Area Calculator

Step 1: Select the shape you want to calculate from the dropdown: Rectangle, Circle, Triangle, or Trapezoid.

Step 2: Enter the required dimensions. The calculator shows only the fields relevant to your selected shape — no extra inputs to confuse you.

Step 3: Click Calculate. The result shows the area in square units. Use consistent units for all inputs (all feet, all meters, etc.) and the result will be in that unit squared.

Area measures the amount of two-dimensional space inside a shape. It is expressed in square units — square feet, square meters, square inches, etc. The "square" prefix means you are measuring a flat surface, not a length.

Why different shapes need different formulas: A rectangle's area is straightforward (length × width) because it tiles perfectly into unit squares. A circle requires π because its curved boundary does not align with a grid. Triangles use base × height ÷ 2 because every triangle is exactly half of a rectangle.

Practical applications: Area calculations are essential for flooring installation, painting walls, landscaping, fabric cutting, carpet ordering, tile laying, concrete pouring, and property assessment. Construction and home improvement projects almost always require area calculations.

Units must be consistent. If you measure length in feet and width in inches, convert one to match the other before calculating. 12 inches × 10 feet is not 120 — you need to convert to 1 foot × 10 feet = 10 sq ft, or 12 inches × 120 inches = 1,440 sq in.

This calculator supports four shapes. For complex shapes, break them into these basic shapes, calculate each piece, and add the areas together.

Rectangle: Area = Length × Width
The simplest area formula. Measure two perpendicular sides.

Circle: Area = π × r²
Where r is the radius (half the diameter). π ≈ 3.14159.

Triangle: Area = ½ × Base × Height
The height must be perpendicular to the base (not a slanted side).

Trapezoid: Area = ½ × (Base₁ + Base₂) × Height
A trapezoid has two parallel sides (bases) of different lengths. The height is the perpendicular distance between them.

Examples:
- Rectangle 10 × 8: 10 × 8 = 80 sq units
- Circle r=5: π × 25 = 78.54 sq units
- Triangle base=12, height=8: ½ × 12 × 8 = 48 sq units
- Trapezoid bases 6,10, height 4: ½ × (6+10) × 4 = 32 sq units

Example 1: Room for Carpet (Rectangle)
Room is 14 × 11 feet. Select Rectangle, enter 14 and 11. Area: 154 sq ft. Add 10% for waste: order 170 sq ft of carpet.

Example 2: Circular Garden (Circle)
Garden has a 6-foot radius. Select Circle, enter 6. Area: 113.1 sq ft. You need about 4 bags of mulch (each covers ~30 sq ft).

Example 3: Triangular Yard Section (Triangle)
A triangular corner of your yard has a 20-foot base and 15-foot height. Select Triangle, enter base 20 and height 15. Area: 150 sq ft.

Use consistent units. All measurements must be in the same unit. Do not mix feet and inches — convert everything to one unit first.

For circles, measure the radius, not the diameter. The radius is half the diameter. If you measured across the full width (diameter), divide by 2 before entering.

Triangle height must be perpendicular. The height is not a side of the triangle — it is the perpendicular distance from the base to the opposite vertex. If you only have side lengths, you need a different formula (Heron's formula).

Break complex shapes into parts. An L-shaped room is two rectangles. A house footprint might be a rectangle plus a triangle (for a peaked section). Calculate each part separately and add.

Add 10-15% for material purchases. When buying flooring, paint, or other materials, add extra for waste, cuts, and mistakes.