This area calculator finds the area of six common shapes — rectangle, triangle, circle, trapezoid, parallelogram, and ellipse — using the standard area formulas. Choose a shape, enter its dimensions, and get the area in square units instantly.
Area measures the amount of surface a flat shape covers, so the result is always in square units: measure in feet and you get square footage (ft²), measure in meters and you get m². Whether you are sizing a room for flooring, a garden bed for soil, or a wall for paint, the same handful of formulas covers nearly every real-world layout.
Area Formulas for Common Shapes
Each shape has its own standard formula:
- Rectangle: A = l × w (length × width)
- Triangle: A = ½ × b × h (half of base × height)
- Circle: A = πr² (pi × radius squared)
- Trapezoid: A = ½ × (a + b) × h — average the two parallel sides, then multiply by the height
- Parallelogram: A = b × h (base × perpendicular height, not the slanted side)
- Ellipse: A = π × a × b, using the semi-major and semi-minor axes
For triangles and parallelograms, the height must be measured perpendicular to the base. Complex floor plans can be split into rectangles and triangles, calculated piece by piece, and added together.
Unit Conversions: Square Feet, Square Meters, Acres
Area units convert with squared factors, not linear ones — 1 yard is 3 feet, but 1 square yard is 9 square feet. Key conversions:
- 1 square foot = 0.0929 square meters
- 1 square meter = 10.764 square feet
- 1 square yard = 9 square feet = 0.8361 square meters
- 1 acre = 43,560 square feet = 4,046.86 square meters
- 1 hectare = 10,000 square meters = 2.471 acres
To convert square feet to square meters, multiply by 0.0929 (a 1,500 ft² house is about 139.4 m²). To convert square feet to acres, divide by 43,560 (a 10,000 ft² lot is about 0.23 acres).
Worked Examples: Trapezoid and Circle
Trapezoid deck with parallel sides a = 8 ft and b = 12 ft, height h = 5 ft:
- Average the parallel sides: (8 + 12) ÷ 2 = 10 ft.
- Multiply by the height: 10 × 5 = 50 ft².
Circular patio with radius r = 4 ft:
- A = πr² = π × 16 ≈ 50.27 ft².
And the default rectangle: a 12 ft × 10 ft room has an area of 120 ft². If flooring costs $4.50 per square foot, the material budget is 120 × $4.50 = $540 — this is the everyday reason square footage matters.
Frequently Asked Questions
How do I calculate square footage?
Measure the length and width of the space in feet and multiply them: a 15 ft × 12 ft room is 180 square feet. For L-shaped or irregular rooms, divide the space into rectangles, compute each area separately, and add the results together. Round measurements to the nearest inch for accuracy.
What is the formula for the area of a triangle?
The area of a triangle is A = ½ × base × height, where the height is measured perpendicular to the base — not along a slanted side. A triangle with a 10 cm base and 6 cm height has an area of ½ × 10 × 6 = 30 cm². Any of the three sides can serve as the base.
How do you find the area of a trapezoid?
Use A = ½ × (a + b) × h: add the two parallel sides, divide by 2 to get their average, then multiply by the height between them. For a trapezoid with parallel sides of 6 and 10 and a height of 4, the area is ½ × 16 × 4 = 32 square units.
How many square feet are in an acre?
One acre equals exactly 43,560 square feet, which is also about 4,046.86 square meters or 0.4047 hectares. A square plot of one acre measures roughly 209 feet on each side. A typical quarter-acre residential lot is about 10,890 square feet.
What is the difference between area and perimeter?
Area measures the surface a shape covers, in square units; perimeter measures the distance around its boundary, in linear units. A 12 × 10 rectangle has an area of 120 square units but a perimeter of 2 × (12 + 10) = 44 units. Use area for flooring and paint, perimeter for fencing and trim.