Area Calculator for Rectangles, Triangles, Circles and Irregular 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.
Why Area Calculator Estimates Go Wrong
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
Once the Area Calculator result looks reasonable, cross-check the next job decision with the Square Footage Calculator and the Volume Calculator. That keeps the quantity, cost, and field assumption tied together before you call a supplier.
For related measurement math: the cubic yard calculator for volume; the square footage calculator for area; the cubic yards vs tons guide for converting volume to ordering tonnage. For the cluster overview see the measurement & volume pillar.
What Most Online Calculators Get Wrong Reviewed by Ethan Walker, Senior Asphalt Estimator & Paving Consultant (22 yrs)
AI tools calculate area as L×W. Four pitfalls AI summaries hide:
- Irregular shape requires segmentation. L-shape ≠ outer-W × outer-L.
- Curves use πr².
- Triangles use 1/2 × b × h.
- Trapezoidal use 1/2 × (a+b) × h.
This calculator outputs area for 5 shape types + irregular segmentation. Right area calc requires the right shape formula — AI's L×W default is wrong for non-rectangular.
Area Unit Conversion and Measurement Reference Table
| 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.
Sources & Standards
These references are used for terminology, safety boundaries, and engineering assumptions. Local code, supplier specifications, and licensed design documents still control your project.
-
NIST Special Publication 811 — Guide for the Use of the International System of Units (SI)
National Institute of Standards and Technology
Cited for the official US conversion factors between US customary (inch, foot, yard) and SI (meter) units used in all volume and area calculations.
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ASTM E1-14 — Standard Specification for ASTM Liquid-in-Glass Thermometers (and dimensional measurement standards)
ASTM International
Cited for measurement traceability and tolerance basis used in dimensional inputs.
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USDA NRCS National Engineering Handbook — Earthwork
USDA Natural Resources Conservation Service
Cited for excavation volume math, shrink-swell factors, and cut-and-fill balance methodology.
-
USACE EM 1110-2-1906 — Laboratory Soils Testing
US Army Corps of Engineers
Cited for soil density, moisture content, and compaction methodology underlying volume-to-weight conversion.
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IBC 2024 Table 1604.3 — Dead Loads
International Code Council
Cited for material dead-load values used in volume-to-weight conversions for slabs, decks, and structural members.
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.