Area calculator
Pick a shape, enter its sizes, get the area instantly.
How do I find the area of a rectangle?
Multiply the length by the width. A 12 by 15 ft room is 12 × 15 = 180 square feet. For a square, multiply the side by itself.
How do I find the area of a triangle?
Half the base times the height: a triangle 10 ft along the base and 6 ft tall is 10 × 6 ÷ 2 = 30 square feet. If you know only the three sides, use Heron's formula: for sides 3, 4 and 5, s = 6 and the area is √(6 × 3 × 2 × 1) = 6.
How do I find the area of a circle?
π times the radius squared. A circle with a 4 ft radius (8 ft across) is 3.1416 × 4 × 4 = 50.27 square feet. A quarter of a circle — a 90° sector — is a quarter of that.
How do I find the area of a trapezoid?
Average the two parallel sides and multiply by the height: with sides 6 and 10 and a height of 5, (6 + 10) ÷ 2 × 5 = 40.
How do I convert square feet to square meters?
Multiply by 0.0929 — a foot is 0.3048 m, and area uses it twice. Pick a unit and the table under the result converts the area into the others.
How do I find the area of an ellipse?
π times the two semi-axes, A = π a b, where a and b are half the long and short widths. An ellipse 12 ft long and 8 ft wide has semi-axes 6 and 4, so its area is 3.1416 × 6 × 4 = 75.40 square feet. With a = b it reduces to the circle formula.
How do I find the area of a regular polygon?
For n equal sides of length s the area is n s² ÷ (4 tan(π ÷ n)). A regular hexagon with 5 ft sides has 6 × 25 ÷ (4 × tan 30°) = 64.95 square feet. A hexagon is six equilateral triangles, which is a handy check.
What is the difference between area and perimeter?
Area counts the surface inside a shape, in square units; perimeter is the distance around its edge, in plain length units. A 10 by 10 ft square and a 5 by 20 ft rectangle both have an area of 100 square feet, but their perimeters are 40 ft and 50 ft.
How the calculation works
Each shape has its own formula, and the calculator applies the one you pick after converting everything to one length unit. The rectangle is length × width; a parallelogram is base × perpendicular height; a triangle is half of base × height, or Heron's formula when only the three sides are known; a trapezoid is the average of the parallel sides times the height; a circle is π r²; an ellipse is π a b; a sector is half of r² times the angle in radians; and a regular polygon follows from its side count. The result is in square units, and the table converts it into square feet, yards, inches, meters and so on. Heights must be measured at right angles to the base, not along a slanted side.
Worked example
A room is 12 ft by 15 ft and has a semicircular bay window with a 6 ft diameter. The rectangle is 12 × 15 = 180 square feet. The bay is half a circle with radius 3 ft, so its area is π × 3² ÷ 2 = 14.14 square feet. The floor area is 180 + 14.14 = 194.14 square feet, which is 18.04 square meters (1 ft² = 0.09290304 m²) or 21.57 square yards. Carpet is often sold by the square yard, so that last figure is the one to use for a first estimate.
Common mistakes
- Mixing units. Multiplying 8 ft by 96 in gives a meaningless number. Convert both sides to the same unit first, and remember that converting an area needs the square of the length factor: 1 ft² is 144 in², not 12.
- Using the diameter in the circle formula. The formula takes the radius. A 10 ft round table has a radius of 5 ft and an area of 78.54 square feet, not 314.
- Using the slanted side as the height. For a triangle or parallelogram the height is the perpendicular distance between the base and the opposite side or vertex.
Sources and related calculators
Formulas: standard plane geometry as in OpenStax Prealgebra 2e, the chapter on math models and geometry; the exact value of the international foot (0.3048 m) comes from NIST Handbook 44, Appendix C. Related: square footage calculator, circle equation calculator and square yards calculator.