2D Shapes Area & Perimeter Calculator
Our 2D Shapes Area and Perimeter Calculator is a high-precision geometry tool designed for students, architects, and hobbyists. Instantly calculate the geometric properties of over 12 unique shapes including circles, complex polygons, and sectors with real-time visual feedback.
Area Studio
METRIC / SI STANDARDS
IMPERIAL / US STANDARDS
Area Formula
Area = Length × WidthCommon conversion: 1 Acre = 43,560 Square Feet.
Common Area Benchmarks
| Acres | Square Feet | Hectares | Square Meters | Square Miles |
|---|---|---|---|---|
| 0.5 | 21,780 | 0.2023 | 2,023.4 | 0.0007 |
| 1 | 43,560 | 0.4046 | 4,046.8 | 0.0015 |
| 2 | 87,120 | 0.8093 | 8,093.7 | 0.0031 |
| 5 | 217,800 | 2.0234 | 20,234.3 | 0.0078 |
| 10 | 435,600 | 4.0468 | 40,468.6 | 0.0156 |
| 20 | 871,200 | 8.0937 | 80,937.2 | 0.0312 |
| 50 | 2,178,000 | 20.234 | 202,343 | 0.0781 |
| 100 | 4,356,000 | 40.468 | 404,686 | 0.1562 |
When to Use Which Unit
Square Feet (sq ft)
Standard unit for residential real estate, room sizes, and apartment listings. Perfect for indoor spaces.
Acres (ac)
Used primarily in the US and UK for large plots of land, farms, and commercial properties. 1 Acre is about the size of a football field.
Hectares (ha)
The standard metric unit for large land areas, used globally in agriculture and forestry. Equal to 10,000 square meters.
Square Meters (m²)
The SI unit for area. Used in construction, flooring, and international real estate for room dimensions.
Square Yards (sq yd)
Commonly used in the UK and US for carpets, fabric, and sometimes land measurement before acres are applied.
Square Inches (sq in)
Used for small areas, mechanical parts, paper sizes, and high-precision engineering calculations.
Square Kilometers (km²)
Used for describing the size of cities, countries, or large geographic regions like forests and lakes in metric system.
Square Miles (sq mi)
Used for describing large geographic areas in the imperial system, equivalent to 640 acres.
Overview & Capabilities
Our 2D Shapes Area and Perimeter Calculator is a high-precision geometry tool designed for students, architects, and hobbyists. Instantly calculate the geometric properties of over 12 unique shapes including circles, complex polygons, and sectors with real-time visual feedback.
How to Use
Key Features
Common Use Cases
Tips & Best Practices
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Frequently Asked Questions
Q How do you calculate the area of a circle?
The area is calculated using the formula πr², where r is the radius of the circle.
Q What is the perimeter of a rectangle?
The perimeter is the sum of all outer sides, calculated as P = 2 * (length + width).
Q What is Ramanujan's formula for the perimeter of an ellipse?
Ramanujan's first approximation is P ≈ π [ 3(a+b) - √((3a+b)(a+3b)) ] where a and b are the semi-major and semi-minor axes respectively. This formula offers extremely high precision for most eccentricities.
Q How does Heron's formula work for scalene triangles?
Heron's formula calculates the area of a triangle when all three side lengths (a, b, c) are known: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter: s = (a + b + c) / 2.
Q What is the difference between regular pentagon, hexagon, and octagon area formulas?
Regular polygons are equilateral and equiangular. Their areas are computed using the side length (s) and specific constants derived from trigonometric functions: Area of Pentagon ≈ 1.72048 * s², Hexagon ≈ 2.59808 * s², and Octagon ≈ 4.82843 * s².
Q How do I calculate the area of a circular sector?
The area of a sector is a fraction of the circle's total area, calculated as Area = (θ / 360) * πr², where θ is the central angle in degrees and r is the radius.