Finding the area of a shape sounds simple, yet in real work it is where flooring quotes, paint budgets, garden beds, and land surveys either add up cleanly or drift off by a wide margin. This area calculator handles the three shapes people actually measure every day — the rectangle, the triangle, and the circle — and converts the result into square feet, square yards, and acres so you can order materials or estimate cost without a second spreadsheet.
Pick a shape, type your numbers in feet, and the area updates instantly. Switch the shape and the same form adapts: rectangles need length and width, a triangle needs a base and a perpendicular height, and a circle needs only its radius.
How to Use
- Enter the Shape number: type
1for a rectangle,2for a triangle, or3for a circle. The same form adapts to each choice. - Enter the Length / Base in feet. For a rectangle this is the long side; for a triangle it is the bottom edge (the base).
- Enter the Width / Height in feet. For a rectangle this is the short side; for a triangle it is the perpendicular height measured straight up from the base, not the sloped edge.
- For a circle only, enter the Radius — the distance from the center to the edge. If you only know the diameter, divide it by two first.
- Read the result card: the main Area is shown in square feet, with Square Yards and Acres conversions below it.
- Multiply the square footage by your material price per square foot to estimate cost — for example carpet at $4.50 per square foot, or sod at $0.35 per square foot.
If you measured in meters or yards instead of feet, convert first: one meter is about 3.281 feet, and one yard is three feet. The formulas themselves do not change — only the unit your answer arrives in.
The Area Formulas
Each shape uses a standard geometry formula taught in middle school and still used by architects, surveyors, and builders:
- Rectangle: Area = length × width. A room that is 12 feet long and 8 feet wide covers 12 × 8 = 96 square feet.
- Triangle: Area = ½ × base × height. The height must be perpendicular to the base; using the sloped side instead will overstate the area.
- Circle: Area = π × radius². With π ≈ 3.14159, a circle of radius 5 feet covers 3.14159 × 25 ≈ 78.54 square feet.
Once you have the square footage, conversions are fixed: there are 9 square feet in a square yard, and 43,560 square feet in an acre. A 96-square-foot room is therefore 10.67 square yards, which is why carpet sold by the square yard costs roughly nine times the per-square-foot price tag on the label.
When to Use Which Shape
Real spaces are rarely a single perfect shape. A living room is a rectangle; a gable end or a pitched roof is a triangle; a circular patio or a flower bed is a circle. The practical trick is to split a complex room into rectangles and triangles, calculate each piece separately, then add the areas together. An L-shaped room, for example, becomes two rectangles. A house with a dormer becomes a rectangle plus a triangle on top.
Land in the US is usually described in acres, but your tape measure gives feet. That is exactly why this calculator shows the acre figure alongside square feet: a lot of 1,600,000 square feet converts to about 36.7 acres, which is the number a real-estate listing would use.
Examples
Example 1 — Flooring a bedroom. A bedroom measures 12 ft by 8 ft. Select rectangle, enter length 12 and width 8. The area is 96 square feet, which equals 10.67 square yards. At $4.50 per square foot for installed carpet, the material cost is roughly 96 × $4.50 = $432 — add 10% for cuts and waste.
Example 2 — Painting a triangular gable. A gable wall has a base of 10 feet and a perpendicular height of 6 feet. Select triangle, enter length 10 and width 6. The area is 30 square feet. A gallon of paint covers about 350 square feet, so this gable needs less than one-tenth of a gallon — a little more than one quart for two coats.
Example 3 — Sodding a circular patio. A circular garden bed has a radius of 5 feet. Select circle, enter radius 5. The area is 78.54 square feet. At $0.35 per square foot for sod, the bed costs about 78.54 × $0.35 = $27.50, plus the soil amendment on top.
Example 4 — Measuring a large lot. A parcel measures 2,000 feet by 800 feet. Select rectangle, enter length 2000 and width 800. The area is 1,600,000 square feet, which converts to 177,778 square yards or about 36.73 acres — the figure you would see on a survey or listing.
FAQ
What is the difference between square feet and square yards?
One square yard equals nine square feet, because a yard is three feet and area scales with the square of the length. To convert square feet to square yards, divide by nine. Carpet and flooring are often quoted by the square yard while paint and sod are quoted by the square foot, so this conversion matters for accurate quotes.
How do I calculate the area of a triangle?
Use the formula area = ½ × base × height, where the height is the perpendicular distance from the base to the opposite corner. Do not use the length of a sloped side as the height — if you only know all three side lengths, use Heron's formula instead, or drop a tape measure straight up from the base and measure the true perpendicular height.
How do I find the area of a circle if I only know the diameter?
Divide the diameter by two to get the radius, then use area = π × radius². For example, a circle with a diameter of 10 feet has a radius of 5 feet, and its area is π × 25 ≈ 78.54 square feet.
How many square feet are in an acre?
Exactly 43,560 square feet. One acre is also 4,840 square yards or about 0.405 hectares. This calculator shows acres automatically whenever your square-foot result is large enough to be useful in land measurement.
How do I measure an irregular or L-shaped room?
Break the room into rectangles and triangles that fit together like puzzle pieces, calculate the area of each piece with this calculator, then add them up. For an L-shape, draw one vertical or horizontal line to split it into two rectangles. Always measure the perpendicular distance between parallel walls — diagonal tape measures will give a hypotenuse, not a side.
Should I add waste to my material order?
Yes. A common rule of thumb is to add 5–10% on top of the calculated area for cuts, seams, and off-cuts. Diagonal layouts, patterned carpet, and tile with a strong pattern need closer to 15%. The calculator gives the clean area; the waste factor is your material order cushion.
Related Calculators
- Rectangle Area Calculator — dedicated tool for rooms, lots and boxes.
- Circle Area Calculator — area and circumference from a radius or diameter.
- Triangle Area Calculator — base-height and Heron's formula variants.
- Perimeter Calculator — the outside distance around the same shapes.
Disclaimer
This area calculator is provided for informational purposes only and does not constitute architectural, engineering, surveying, or real-estate advice. Results assume accurate linear measurements in feet and the standard planar geometry formulas; complex, curved, sloped, or irregular surfaces may require a professional survey. Always double-check measurements and confirm material quantities with your supplier before purchasing.