Area Calculator
Area and perimeter of any shape (circle, triangle, trapezoid, polygon or an irregular plot), with a diagram to scale and the formula worked.
In feet, a length can also be feet and inches: 12' 6" or 12 ft 6 in.
120 ft²
- Square metre
- 11.15 m²
- Perimeter
- 44 ft
- Diagonal
- 2√61 ≈ 15.62 ft
Working
Pick a shape, type its dimensions, and get its area and perimeter with the formula worked in your own numbers and a diagram drawn to scale. The 16 shapes run from rectangles, circles and trapezoids to a sector, a ring, a regular polygon, a plot measured by its four sides and a diagonal, and any polygon given by the coordinates of its corners.
Measurements are read exactly, so a circle of radius 5 gives 25π, not only 78.54, and a triangle with sides 5, 6 and 7 gives 6√6. Feet and inches can be typed as written on a tape (12' 6"), and the area can be shown in square feet, acres, hectares or the land units used in India and nearby.
How to use it
One shape: choose it from the grid, then how it is given where there is a choice (a circle by its radius, diameter, circumference or area; a triangle by base and height, three sides, or two sides and the angle between them). Every length is in the one unit chosen below the fields. In feet, a field also takes feet and inches: 12' 6", 12 ft 6 in, or 12.5. Angles are in degrees.
Polygon from points takes up to 500 corners, one x, y pair per line, in order around the shape; two columns pasted from a spreadsheet work. A regular polygon takes 3 to 1,000 sides.
Combined shapes adds and subtracts several shapes: an L-shaped room is a large rectangle minus the missing corner, a lawn is its outline minus a pond. A combined area has no single perimeter, since the shapes share edges, so only the total area is given.
The area appears in the square of the chosen unit and, through Area in, in any other area unit. Rectangles, triangles, plots and the other shapes land is measured in also offer the sourced land units of the Land Area Converter. Answers show up to 2 decimal places; Decimal places changes that, and Auto gives ten significant figures.
How it works
Exact inputs give exact areas wherever the formula allows: a product, a multiple of π, or a square root that simplifies. Heron's formula for a triangle's three sides is exact when its square root simplifies (sides 3, 4 and 5 give 6). Angles that are multiples of 15° have exact sines, so a sector of 60° or a regular hexagon stays exact; other angles give decimals. Very long exact forms are left out, leaving the decimal.
An ellipse's perimeter has no formula in elementary terms. The tool uses Ramanujan's second approximation, which is at worst about 0.04% out, for an ellipse flattened to a line, and closer than one part in a million when one semi-axis is under three times the other. It is marked with ≈.
A plot measured by its four sides alone is not fixed: the same four sides can lean into many shapes with different areas. A diagonal AC splits it into triangles ABC and ACD, each fixed by its three sides, and the plot's area is their sum. The tool takes B and D on opposite sides of AC, as the diagram shows. A polygon from points uses the shoelace formula, which is the enclosed area only when the sides do not cross, so crossing or touching sides are refused.
Rectangle: A = l × w, P = 2(l + w)
Triangle: A = ½ × b × h; from three sides, A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
Triangle from two sides and the angle between: A = ½ × a × b × sin C
Circle: A = πr², C = 2πr
Trapezoid: A = ½ × (a + b) × h
Parallelogram: A = b × h = a × b × sin θ
Rhombus and kite: A = ½ × p × q
Sector: A = (θ ÷ 360°) × πr², arc = (θ ÷ 180°) × πr
Segment: A = (θ ÷ 360°) × πr² − ½r² sin θ
Ellipse: A = πab
Ring: A = π(R² − r²)
Regular polygon: A = n × s² ÷ (4 tan(180° ÷ n))
Polygon from points: A = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|
Examples
A room 12 ft 6 in by 10 ft
With Rectangle and the unit in feet, type 12' 6" for the length and 10 for the width. The floor is 125 ft², which is 11.61 m², and the perimeter for skirting is 45 ft.
- Area = length × width A = 12.5 × 10 = 125 ft²
- Perimeter = 2 × (length + width) P = 2 × (12.5 + 10) = 45 ft
A circle of radius 7 cm
The area is exactly 49π cm², about 153.94 cm² to two places. The circumference is 14π cm. The textbook shortcut π ≈ 22/7 gives 154 cm², slightly high.
A plot from four sides and a diagonal
Sides AB 40, BC 30, CD 42, DA 28 and diagonal AC 50, in feet. The plot is 600 + 240√6 ≈ 1,187.877538 ft², or 131.99 gaj with Area in set to Gaj (India).
- The diagonal AC splits the plot into triangles ABC and ACD; each by Heron's formula ABC: sides 40, 30, 50 → 600 ft²
- ACD: sides 42, 28, 50 → 240√6 ≈ 587.8775383 ft²
- Area = ABC + ACD A = 600 + 240√6 ≈ 1,187.877538 ft²
- Perimeter = AB + BC + CD + DA P = 40 + 30 + 42 + 28 = 140 ft
A polygon from five corners
The corners (0, 0), (12, 0), (12, 8), (5, 12), (0, 8), in metres, outline a house shape. The shoelace formula gives 120 m², and the perimeter is 28 + √41 + √65 ≈ 42.46538199 m.
An L-shaped room
With Combined shapes, a 20 × 15 ft rectangle added and an 8 × 6 ft corner subtracted leave 252 ft²: A = 300 − 48 = 252 ft².
Area units
| Unit | Square metres | Square feet |
|---|---|---|
| Square centimetre (cm²) | 0.0001 | 0.001076391042 |
| Square metre (m²) | 1 | 10.76391042 |
| Square inch (in²) | 0.00064516 | 0.006944444444 |
| Square foot (ft²) | 0.09290304 | 1 |
| Square yard (yd²) | 0.83612736 | 9 |
| Acre (ac) | 4,046.856422 | 43,560 |
| Hectare (ha) | 10,000 | 107,639.1042 |
| Square kilometre (km²) | 1,000,000 | 10,763,910.42 |
| Square mile (mi²) | 2,589,988.11 | 27,878,400 |
Frequently asked questions
See also
- Area Converter — to convert an area between any two units.
- Land Area Converter — for bigha, katha, guntha and other land units by state.
- Triangle Calculator — to solve a triangle from its sides or angles, with its area.
- Volume Calculator — for the volume and surface area of solids and tanks.