Area Calculator
Calculate the area and perimeter of 12 common 2D shapes — Circle, Triangle, Rectangle, Trapezoid, and more.
Select a shape, enter the required dimensions with your preferred unit, then press Calculate to get the area, perimeter, and full unit conversions instantly.
Enter the lengths of all three sides.
What Is Area?
Area is the measure of the two-dimensional space enclosed within a boundary. It tells you how much surface a flat shape covers. The SI unit for area is the square meter (m²), but area can be expressed in any squared unit of length — square feet, square inches, square kilometers, and so on. Area is one of the most fundamental measurements in geometry, engineering, construction, and everyday life.
Area Formulas for All Shapes
| Shape | Area Formula | Perimeter Formula |
|---|---|---|
| Circle | A = πr² | P = 2πr |
| Triangle (b & h) | A = ½ × b × h | P = a + b + c |
| Triangle (Heron’s) | A = √(s(s−a)(s−b)(s−c)) | P = a + b + c |
| Rectangle | A = l × w | P = 2(l + w) |
| Square | A = a² | P = 4a |
| Parallelogram | A = b × h | P = 2(b + s) |
| Rhombus | A = (d1 × d2) / 2 | P = 4 × √((d1/2)² + (d2/2)²) |
| Trapezoid | A = ½ × (a + b) × h | P = a + b + c + d |
| Ellipse | A = π × a × b | P ≈ π × (3(a+b) − √((3a+b)(a+3b))) |
| Circle Sector | A = ½ × r² × θ (rad) | P = r × θ + 2r |
| Annulus (Ring) | A = π(R² − r²) | P = 2π(R + r) |
| Regular Polygon | A = (n × s² × cot(π/n)) / 4 | P = n × s |
Circle
A circle is a perfectly round shape where every point on the boundary is equidistant from the center. The distance from the center to the boundary is the radius (r). The diameter is twice the radius. Circles appear everywhere in nature and engineering — wheels, pipes, coins, and planetary orbits are all circular.
Triangle
A triangle is a three-sided polygon. If you know the base and height, area is simply half their product. If you only know the three side lengths, Heron’s formula uses the semi-perimeter (s = half the perimeter) to compute the area without needing the height at all.
Rectangle
A rectangle is a four-sided shape with four right angles and two pairs of equal, parallel sides. It is one of the most common shapes in the built world — rooms, windows, screens, and doors are almost always rectangular.
Square
A square is a special rectangle where all four sides are equal length. All interior angles are 90°. The area is simply the side length squared, and the diagonal of a square equals the side length multiplied by √2.
Parallelogram
A parallelogram has two pairs of parallel sides. Unlike a rectangle, the angles are not necessarily 90°. The area is the base multiplied by the perpendicular height — not the slant side length. Rhombuses and rectangles are special cases of parallelograms.
Rhombus
A rhombus is a parallelogram with all four sides equal. Its area is most easily calculated using the two diagonals, which bisect each other at right angles. Diamonds on playing cards are rhombuses.
Trapezoid
A trapezoid (or trapezium) has exactly one pair of parallel sides called the bases. The area is the average of the two bases multiplied by the height. Buckets, certain road signs, and cross-sections of canals are often trapezoidal.
Ellipse
An ellipse is a stretched circle with two axes — the semi-major axis (a, the longer half) and the semi-minor axis (b, the shorter half). When both axes are equal, an ellipse becomes a circle. Orbits of planets around the sun follow elliptical paths.
Circle Sector
A sector is a “pie slice” of a circle — the region bounded by two radii and an arc. The angle θ determines what fraction of the full circle the sector represents. A 90° sector is a quarter circle; a 180° sector is a semicircle.
Annulus (Ring)
An annulus is the region between two concentric circles — like a washer, a ring, or a cross-section of a pipe wall. Its area is simply the area of the outer circle minus the area of the inner circle.
Regular Polygon
A regular polygon has all sides equal and all interior angles equal. Triangles, squares, pentagons, hexagons, and octagons are all regular polygons when their sides are equal. As the number of sides increases, a regular polygon approaches the shape of a circle.
Common Area Unit Conversions
| Unit | Square Meters (m²) | Square Feet (ft²) | Square Inches (in²) |
|---|---|---|---|
| 1 mm² | 0.000001 | 0.0000108 | 0.00155 |
| 1 cm² | 0.0001 | 0.001076 | 0.155 |
| 1 in² | 0.000645 | 0.00694 | 1 |
| 1 ft² | 0.0929 | 1 | 144 |
| 1 yd² | 0.8361 | 9 | 1,296 |
| 1 m² | 1 | 10.7639 | 1,550 |
| 1 acre | 4,046.86 | 43,560 | 6,272,640 |
| 1 km² | 1,000,000 | 10,763,910 | 1,550,003,100 |
| 1 mi² | 2,589,988 | 27,878,400 | 4,014,489,600 |
Real-World Applications of Area
Area calculations are essential in construction and architecture for calculating floor space, wall coverage, and roofing material. In agriculture, field areas determine crop yield estimates and irrigation planning. Interior designers use area to determine paint, tile, and flooring quantities. Land surveyors measure plot areas for property boundaries. Engineers use area in structural and thermal calculations.