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Area Calculator – Find Area of Any 2D Shape Online

Calculate the area of any 2D shape with our free online area calculator. Supports circle, rectangle, triangle, trapezoid, parallelogram, and more with formula explanations.

Formula
A = l × w
Examples:

Area Calculator – Find Area of Any 2D Shape Online

Area measures the space inside a 2D shape. Whether you're calculating floor space for new carpet, figuring out how much paint you need, or solving geometry homework, this calculator handles the most common shapes with clear formulas and step-by-step solutions.

Pick your shape, enter the required dimensions, and get instant results. Each shape uses its specific formula – rectangles multiply length by width, circles use πr², triangles take half the base times height. The calculator shows the formula and walks through each step.

Area Formulas Reference

Rectangle

A = l × w
A = length × width

Square

A = s²
A = side²

Triangle

A = ½ × b × h
A = ½ × base × height

Circle

A = πr²
A = π × radius²

Trapezoid

A = ½(a + b)h
A = ½ × (base1 + base2) × height

Parallelogram

A = b × h
A = base × height

Rhombus

A = ½ × d₁ × d₂
A = ½ × diagonal1 × diagonal2

Kite

A = ½ × d₁ × d₂
A = ½ × diagonal1 × diagonal2

Ellipse

A = πab
A = π × semi-major × semi-minor

Shape Descriptions

Rectangle

A four-sided shape with opposite sides equal and all angles 90°. Multiply length by width. A 10 ft by 12 ft room has an area of 120 square feet.

Square

A special rectangle where all four sides are equal. Side squared gives the area. A 6-inch square tile covers 36 square inches.

Triangle

Half of a parallelogram with the same base and height. The height must be perpendicular to the base. Works for any triangle type – right, acute, or obtuse.

Circle

Uses π (pi, approximately 3.14159). The radius is the distance from center to edge. A circle with radius 5 has area π × 25 ≈ 78.54 square units.

Trapezoid

A four-sided shape with one pair of parallel sides (the bases). Average the two bases, then multiply by height. Common in architecture and engineering.

Parallelogram

Opposite sides are parallel and equal. The height is the perpendicular distance between bases, not the slanted side length. Think of it as a "slanted rectangle."

Rhombus

All four sides equal (like a tilted square). Use the diagonals: half their product gives the area. The diagonals always cross at right angles.

Kite

Two pairs of adjacent equal sides. Same formula as rhombus – half the product of diagonals. Kites have one diagonal that bisects the other at 90°.

Ellipse

An oval or "stretched circle." Uses the semi-major axis (longest radius) and semi-minor axis (shortest radius). Formula is π times both axes.

Worked Examples

Example 1: Rectangle Area

Find the area of a rectangular garden that is 24 feet long and 15 feet wide.

Length = 24 ft, Width = 15 ft
A = l × w
A = 24 × 15
A = 360 square feet

Example 2: Circle Area

Calculate the area of a circular pizza with a 14-inch diameter.

Diameter = 14 in, so Radius = 7 in
A = πr²
A = π × 7²
A = π × 49
A ≈ 3.14159 × 49 = 153.94 square inches

Example 3: Triangle Area

A triangular sail has a base of 12 feet and a height of 18 feet. What's its area?

Base = 12 ft, Height = 18 ft
A = ½ × b × h
A = ½ × 12 × 18
A = 6 × 18 = 108 square feet

Example 4: Trapezoid Area

A trapezoidal table has parallel sides of 36 inches and 48 inches, with a height of 24 inches.

Base₁ = 36 in, Base₂ = 48 in, Height = 24 in
A = ½(a + b)h
A = ½(36 + 48) × 24
A = ½(84) × 24
A = 42 × 24 = 1,008 square inches

Example 5: Ellipse Area

An elliptical pool table has a semi-major axis of 5 feet and semi-minor axis of 3 feet.

a = 5 ft, b = 3 ft
A = πab
A = π × 5 × 3
A = π × 15 ≈ 47.12 square feet

Quick Fact

The formula for circle area (A = πr²) was first rigorously proven by Archimedes around 250 BCE. He used the "method of exhaustion," inscribing and circumscribing polygons with increasing numbers of sides around a circle. His approach anticipated calculus by nearly 2,000 years.

Frequently Asked Questions

What units should I use?

Any consistent units work – inches, feet, meters, centimeters. The area will be in square units (sq in, sq ft, m², etc.). Convert all dimensions to the same unit before calculating.

How do I find the height of a triangle?

The height is the perpendicular distance from the base to the opposite vertex. For right triangles, it's one of the legs. For other triangles, you may need to measure or calculate it separately.

Why is π used for circles and ellipses?

π (pi) is the ratio of a circle's circumference to its diameter. It appears in circle area because the relationship between radius and area is fundamental to circular geometry. π ≈ 3.14159...

Can I calculate irregular shapes?

Break irregular shapes into regular pieces (rectangles, triangles, etc.), calculate each area separately, then add them together. This calculator handles the regular component shapes.

What's the difference between area and perimeter?

Area measures the space inside a shape (square units). Perimeter measures the distance around the outside (linear units). A 4×4 square has area 16 sq units and perimeter 16 units – same number, different meaning.

How do I calculate the area of a rhombus without diagonals?

If you know the side length and any interior angle, use A = s² × sin(angle). If you know the side and height (perpendicular distance between opposite sides), use A = base × height, same as a parallelogram.

Is a square a rectangle?

Yes, a square is a special type of rectangle where all four sides are equal. Both formulas work: you can use length × width (where length = width) or side² – they give the same result.

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Area Calculator – Find Area of Any 2D Shape Online

Calculate the area of any 2D shape with our free online area calculator. Supports circle, rectangle, triangle, trapezoid, parallelogram, and more with formula explanations.