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Calculate the area of common geometric shapes like rectangles, triangles, circles, and more.
50.0000
A = length × width
Everything you need to know
The concept of area — the amount of space inside a two-dimensional shape — is one of the most practical applications of mathematics in everyday life. From calculating how much carpet you need for a bedroom to determining the size of a garden plot, understanding how to compute area accurately saves time, money, and frustration.
Our area calculator handles all the most common geometric shapes: squares, rectangles, triangles, circles, trapezoids, parallelograms, and ellipses. Each calculation includes the formula, a worked example, and practical context to help you understand not just the answer, but how to arrive at it.
Flooring, roofing, painting, tiling, sod, and mulch are all sold by the square foot or square meter. Accurate area calculations ensure you buy the right amount of material the first time.
Property size, room dimensions, and land parcels are all expressed in terms of area. Buyers, sellers, and agents rely on precise measurements for valuation and comparison.
Farmers calculate field areas to determine seed quantities, fertilizer needs, irrigation requirements, and expected crop yields.
Product packaging, fabric cutting, sheet metal work, and screen printing all require precise area measurements to minimize waste and control costs.
Area calculations are a cornerstone of geometry curricula from middle school through university-level mathematics and engineering.
A square has four equal sides and four right angles.
Formula: Area = Side × Side = s²
Example: A square patio measures 15 feet on each side. Area = 15 × 15 = 225 square feet
A rectangle has opposite sides that are equal and four right angles.
Formula: Area = Length × Width
Example: A rectangular swimming pool measures 30 feet long and 15 feet wide. Area = 30 × 15 = 450 square feet
A triangle has three sides and three angles. The area depends on the base and the perpendicular height.
Formula: Area = (Base × Height) ÷ 2
Example: A triangular roof gable has a base of 24 feet and a height of 10 feet. Area = (24 × 10) ÷ 2 = 120 square feet
A circle is defined by its radius — the distance from the center to any point on the edge.
Formula: Area = π × Radius² (where π ≈ 3.14159)
Example: A circular dining table has a radius of 3 feet. Area = 3.14159 × 3² = 3.14159 × 9 = 28.27 square feet
A trapezoid has one pair of parallel sides (called bases).
Formula: Area = (Base₁ + Base₂) ÷ 2 × Height
Example: A trapezoidal garden bed has parallel sides of 12 feet and 8 feet, with a height of 5 feet. Area = (12 + 8) ÷ 2 × 5 = 10 × 5 = 50 square feet
A parallelogram has opposite sides that are parallel and equal in length.
Formula: Area = Base × Height
Example: A parallelogram-shaped driveway section has a base of 20 feet and a height of 12 feet. Area = 20 × 12 = 240 square feet
An ellipse is an elongated circle defined by two radii: a semi-major axis and a semi-minor axis.
Formula: Area = π × a × b
Where a is the semi-major axis (half the longest diameter) and b is the semi-minor axis (half the shortest diameter).
Example: An elliptical garden pond measures 10 feet long and 6 feet wide. a = 5 feet, b = 3 feet Area = 3.14159 × 5 × 3 = 47.12 square feet
For shapes that do not fit standard geometric formulas, break them into simpler shapes, calculate each area, and add them together.
Example: An L-shaped living room can be divided into two rectangles.
Alternatively, calculate the area of the complete outer rectangle and subtract the missing section.
| Unit | Used In | Equivalent |
|---|---|---|
| Square inch (in²) | Small crafts, electronics | 1/144 sq ft |
| Square foot (ft²) | US construction, real estate | 144 sq in |
| Square yard (yd²) | Carpeting, landscaping | 9 sq ft |
| Square meter (m²) | International standard | 10.764 sq ft |
| Acre | Land measurement | 43,560 sq ft |
| Hectare | Metric land measurement | 10,000 m² |
| Square mile (mi²) | Large land areas | 640 acres |
Room: 14' × 16' with 9-foot ceilings Wall area: Perimeter × Height = (14+16+14+16) × 9 = 540 sq ft Subtract openings: Two windows (30 sq ft each) + one door (21 sq ft) = 81 sq ft Paintable area: 540 - 81 = 459 square feet Paint needed: One gallon covers ~400 sq ft → 2 gallons
Yard: Irregular shape decomposed into a 40' × 30' rectangle and a triangle with base 40' and height 15' Rectangle: 40 × 30 = 1,200 sq ft Triangle: (40 × 15) ÷ 2 = 300 sq ft Total lawn: 1,500 sq ft Sod pallets: One pallet covers ~450 sq ft → 4 pallets
Roof: Two rectangular sections, each 30' × 20', with a 6/12 pitch Footprint: 30 × 20 × 2 = 1,200 sq ft Pitch adjustment (6/12 = 1.118 multiplier): 1,200 × 1.118 = 1,342 sq ft Waste (10%): 1,342 × 1.10 = 1,476 sq ft Shingles: 1,476 ÷ 100 = 15 squares (a square = 100 sq ft)
Mixing feet and inches without converting causes major errors. Always convert to a single unit before calculating.
Perimeter is the distance around a shape (measured in linear units like feet). Area is the space inside (measured in square units like square feet). These are fundamentally different.
When calculating the area of a circle, remember to square the radius (multiply it by itself), not double it. π × r² is very different from π × 2r.
The circle area formula uses radius. If you only know the diameter, divide by 2 first.
In real-world projects, always add 5-15% to your calculated area to account for cuts, overlaps, and errors.
See the calculator above for step-by-step examples.
For 2D shapes, area represents the space inside the shape measured in square units.
Common Area Formulas:
For 3D shapes, volume represents the space inside measured in cubic units.
Common Volume Formulas:
Break it into standard shapes (rectangles, triangles, circles), calculate each area, and add them together.
Area measures the space inside a shape in square units. Perimeter measures the distance around the outside in linear units.
No. Area is always a positive value representing physical space.
For flooring, use the floor dimensions (length × width). For wall painting, calculate each wall section individually.
Circular areas appear in pools, ponds, tables, pipes, wheels, gardens, and architecture.
This calculator is provided for informational and educational purposes only. Results are calculated based on standard mathematical formulas and your inputs. While we strive for accuracy, we do not guarantee that results are error-free. Always verify important calculations independently. Users are responsible for the accuracy of their inputs and should consult appropriate references or professionals for critical applications. We are not liable for any decisions made based on these calculations.
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