Area Calculator
Enter dimensions to find the area of the most common shapes. Select your shape and enter the relevant measurements. The primary result shows the rectangle area (length × width); the content below covers all four shapes with their formulas and explains when each is relevant.
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Formula
Rectangle: A = l×w | Circle: A = π r² | Triangle: A = ½ b×h
Rectangle: multiply length by width. Circle: the radius is half the diameter; area = π × radius². Triangle: area equals half the product of base and height (the height must be perpendicular to the base). Trapezoid: area = ½ × (base1 + base2) × height, where base1 is the 'length' field, base2 is the 'width' field, and height is the perpendicular distance between the parallel sides.
How to use the Area Calculator
- 1
Enter your shape
- 2
Enter your length / diameter
Value should be in m.
- 3
Enter your width / base 2 (trapezoid)
Value should be in m.
- 4
Enter your height
Value should be in m.
- 5
Read your results instantly
Results update in real time as you type.
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Area of rectangles and squares
A rectangle's area is simply length times width: A = l × w. A square is a special rectangle where l = w, so A = s² (side squared — which is why square units like m² have 'square' in the name).
Rectangle area appears everywhere: room dimensions (flooring, paint), screen resolution (pixels = width × height), farmland productivity, and more. When planning how much material to buy, always calculate area and add 10–15% for waste and mistakes.
For irregular rectilinear shapes (L-shapes, U-shapes), divide them into rectangles, calculate each area separately, then add (or subtract) as needed.
Area of circles
The area of a circle is A = π × r², where r is the radius (half the diameter). π ≈ 3.14159. For a circle with diameter 10 m, radius = 5 m, so A = π × 25 ≈ 78.54 m².
Circle area appears when sizing cylindrical tanks (the circular cross-section determines flow), planning round tables, calculating sprinkler coverage, and in optics (beam cross-section determines power density).
A circle encloses more area per unit of perimeter than any other shape — this is why bubbles are spherical and why honeycomb cells are hexagonal (the closest-packing shape to circles).
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Area of triangles and trapezoids
Triangle area = ½ × base × height. The height must be perpendicular to the base — not a slant side. For any triangle, pick any side as the base and drop a perpendicular from the opposite vertex.
When you don't know the height but know all three sides (a, b, c), use Heron's formula: s = (a+b+c)/2 (semi-perimeter), then A = √(s(s−a)(s−b)(s−c)).
Trapezoid area = ½ × (b₁ + b₂) × h, where b₁ and b₂ are the two parallel sides and h is the perpendicular height. This formula reduces to the rectangle formula when b₁ = b₂, and to the triangle formula when b₂ = 0 — a nice unifying structure.
Tips & Insights
Always use consistent units
If length is in meters and width in centimeters, you must convert before multiplying. 5 m × 30 cm = 5 m × 0.3 m = 1.5 m² (not 150 cm × 30 cm or some inconsistent mix). The area unit is always the length unit squared.
A circle is the most area-efficient shape
For a fixed perimeter (circumference), a circle encloses the maximum possible area. A circle with perimeter 100 m has area ≈ 796 m². A square with perimeter 100 m has area 625 m². This is the isoperimetric inequality and explains why circular designs maximize enclosed space.
Add 10–15% for real-world materials
When buying flooring, paint, or turf based on area calculations, add 10–15% to account for cuts, pattern matching, waste, and future repairs. Triangular and diagonal cuts are particularly wasteful — if a room has many angles, bump up to 20%.
Worked Examples
Living room flooring
Area = 6 × 4.5 = 27 m². Add 10% for waste: 29.7 m². Order at least 30 m² of flooring material.
Circular garden bed
Radius = 1.5 m. Area = π × 1.5² = π × 2.25 ≈ 7.07 m². You need about 7 bags of mulch at 1 m² coverage per bag, plus one spare.
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Frequently Asked Questions
What is the formula for the area of a circle?
A = π × r², where r is the radius. If you know the diameter d, then r = d/2, so A = π × (d/2)². For a circle with diameter 10 cm: A = π × 25 ≈ 78.54 cm².
How do I find the area of an irregular shape?
Decompose it into regular shapes (rectangles, triangles, semicircles), calculate each area, then add them together. Subtract any interior cutouts. For organic shapes, planimeters or numerical integration (counting grid squares) are used.
What is the difference between area and perimeter?
Area measures the space inside a 2D shape (in square units: cm², m²). Perimeter measures the total length of the boundary (in linear units: cm, m). A shape can have a large perimeter and small area (a very thin rectangle) or vice versa.
Why is the height of a triangle perpendicular to the base?
The formula A = ½ × base × height comes from the definition of height as the perpendicular distance between the base line and the opposite vertex. Using a slant side instead of the true perpendicular height gives the wrong answer.
What units does the area answer come in?
Area is in squared units of whatever you input. If length and width are in meters, area is in m². If in feet, it's ft². To convert: 1 m² = 10.764 ft², 1 ft² = 0.0929 m².
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