Area Calculator
The area of a rectangle, square, triangle, circle, ellipse, trapezoid, parallelogram, sector or regular polygon, in any unit.
Result
Area: 120 ft²
A measurement, not a material estimate. Nothing is added for waste or offcuts.
- Perimeter
- 44 ft (528 in, 13.4112 m)
- Shown only where the entered parts fix the outline
https://calcgallery.com/geometry/area-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Area Calculator
- Choose the shape.
- Enter the measurements it asks for, each in whatever unit you measured in. The units can differ from field to field.
- Read the area, shown in square feet or square metres with the other common units beside it.
The formulas
| Shape | Area | What the letters are |
|---|---|---|
| Rectangle | l × w | length and width |
| Square | s² | the side |
| Triangle | ½ × b × h | base, and the height square to it |
| Triangle from three sides | √(p(p − a)(p − b)(p − c)) | the sides, and p = (a + b + c) ÷ 2 |
| Circle | π r² | radius |
| Ellipse | π × a × b | the two semi-axes, half the longest and shortest widths |
| Trapezoid | ½ × (b₁ + b₂) × h | the two parallel sides and the height between them |
| Parallelogram | b × h | base and perpendicular height |
| Circle sector | ½ × r² × θ | radius, and the central angle θ in radians |
| Regular polygon | ¼ × n × s² × cot(π ÷ n) | number of sides and side length |
Heights are measured square to the base
The triangle, trapezoid and parallelogram all use a perpendicular height: the straight line from the base to the opposite side or corner, meeting the base at a right angle. The length of a sloping side is not the height. Using it overstates the area, and the error grows as the slope flattens, which is why the triangle-from-three-sides option exists for when a true height is hard to measure.
Heron’s formula and the triangle inequality
Heron’s formula finds a triangle’s area from its three sides alone. It first takes half the perimeter, p, then multiplies p by how far it exceeds each side. A 3, 4 and 5 triangle gives p = 6 and √(6 × 3 × 2 × 1) = 6, the same answer as half of 3 × 4, because that triangle is right-angled.
The formula only makes sense for sides that can close into a triangle. If one side is as long as the other two combined, the product under the square root is zero; if it is longer, it is negative and there is no real answer. This page checks first and gives no area rather than an error value or a wrong number.
Units
Enter each measurement in the unit you took it in. The page converts everything to metres before multiplying, so a radius typed in centimetres gives the correct area. That area is shown in square feet or square metres, depending on the unit system, with other units alongside it. One square metre is ten thousand square centimetres, not a hundred: squaring a length squares its conversion factor too, which is the most common unit mistake made by hand.
Where the perimeter is shown
Where the measurements you entered fix the outline, the perimeter is shown too: rectangles, squares, circles, sectors, regular polygons and triangles from three sides. A triangle from its base and height could have any number of different sloping sides, so no perimeter is given for it. The same applies to the trapezoid and the parallelogram. An ellipse has no exact perimeter formula; the perimeter calculator gives the standard approximation and says that it is one.
With your numbers
- Area = 12 ft × 10 ft
- Area = 120 ft²
Quick reference
A measurement, not a material estimate. Nothing is added for waste or offcuts.
| Example | Area |
|---|---|
| Rectangle, 12 × 10 ft | 120 ft² |
| Circle, radius 2.5 m | 19.635 m² |
| Triangle, sides 3, 4 and 5 m | 6 m² |
| Trapezoid, 4 and 6 m sides, 3 m high | 15 m² |
| Hexagon, 2 m sides | 10.3923 m² |
| Quarter circle, radius 3 m | 7.0686 m² |
| Ellipse, 5 × 3 ft semi-axes | 47.1239 ft² |
| Square, 5 ft sides | 25 ft² |
Common questions about the Area Calculator
- How do I find the area of an irregular shape?
- Split it into shapes this page knows: an L-shaped room is two rectangles, a room with a bay is a rectangle plus a trapezoid, a gable wall is a rectangle plus a triangle. Work out each piece and add them. Where a piece is cut out, such as a pond in a lawn, work it out separately and subtract it.
- What is the difference between area and surface area?
- Area is the size of a flat shape. Surface area is the total area of every face of a solid, so a box has six rectangles to add up and a cylinder has two circles and a curved side. The surface area calculator does that sum for seven common solids.
- Why does the sector need its angle in radians?
- Because the formula ½ r² θ is only true when θ is in radians. In degrees it would need an extra factor of π ÷ 180. You can type the angle in degrees here; the page converts it to radians before using it, and the working shows both.
- When do I use Heron’s formula instead of half base times height?
- When you know the three sides but not the height. Measuring a height means finding the line square to the base, which is awkward on a real plot or a sloping roof. Three sides are easy to measure with a tape, and Heron’s formula needs nothing else.
- Why does the page refuse my triangle?
- Because those three lengths cannot meet. Each side of a triangle must be shorter than the other two added together. With sides of 1, 2 and 10, the two short sides together reach 3, nowhere near the far end of the 10. With 1, 2 and 3 they reach exactly, and the triangle lies flat with no area.