What are the main area formulas?

Rectangle: A = length × width. Square: A = side². Triangle: A = (base × height) / 2. Circle: A = π × radius². Trapezoid: A = (a + b) / 2 × height. Parallelogram: A = base × height. Ellipse: A = π × a × b (where a and b are semi-major and semi-minor axes). Regular polygon: A = (perimeter × apothem) / 2.

How do I calculate the area of an irregular shape?

Several methods: (1) Decompose into regular shapes — divide the irregular shape into rectangles, triangles, and circles, calculate each area, then add them up. (2) Shoelace formula (for polygons with known vertices): A = |Σ(x_i × y_{i+1} − x_{i+1} × y_i)| / 2. (3) Grid counting — place a grid over the shape and count squares. (4) Integration — for curved shapes with a known equation, integrate the boundary function.

How do I convert square feet to square meters?

1 square foot = 0.0929 square meters. Multiply square feet by 0.0929 to get square meters. Example: 1,500 sq ft × 0.0929 = 139.4 sq meters. Reverse: sq meters × 10.764 = sq feet. Common conversions: 100 sq ft = 9.29 sq m; 500 sq ft = 46.45 sq m; 1,000 sq ft = 92.9 sq m.

What is the area of a circle with radius 5?

A = π × r² = π × 5² = π × 25 ≈ 78.54 square units. With diameter (d) instead of radius: A = π × (d/2)². For a circle with diameter 10: A = π × (10/2)² = π × 25 ≈ 78.54.

Area Calculator

Select a shape and enter its dimensions to calculate the area.

Area Formulas

Frequently Asked Questions

What is the area of a rectangle 12 × 8?

A = 12 × 8 = 96 square units.

How do I find the area of a right triangle with legs 6 and 8?

A = (base × height) / 2 = (6 × 8) / 2 = 24 square units. The hypotenuse would be √(6²+8²) = √100 = 10 (3-4-5 scaled by 2).

What is the area of a circle with diameter 10?

Radius = diameter / 2 = 5. A = π × 5² = π × 25 ≈ 78.54 square units.

Shape	Formula
Square	A = s²
Rectangle	A = l × w
Circle	A = πr²
Triangle	A = ½ × b × h
Trapezoid	A = ½(b₁ + b₂) × h
Ellipse	A = πab
Parallelogram	A = b × h

Related Calculators

How to Calculate Area

Area is the amount of two-dimensional space a shape occupies, measured in square units such as square inches, square feet, square meters, or square kilometers. Each shape has its own formula. A rectangle uses length × width. A triangle uses ½ × base × height. A circle uses π × radius². A trapezoid uses ½ × (base₁ + base₂) × height. Our calculator handles all these shapes automatically — just select the shape, enter the dimensions, and get the result instantly.

Always use consistent units. If you enter length in feet and width in inches, the result will be incorrect. Convert all measurements to the same unit before calculating. For irregular shapes, divide the area into regular sub-shapes, calculate each one, then add them together.

Area Formulas Quick Reference

Shape	Formula	Example
Rectangle	L × W	5 m × 3 m = 15 m²
Triangle	½ × B × H	8 m × 4 m ÷ 2 = 16 m²
Circle	π × r²	π × 5² = 78.54 m²
Trapezoid	½(b₁+b₂) × H	½(4+6) × 3 = 15 m²

How Area Calculation Works in Practice

Area measurement underlies architecture, construction, landscaping, and interior design. It tells you how much two-dimensional surface is enclosed within a boundary, expressed in square units such as square feet, square meters, or square yards. The formula you apply depends entirely on the shape you are measuring. For rectangles and squares, multiply length by width. For triangles, multiply base by height and divide by two. For circles, square the radius and multiply by pi (approximately 3.14159). For irregular shapes, divide the region into simpler components, calculate each piece separately, and add the results together. Engineers use area when sizing structural members and determining load distributions across floors or roofs. Flooring contractors calculate area to order the correct quantity of tile, hardwood, or carpet. Landscapers determine how much mulch, seed, or fertilizer a lot requires by calculating its total area. Painters estimate paint quantities from wall area measurements. Always use consistent units throughout a calculation to prevent conversion errors that lead to costly material shortfalls or overages on a project. Converting between area units is straightforward: one square meter equals approximately 10.764 square feet, and one acre equals exactly 43,560 square feet.

Area Formulas Reference Table

Shape	Formula	Example
Rectangle	A = l × w	8 ft × 5 ft = 40 sq ft
Square	A = s²	6 m × 6 m = 36 m²
Triangle	A = ½ × b × h	½ × 10 × 4 = 20 sq ft
Circle	A = πr²	π × 5² ≈ 78.5 sq m
Trapezoid	A = ½(a + b) × h	½(6 + 10) × 4 = 32 sq in
Ellipse	A = π × a × b	π × 3 × 5 ≈ 47.1 sq m