Area Calculator
Calculate the area of a square, rectangle, circle, triangle, trapezoid, parallelogram, ellipse, or sector, with instant unit conversions.
Area
96.0000 ft²
area = length × width
A rectangle with these dimensions has an area of 96.00 ft², using area = length × width.
Converted to Other Units
| Square Meters (m²) | 8.9187 |
| Square Feet (ft²) | 96 |
| Square Yards (yd²) | 10.6667 |
| Square Kilometers (km²) | 0.000009 |
| Acres | 0.002204 |
| Hectares | 0.000892 |
What is Area?
Area is a quantity that describes the size, or extent, of a two-dimensional shape — how much surface it covers. A useful way to picture it: area is the amount of paint it would take to fully cover the shape once, at a fixed thickness. The standard scientific unit is the square meter (m²), though square feet, acres, and hectares are common in everyday and real-estate use.
Every shape has its own formula for area, derived from its specific geometry. This calculator covers eight of the most common shapes, and can also help estimate land or floor area by breaking a complex shape into simpler pieces and adding their areas together.
Area Formulas for Every Shape
A circle is really just a special ellipse where both axes are equal, which is why the circle and ellipse formulas share the same π × (axis) × (axis) shape. A sector is a "pie slice" proportion of a full circle — the (θ/360°) term is simply what fraction of the full 360° circle the slice's angle represents.
Why Triangle Area Needs Three Different Approaches
When you know a triangle's base and height, area is simply ½ × base × height. But when you only know the three side lengths — with no height given directly — Heron's formula solves the same problem without needing to find the height first. It works by computing the semi-perimeter s (half the total perimeter), then combining s with each side's difference from s under a square root. This calculator uses Heron's formula since side lengths are the most common information available for an arbitrary triangle.
Not every set of three lengths can form a real triangle — each side must be shorter than the sum of the other two (the "triangle inequality"). If you enter side lengths that violate this, the calculator will flag it rather than return a nonsensical result.
Estimating Complex or Irregular Shapes
Real-world shapes — an oddly shaped yard, an L-shaped room, an irregular plot of land — rarely match one of these eight clean geometric forms exactly. The standard approach is to break the complex shape down into simpler shapes that do fit (rectangles, triangles, etc.), calculate each piece's area separately, and add them together for the total. An L-shaped room, for instance, is just two rectangles combined — calculate each one here and sum the results.
For shapes with curved or irregular boundaries that can't be cleanly decomposed, professional land surveys typically use more advanced techniques (like the shoelace formula applied to GPS coordinate points), which is beyond what a simple shape-based calculator can handle.
Example — Your Current Inputs
A rectangle with these dimensions has an area of 96.00 ft², using area = length × width.
Additional Example — A Backyard Lawn
A rectangular backyard measuring 40 ft by 25 ft has an area of 1,000 ft² — about 0.023 acres. A bag of grass seed that covers "up to 1,000 sq ft" would be exactly right for this lawn with no leftover, while a smaller bag covering 500 sq ft would need to be bought twice, or the yard split into two 500 ft² passes.
Converting to square meters (about 92.9 m²) is useful when comparing against products or landscaping quotes priced in metric units, which is exactly what the conversion table above does automatically for whatever shape and unit you enter.
About These Parameters
- Shape
- Selects which formula is used. Each shape shows only the specific dimensions its formula actually needs — for example, a circle only needs a radius, while a triangle needs three side lengths for Heron's formula.
- Unit
- The unit every dimension is entered in. The headline result is shown in this unit squared (for example, ft²), and the conversion table below translates that same area into square meters, square feet, square yards, square kilometers, acres, and hectares automatically.
Frequently Asked Questions
What's the difference between area and perimeter?
Area measures the surface a shape covers (in squared units, like ft² or m²); perimeter measures the total length of its boundary (in linear units, like ft or m). Two shapes can share the same perimeter but have very different areas — a long, thin rectangle has much less area than a square with the same perimeter.
How many square feet are in an acre?
One acre equals 43,560 square feet — roughly the size of a rectangle measuring about 209 ft × 209 ft. This calculator's conversion table converts your entered shape's area into acres automatically, useful for anything land-related, from real estate listings to farmland measurements.
Why did the calculator say my triangle sides are invalid?
Three lengths only form a real triangle if each one is shorter than the sum of the other two — known as the triangle inequality. For example, sides of 2, 3, and 10 can't form a triangle, since 2 + 3 is less than 10; the two shorter sides would never be able to "reach" each other to close the shape.
How do I find the area of an irregular shape, like an L-shaped room?
Split it into simpler shapes this calculator already covers — an L-shaped room is just two rectangles. Calculate each rectangle's area separately here, then add the results together for the total. This "decompose into simple shapes" approach works for most real-world irregular areas, as long as the boundaries are made of straight lines.