major axis (a, the longer half) and the semi-minor axis (b, the shorter half). Area = pi x a x b. When a equals b, this reduces to the standard circle formula. Ellipses appear in orbital mechanics, architecture (elliptical windows and rooms), and optics.

Sector

A sector is a pie-slice portion of a circle, defined by a radius and a central angle. Area = (1/2) x r2 x theta, where theta is in radians. To convert degrees to radians, multiply by pi divided by 180. A quarter-circle (90-degree sector) has area equal to one-fourth of the full circle. Sectors appear in pie charts, gear tooth design, and the swept area of rotating blades or arms.

Regular Polygon

A regular polygon has equal sides and equal angles. Area = (n x s2) divided by (4 x tan(pi/n)), where n is the number of sides and s is the side length. As the number of sides increases, the polygon approaches a circle. A regular hexagon with side 5 has area approximately 64.95 square units, which is about 82.7 percent of the circumscribed circle's area. Regular polygons appear in floor tile patterns, architectural facades, and natural structures like honeycomb.

Practical Uses of Area Calculations

Flooring and Tiling

Calculate the room area and add 10 to 15 percent for cuts and waste. Tiles and flooring materials are sold by the square foot or square meter, so knowing the total area determines how much to order. For diagonal tile layouts, allow an additional 15 percent due to extra cuts at the edges.

Painting Walls

Measure each wall's area (width times height), subtract the area of doors and windows, and divide by the paint's coverage rate (typically 350 to 400 square feet per gallon for one coat). Two coats require double the paint. Knowing the square footage prevents buying too much or too little.

Land and Agriculture

Lot sizes in the US are measured in acres (1 acre = 43,560 square feet). Field sizes in most other countries are measured in hectares (1 hectare = 10,000 square meters). Knowing the area of a field determines seed, fertilizer, and irrigation requirements. Center-pivot irrigation systems cover the circular area swept by the rotating arm.