Area Calculator
Calculate the area of rectangles, squares, triangles, circles, trapezoids, parallelograms, and ellipses. Enter your dimensions and get instant results with formulas and a visual breakdown. Perfect for students, teachers, and professionals.
What Is Area?
Area is the measure of the amount of space inside a two-dimensional shape. It is measured in square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²). Area is a fundamental concept in geometry with countless real-world applications — from measuring floor space for carpeting to calculating land size for farming and construction.
This calculator supports seven common shapes: rectangles, squares, triangles, circles, trapezoids, parallelograms, and ellipses. Each shape has a specific formula that uses its dimensions to calculate the area.
How Does the Area Calculator Work?
The calculator uses standard geometric formulas for each shape:
Rectangle: Area = Length × Width
Square: Area = Side²
Triangle: Area = ½ × Base × Height
Circle: Area = π × Radius²
Trapezoid: Area = ½ × (Base₁ + Base₂) × Height
Parallelogram: Area = Base × Height
Ellipse: Area = π × Semi-Major Axis × Semi-Minor Axis
Simply select a shape, enter the required dimensions, and the calculator will instantly compute the area. You can switch between metric and imperial units, and choose how many decimal places to display.
Why Use This Area Calculator?
- Seven Shapes: Supports rectangles, squares, triangles, circles, trapezoids, parallelograms, and ellipses.
- Unit Flexibility: Switch between metric (meters, centimeters) and imperial (feet, inches).
- Formula Display: See the formula used and the step-by-step calculation.
- Visual Comparison: A bar chart shows the relative dimensions of the shape.
- Free & Private: No registration, no data storage.
Real-World Applications of Area
- Construction: Calculating floor area for tiles, carpet, or paint.
- Landscaping: Measuring garden beds, lawns, and patios.
- Agriculture: Determining crop planting areas and field sizes.
- Design: Sizing artwork, furniture, and room layouts.
- Education: Learning geometry and solving math problems.
❓ Area Calculator FAQ
What is area?
Area is the measure of the amount of space inside a two-dimensional shape. It is measured in square units (e.g., m², ft², cm²).
How do I calculate the area of a rectangle?
Multiply the length by the width. Formula: A = L × W. For example, a rectangle with length 10 m and width 6 m has an area of 60 m².
How do I calculate the area of a square?
Square the side length. Formula: A = s². For example, a square with side 8 m has an area of 64 m².
How do I calculate the area of a triangle?
Multiply the base by the height, then divide by 2. Formula: A = ½ × b × h. For example, a triangle with base 10 m and height 8 m has an area of 40 m².
How do I calculate the area of a circle?
Multiply π (3.14159) by the radius squared. Formula: A = π × r². For example, a circle with radius 5 m has an area of 78.54 m².
How do I calculate the area of a trapezoid?
Add the two bases, multiply by the height, then divide by 2. Formula: A = ½ × (b₁ + b₂) × h.
How do I calculate the area of a parallelogram?
Multiply the base by the height. Formula: A = b × h. This is the same as a rectangle but the sides may not be perpendicular.
How do I calculate the area of an ellipse?
Multiply π by the semi-major axis (a) and the semi-minor axis (b). Formula: A = π × a × b.
What is the difference between area and perimeter?
Area measures the space inside a shape (2D). Perimeter measures the distance around the outside of a shape. They are different measurements used for different purposes.
How do I convert square meters to square feet?
Multiply square meters by 10.7639 to get square feet. The calculator automatically converts between units.
How do I convert square feet to square meters?
Divide square feet by 10.7639 to get square meters. The calculator does this conversion for you.
What is the area of a circle with diameter 10?
Radius = Diameter/2 = 5. Area = π × 5² = 78.54 square units. The calculator can use either radius or diameter.
What is the area of a triangle with base 12 and height 5?
Area = ½ × 12 × 5 = 30 square units.
What is the area of a trapezoid with bases 10 and 6 and height 4?
Area = ½ × (10 + 6) × 4 = ½ × 16 × 4 = 32 square units.
What is the area of a parallelogram with base 8 and height 5?
Area = 8 × 5 = 40 square units.
What is the area of an ellipse with semi-major axis 6 and semi-minor axis 4?
Area = π × 6 × 4 = 75.40 square units.
What units can I use for area?
Area can be measured in square meters (m²), square centimeters (cm²), square feet (ft²), square inches (in²), and many other square units. This calculator supports metric and imperial systems.
How do I calculate the area of an irregular shape?
Irregular shapes can often be divided into regular shapes (rectangles, triangles, etc.). Calculate the area of each part and add them together. This calculator focuses on seven common regular shapes.
What is π (Pi) in area calculations?
π (Pi) is a mathematical constant approximately equal to 3.14159. It is used in formulas for circles, ellipses, and other curved shapes. The calculator uses π to compute areas of circles and ellipses.
How do I calculate the area of a room for flooring?
Measure the length and width of the room in feet or meters. Multiply them to get the area. For irregular rooms, divide into rectangles and add the areas. Use this calculator with the rectangle shape to get the total area.