Area Calculator
Pick a shape: rectangle, triangle, circle, trapezoid, ellipse, parallelogram or sector. Enter its sizes, all in the same unit, and press Calculate Area. The calculator shows the area in that unit squared, rounded to 4 decimal places. Sizes in feet give square feet, sizes in meters give square meters. It does not convert between units.
How to use the Area Calculator
- Enter your numbers in the Area Calculator above.
- Press the Calculate Area button to see the result.
- To try other numbers, change any value and press the button again.
The area formulas
Rectangle: a·b · · · Triangle: ½·a·h · · · Circle: π·r² · · · Trapezoid: ½(a + b)·h · · · Ellipse: π·a·b · · · Parallelogram: a·b · · · Sector: (θ ÷ 360)·π·r²
Area measures flat space in square units. For the triangle and the trapezoid, h is the height at a right angle to the base. For the ellipse, a and b are the two semi-axes, half the longest and half the shortest width. For the parallelogram, a is the base and b is the height at a right angle to it, not the slanted side. For the sector, θ is the central angle in degrees, from 0 to 360, so the sector is that share of the whole circle.
Worked example
A 12 ft × 8 ft rectangular room is 96 square feet. A circular pool with a radius of 10 ft is π × 100, which the calculator shows as 314.1593 square feet. A trapezoid-shaped plot with parallel sides of 50 m and 80 m and a height of 30 m is ½ × (50 + 80) × 30 = 1,950 square meters. A sector with a radius of 10 ft and a 90° angle is a quarter of that pool, 78.5398 square feet.
Frequently asked questions
How is area different from volume?
Area measures 2D surface (length × width). Volume measures 3D space (length × width × height). A 10 ft × 10 ft floor has 100 ft² of area; an 8 ft tall room with that floor has 800 ft³ of volume.
How do I find the area of an irregular shape?
Split it into shapes the calculator knows, such as rectangles and triangles. Work out each area in the same unit and add them up. An L-shaped room is two rectangles.
How do I find the area of a sector?
Pick Sector and enter the radius and the central angle in degrees. A radius of 10 and an angle of 90° give (90 ÷ 360) × π × 100 = 78.5398. For an angle in radians, or for the arc length and chord as well, use the circle calculator.
Why is the area of a circle πr²?
Derived by integration — the area is the limit of approximating polygons inscribed in the circle. The constant π represents the ratio of circumference to diameter and shows up in all circle geometry.