Pick a shape, enter its dimensions, get the area — and the perimeter where the shape has one worth quoting.
Area is a count of how many unit squares fit inside a shape, and every formula on this page is a shortcut for that count rather than a separate rule to memorise. A 10 × 6 rectangle — this page’s own default — fits exactly 60 unit squares, which is why length times width works. A triangle is exactly half of the rectangle that encloses it, which is the entire reason its formula carries that ½: base 10, height 6 gives 30, not 60. A parallelogram skips the half because tilting a rectangle's sides does not change how much floor it covers — base times height still applies directly.
Scale every dimension of any flat shape by a factor of 2, and the area grows by 2² = 4, not 2. A circle of radius 5 covers 78.54 square units; double the radius to 10 and it covers 314.16 — exactly four times as much, not twice. This is not specific to circles: it is true for every shape on this page, because area is a two-dimensional quantity and scaling multiplies both dimensions at once. It is the reason a pizza twice the diameter is not twice the food, and why a room 20% longer and 20% wider is 44% bigger, not 40%.
A circular sector is the pie-slice fraction of a full circle: area = πr² × (angle ÷ 360). A 90-degree sector of a radius-10 circle is a quarter of the full circle’s 314.16 square units — 78.54 — and its perimeter includes the two straight radius edges as well as the curved arc, which is why the sector is one of only three shapes on this page (with the rectangle and circle) that has a perimeter formula at all.
Area only needs the base and the perpendicular height, but a perimeter needs the length of every side — and neither shape's side lengths follow from base and height alone. Two triangles can share an identical base and height and therefore an identical area, while having completely different perimeters depending on how the third point sits relative to the base. Getting a real perimeter for either shape means entering all three (or four) side lengths directly, which is a different, longer calculation this quick-area tool intentionally does not attempt.
| Shape | Area |
|---|---|
| Rectangle | length × width |
| Triangle | ½ × base × height |
| Circle | πr² |
| Trapezoid | ½ × (a + b) × height |
| Parallelogram | base × height |
| Ellipse | πab (semi-axes a and b) |
| Sector | πr² × (angle ÷ 360) |
This is the single most common mistake. For a triangle or parallelogram, the height is the perpendicular distance from the base to the opposite vertex or side — not the length of a slanted side. On a leaning parallelogram the slanted side is longer than the height, and using it inflates the area.
The give-away is that a parallelogram and a rectangle with the same base and the same perpendicular height have exactly the same area, however far the parallelogram leans. Shearing a shape sideways does not change how much surface it covers.
Area is always in square units. Converting between them trips people up because the conversion factor gets squared too: one metre is 100 centimetres, but one square metre is 10,000 square centimetres, not 100. One square foot is 144 square inches, not 12.
The perpendicular height from the base to the opposite vertex, not the length of a sloping side. If you only know the three side lengths, use the Triangle Calculator instead, which applies Heron’s formula and needs no height.
Because area needs only the base and height, while the perimeter needs every side length — information this shape selector does not ask for. The Triangle Calculator takes all three sides and returns the perimeter.
Multiply by 10.7639. Take care with any area conversion: the linear factor gets squared, so 1 m = 3.28084 ft becomes 1 m² = 10.7639 ft².
A wedge of a circle, like a slice of pie, defined by a radius and the angle at the centre. Its area is the full circle’s area scaled by the fraction of 360° the angle covers.
Every shape on this page is the flat cross-section of a solid on the Volume Calculator — a rectangle extruded upward becomes a box, a circle becomes a cylinder, and the same base-times-height logic carries straight through from two dimensions into three.
For circle-specific work use the Circle Calculator, and for three dimensions the Volume Calculator and Surface Area Calculator. Working from three side lengths? The Triangle Calculator handles that. For flooring and materials, see the Unit Converter. For building and landscaping work specifically: the Square Footage Calculator converts to acres and hectares, the Tile Calculator turns an area into a tile count, and the Roofing Calculator adjusts a footprint for roof pitch.