Area Calculator
Calculate the area and perimeter of various geometric shapes
How It Works
Overview
The area calculator computes the two-dimensional space enclosed by a flat geometric shape, along with its perimeter (or circumference for a circle). Pick a shape, enter the required dimensions, and you get both measurements plus the formula used. Area is reported in square units; perimeter in linear units.
Each shape has a distinct formula because area depends on how the boundary is constructed. Straight-sided shapes use multiplication of base and height; circular and elliptical shapes involve π (pi ≈ 3.14159) to account for the curve. Use this calculator for flooring, painting, landscaping, drafting, geometry homework, or any task where you need to know how much surface a shape covers.
The Formula
The formula depends on the shape:
- Rectangle / Parallelogram: A = base × height
- Square: A = side²
- Triangle: A = ½ × base × height (height is perpendicular to the base)
- Circle: A = π × r²
- Trapezoid: A = ½ × (a + b) × h, where a and b are the parallel sides
- Ellipse: A = π × a × b, where a and b are the semi-axes
- Rhombus: A = ½ × d₁ × d₂, where d₁ and d₂ are the diagonals
Worked Example
Suppose you want to tile a rectangular kitchen floor that measures 12 ft × 9 ft, plus a circular dining nook of radius 4 ft.
- Rectangle area: 12 × 9 = 108 ft²
- Rectangle perimeter: 2 × (12 + 9) = 42 ft
- Circle area: π × 4² = π × 16 ≈ 50.27 ft²
- Circle circumference: 2π × 4 ≈ 25.13 ft
- Total tile needed: 108 + 50.27 ≈ 158.3 ft²
Always add 10–15% for cuts and waste when ordering tile or flooring, so you'd actually buy about 175 ft².
When to Use This
- Flooring or carpeting — calculate exact square footage to order materials.
- Painting walls — measure each wall as a rectangle, subtract doors and windows.
- Landscaping — figure sod, mulch, or paving area for a lawn or patio.
- Real estate — verify a room's listed square footage from blueprints.
- Geometry classwork — check homework or visualize how formulas behave with different inputs.
Common Mistakes to Avoid
- Mixing units. Convert all dimensions to the same unit before calculating; never multiply feet by inches.
- Confusing radius and diameter. A circle's area uses radius. If you measured the diameter (12 inches across), divide by 2 first.
- Using slant height instead of perpendicular height. Triangle and trapezoid formulas need the height drawn at 90° to the base, not the sloped side.
- Forgetting to subtract cutouts. When figuring paint or flooring, subtract doors, windows, columns, and built-ins from the gross area.
- Reporting in linear units. Area is always squared (ft², m²); writing "108 ft" for floor area is dimensionally wrong.
Frequently Asked Questions
Ad Space