Area Calculator (All Shapes)
Calculate area for any geometric shape — rectangles, triangles, circles, trapezoids, parallelograms, L-shapes, and irregular polygons.
Area Calculator
Enter project dimensions below — results update instantly. Switch units freely.
Estimates assume typical industry density and waste factors. Always verify with your supplier and local building code before purchasing material.
Area Is the Input to Every Construction Estimate
Every material estimate starts with area. Flooring, paint, roofing, concrete, asphalt, pavers, mulch, drywall — all computed as area × depth × density or area × unit cost. Getting area wrong compounds through every downstream calculation.
The five most common shapes for construction areas:
- Rectangle — most rooms, slabs, and lots
- L-shape — houses with room additions, properties on corners
- Triangle — roof sections, lot corners, ornamental beds
- Circle / arc — patios, cul-de-sacs, fire pits, round rooms
- Trapezoid — angled walls, tapered lots
For any irregular polygon, decompose into these basic shapes, calculate each, and sum.
Area Formulas Cheat Sheet
Triangle: A = (b × h) ÷ 2
Circle: A = π × r²
Trapezoid: A = ((a + b) ÷ 2) × h
Parallelogram: A = b × h
Ellipse: A = π × a × b (a, b = semi-axes)
Special shortcut formulas:
- Triangle (any 3 sides): Heron's formula — s = (a+b+c)/2, then A = √(s(s-a)(s-b)(s-c))
- Regular polygon: A = (n × s²) / (4 × tan(π/n)) where n = sides, s = side length
- Sector of circle: A = (θ/360) × π × r² where θ is in degrees
| Shape | Formula | Example (5-unit dims) | Result |
|---|---|---|---|
| Rectangle 5 × 5 | L × W | 5 × 5 | 25 units² |
| Square 5 × 5 | s² | 5² | 25 units² |
| Triangle base 5, ht 5 | (b × h) ÷ 2 | (5 × 5) ÷ 2 | 12.5 units² |
| Circle radius 5 | π × r² | π × 25 | 78.54 units² |
| Ellipse 5 × 3 | π × a × b | π × 5 × 3 | 47.12 units² |
| Trapezoid (top 4, bot 6, ht 5) | ((a+b)/2) × h | ((4+6)/2) × 5 | 25 units² |
| Parallelogram base 5, ht 5 | b × h | 5 × 5 | 25 units² |
| Regular hexagon side 5 | (3√3/2) × s² | 2.598 × 25 | 64.95 units² |
For consistent units: feet produce ft², inches produce in², meters produce m². Always convert to consistent units before calculating.
| From | To ft² | To m² | To yd² |
|---|---|---|---|
| 1 in² | 0.00694 | 0.000645 | 0.000772 |
| 1 ft² | 1 | 0.0929 | 0.1111 |
| 1 yd² | 9 | 0.8361 | 1 |
| 1 m² | 10.76 | 1 | 1.196 |
| 1 acre | 43,560 | 4,047 | 4,840 |
| 1 hectare | 107,639 | 10,000 | 11,960 |
Flooring and fabric often priced by yard². Paint coverage in ft². Agriculture/land in acres or hectares.
Real-World Example Calculations
Standard Rectangle 24 × 36 ft
Small ranch house footprint for siding or paint estimate.
- Length
- 36 ft
- Width
- 24 ft
Takeaway: Direct multiplication. Equivalent: 96 yd² or 80.3 m².
Triangular Front Lawn
Triangular corner lawn area, base 50 ft along street, 30 ft setback.
- Base
- 50 ft
- Height
- 30 ft
Takeaway: (50 × 30) ÷ 2 = 750 ft². Base and height must be perpendicular for this formula.
Circular Patio 14 ft Diameter
Round patio with fire pit center.
- Diameter
- 14 ft
- Radius
- 7 ft
Takeaway: π × 7² = 153.9 ft². With 4 in concrete depth: 51.3 ft³ = 1.9 yd³ — small-pour ready-mix territory.
Frequently Asked Questions
How do I calculate the area of a circle?
A = π × r² where r is the radius. If you have the diameter instead, radius = diameter ÷ 2. For a 10-ft diameter circle: radius = 5 ft, area = π × 25 = 78.54 ft².
How do I calculate the area of a triangle?
For base/height triangles: A = (base × height) ÷ 2. Base and height must be perpendicular. For triangles where you know only the three sides, use Heron's formula.
What's the area formula for a trapezoid?
A = ((parallel side 1 + parallel side 2) ÷ 2) × height. The two parallel sides can be any length; the height is the perpendicular distance between them.
How do I find the area of an irregular shape?
Decompose into simple shapes (rectangles, triangles, circles), calculate each area, and sum. For shapes with curves, approximate with multiple small triangles or trapezoids. Aim for ±2-3% accuracy for construction estimates.
How many square feet in an acre?
One acre = 43,560 ft². Visualize as a rectangle ~209 × 209 ft, or a 1/8 mile (660 ft) × 66 ft strip. 640 acres = 1 mi² = 1 section of land.
What unit should I use for area?
US construction: square feet (ft²) primary, square yards for flooring. Metric: square meters (m²). Large land areas: acres (US) or hectares (metric). Maintain consistency throughout a project to avoid conversion errors.
How do I calculate the area of a parallelogram?
A = base × height where height is the perpendicular distance between the two parallel base lines (NOT the length of the slanted side). Same formula as a rectangle, just with a slant.