Area Calculator

How to use the area calculator

1. Pick the shape. There are two triangle options: base and height, or three side lengths when you can’t measure the height.
2. Pick the unit you measured in. Feet, inches, yards and miles, or meters, centimeters, millimeters and kilometers. Every length must be in that unit.
3. Enter the measurements. The labels change with the shape. For a sector, also enter the angle of the slice in degrees.
4. Read the results. The large figure is the area in square units of what you measured. The cards show the perimeter (or circumference) when every side is known, plus the area in square feet, square yards, acres and square meters, or in square meters, hectares, square feet and acres if you measured in metric.

Area formulas

The rectangle, triangle, trapezoid and circle formulas are the ones taught in OpenStax’s Prealgebra 2e (sections 9.4 and 9.5), and the calculator reproduces their worked examples:

• A rectangle 32 meters by 20 meters has an area of 640 m² and a perimeter of 104 meters.
• A triangle with an 11-inch base and 8-inch height has an area of ½ × 11 × 8 = 44 square inches.
• A trapezoid 6 inches high with bases of 14 and 11 inches has an area of ½ × 6 × 25 = 75 square inches.
• A circular sandbox with a 2.5-foot radius has an area of about 19.6 square feet. The textbook uses π ≈ 3.14 and gets 19.625; the calculator uses π to full precision and gets 19.635.

Height means the perpendicular height

For triangles, trapezoids and parallelograms, the height is measured straight up from the base at a right angle, not along a slanted side. A parallelogram with a 10-foot base and slanted 6-foot sides that stand 5 feet tall has an area of 10 × 5 = 50 square feet, not 60.

When you only know the three sides of a triangle, choose “Triangle (three sides)”. The calculator uses Heron’s formula, which OpenStax’s Algebra and Trigonometry 2e covers alongside the Law of Cosines:

Sides of 13, 14 and 15 give s = 21 and an area of √(21 × 8 × 7 × 6) = √7,056 = 84. If the two shorter sides don’t add up to more than the longest one, no triangle exists and the calculator says so.

Square feet, square yards and acres

Area units are the length unit squared, so conversion factors get squared too. One foot is 12 inches, so one square foot is 12 × 12 = 144 square inches. One yard is 3 feet, so one square yard is 9 square feet. Dividing square feet by 3 instead of 9 is a classic carpet-ordering mistake.

Since January 1, 2023, NIST uses the international foot, exactly 0.3048 meter, for all but historic and legacy work, and the acre as exactly 43,560 square feet, or 4,046.8564224 square meters. One square meter is about 10.764 square feet, and a hectare (10,000 m²) is about 2.471 acres.

For example, a 12 × 15 foot room is 180 square feet, which is 20 square yards or about 16.72 m². A 100 × 200 foot lot is 20,000 square feet, about 0.459 acre.

Irregular rooms and yards

Most real spaces aren’t one shape. The textbook approach (section 9.5) is to split the figure into pieces you can measure, find each area, and add them. An L-shaped room becomes two rectangles. A running track becomes a rectangle with a half circle at each end; two half circles make one full circle.

To subtract a cutout, such as a kitchen island that won’t get flooring, calculate it separately and subtract it from the total. Run the calculator once per piece and keep a running sum.

For a lawn or garden bed with curved edges, a rough but practical method is to measure several evenly spaced widths across it, average them, and multiply by the length. The result is an estimate, so buy a little extra.

Common uses

• Flooring, tile and carpet: sold by the square foot or square yard.
• Paint: coverage is listed in square feet per gallon. Wall area is width × height for each wall, minus windows and doors.
• Sod, seed and fertilizer: sold by the square foot or by coverage per bag; large yards and farmland are measured in acres.
• Pizza and pans: a 16-inch pizza has about 201 square inches, almost 1.8 times the 113 square inches of a 12-inch one, because area grows with the square of the diameter. Divide each price by its area to see which is the better deal.

Area and perimeter are not the same

Area is the space inside a shape, in square units. Perimeter is the distance around it, in plain length units. Shapes with the same area can have very different perimeters. A 12 × 15 foot room, a 9 × 20 foot room and a 6 × 30 foot room each cover 180 square feet, but their perimeters are 54, 58 and 72 feet. Flooring is priced by area; baseboard, fencing and edging are priced by perimeter. The calculator shows both so you can order each one.

Area also grows faster than length. Doubling every side of a shape multiplies its area by 4, and tripling multiplies it by 9. A 24 × 30 foot room is twice as long and twice as wide as a 12 × 15 foot room, and it needs 720 square feet of flooring, four times as much.

Units follow the same rule. There are 3 feet in a yard but 9 square feet in a square yard, and 12 inches in a foot but 144 square inches in a square foot. Converting a length factor without squaring it is one of the most common errors in area problems.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Rectangle LW, square s², triangle ½bh, trapezoid ½h(b₁ + b₂), parallelogram bh, circle πr², ellipse πab, sector (θ ÷ 360°)πr²; three-sided triangles use Heron’s formula.
• π is used to full precision, so results differ slightly from textbook answers that use 3.14.
• Unit conversions use 1 ft = 0.3048 m exactly, 1 yd = 3 ft, 1 acre = 43,560 ft² and 1 hectare = 10,000 m².

Sources

1. OpenStax (Rice University), Prealgebra 2e, 9.4 Use Properties of Rectangles, Triangles, and Trapezoids. Rectangle A = LW and P = 2L + 2W (Example 9.27: 32 m × 20 m), triangle A = ½bh (Example 9.33: base 11 in, height 8 in), trapezoid A = ½h(b + B) (Example 9.38: height 6 in, bases 14 and 11 in; Example 9.39: height 5 ft, bases 10.3 and 13.7 ft).
2. OpenStax (Rice University), Prealgebra 2e, 9.5 Solve Geometry Applications: Circles and Irregular Figures. Circle C = 2πr and A = πr², with Example 9.41 (a sandbox of radius 2.5 ft, using π ≈ 3.14) and irregular figures split into rectangles, triangles and semicircles (Examples 9.44–9.46).
3. OpenStax (Rice University), Algebra and Trigonometry 2e, 10.2 Non-right Triangles: Law of Cosines. Law of Cosines for SAS and SSS (Examples 1, 2 and 4) and Heron’s formula (Example 5: area ≈ 29.4).
4. National Institute of Standards and Technology, U.S. Survey Foot: Revised Unit Conversion Factors. Since January 1, 2023 the foot is 0.3048 m exactly; 1 acre = 43,560 ft² = 4,046.8564224 m², 1 mile = 5,280 ft and 1 acre-foot = 43,560 ft³.

Last reviewed November 2, 2026. For materials, add the allowance for waste the manufacturer recommends.