- What are the area formulas for each shape?
- Rectangle: length × width. Square: side². Triangle: ½ × base × height. Circle: π × radius². Trapezoid: ½ × (a + b) × height, where a and b are the two parallel sides. Parallelogram: base × height. Ellipse: π × a × b, where a and b are the two semi-axes. Sector: (angle ÷ 360) × π × radius². The calculator shows the formula for the shape you picked with your numbers filled in, so a 5 cm circle reads π × 5² = 78.5398 cm².
- Which height do I use for a triangle, trapezoid or parallelogram?
- The perpendicular height: the straight-line distance from the base to the opposite point or side, measured at a right angle to the base. It's not the length of a slanted side. A parallelogram with a 10 ft base and 6 ft slanted sides can have a height of only 4 ft, and its area is 40 ft², not 60 ft². The dashed line on the diagram shows where the height goes.
- Why does 1 foot equal 12 inches but 1 square foot equal 144 square inches?
- Area is two lengths multiplied, so the conversion factor gets squared too. A 1 ft × 1 ft square is 12 in × 12 in, which is 144 in². The same goes for metric: 1 m is 100 cm, but 1 m² is 10,000 cm². This is the most common area mistake, and it's why the calculator converts from square meters using the squared length factors (1 ft = 0.3048 m exactly, so 1 ft² = 0.09290304 m²).
- How many square feet are in an acre, and how big is a hectare?
- One acre is 43,560 ft², or 4,046.8564224 m². One hectare is 10,000 m², a square 100 m on each side, which is about 2.4711 acres. A square mile is exactly 640 acres, or about 2.59 km². So a 100 m × 100 m plot shows 10,000 m², 1 ha and 2.4711 acres, and a 12 ft × 10 ft bedroom is 0.002755 acres.
- How do I find the area of an L-shaped room or an irregular plot?
- Split it into shapes this calculator handles, find each area, and add them up. An L-shaped room is two rectangles. A plot with one slanted edge is often a rectangle plus a triangle, or a single trapezoid. If you're adding up several rooms for flooring or a listing, the Square Footage Calculator keeps a running total for you. For a lot described by corner coordinates, a surveyor's plat is the reliable source.
- What's the difference between a radius, a diameter and a semi-axis?
- The radius is the distance from the center of a circle to its edge, half the diameter. If you measured straight across a round table at 48 in, the radius is 24 in. An ellipse has two semi-axes: half its longest width (a) and half its shortest width (b). An 8 ft × 5 ft oval rug has a = 4 and b = 2.5, so its area is π × 4 × 2.5 = 31.4159 ft². Entering the full width instead of half makes the answer four times too big.
- What is a sector, and when would I use it?
- A sector is a slice of a circle between two radii, like a slice of pizza or a garden bed shaped like a fan. Its area is the fraction of the full circle the angle covers: angle ÷ 360 × π × r². A 90° sector is a quarter circle, so a radius of 10 ft gives 78.5398 ft². One of 8 equal slices of a 16-inch pizza has a 45° angle and an 8 in radius, which works out to 25.1327 in².
- Why do some results show up like 1.2346 × 10¹⁴?
- Very large and very small areas are written in scientific notation so they stay readable: anything of 1,000,000,000,000 or more, or under 0.000001. 1.2346 × 10¹⁴ means 1.2346 with the decimal point moved 14 places right. You'll usually see it when the unit doesn't fit the job, like measuring a country in square millimeters. Switch to a larger unit and the number goes back to plain digits.
- How precise are the results?
- The math uses exact definitions: 1 in = 0.0254 m, 1 ft = 0.3048 m, 1 yd = 0.9144 m, 1 mi = 1,609.344 m, and 1 acre = 4,046.8564224 m². Results are rounded to at most 4 decimal places, and values under 0.01 keep 4 significant figures so small areas don't round to zero. Your measurements are the real limit: reading a tape to the nearest inch on a 12 ft × 10 ft room can move the area by almost 1 ft² either way.
