Area and Perimeter Calculator
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Area (A):
Perimeter (P):
Diagonal (d):
Interior angle:
Calculation:
This calculator gives the area and perimeter of the most common shapes: square, rectangle, triangle, circle, trapezoid, parallelogram, rhombus and regular polygons. Pick the shape, enter its measurements and see the result with the formula and the steps.
Below you will find a table with every formula, worked examples, a table of regular polygons and the most common questions.
How to use the area and perimeter calculator
Step 1: Choose the shape from the list. A triangle has two options: base and height (area only) or three sides (area and perimeter).
Step 2: Pick a unit if you like (for example in or ft) and enter the measurements. You can type a decimal point or a comma, for example 7.5 or 7,5. Every measurement must use the same unit.
Step 3: Click Calculate or press Enter.
Step 4: The area and the perimeter (or circumference) appear in the panel, along with other facts about the shape. The Calculation box shows the formula and every operation with your numbers.
Area and perimeter formulas
The perimeter is the distance around a shape and is measured in length units (in, ft). The area is the surface it covers and is measured in square units (in², ft²). These are the formulas the calculator uses:
| Shape | Area | Perimeter |
|---|---|---|
| Square | A = s² | P = 4s |
| Rectangle | A = b × h | P = 2(b + h) |
| Triangle (base and height) | A = b × h ÷ 2 | P = a + b + c |
| Triangle (three sides, Heron) | A = √[s(s - a)(s - b)(s - c)] | P = a + b + c |
| Circle | A = πr² | C = 2πr |
| Trapezoid | A = (B + b) × h ÷ 2 | P = B + b + c + d |
| Parallelogram | A = b × h | P = 2(b + a) |
| Rhombus | A = d1 × d2 ÷ 2 | P = 4s |
| Regular polygon | A = ns² ÷ (4 tan(180° ÷ n)) | P = ns |
For a triangle with three known sides, the area comes from Heron's formula. First find the semiperimeter s = (a + b + c) ÷ 2. Three lengths only make a triangle if the two shorter sides add up to more than the longest side (the triangle inequality). If they do not, the calculator tells you.
For a trapezoid and a parallelogram, the height is the perpendicular distance between the parallel sides, not the length of the slanted side. The perimeter needs the slanted sides, which are optional. For a rhombus the two diagonals are enough: the calculator finds the side with the Pythagorean theorem.
Area and perimeter examples
Example 1: A rectangle that is 8 by 5
A rectangular lot is 8 ft wide and 5 ft tall:
A = b × h = 8 × 5 = 40
P = 2(b + h) = 2 × (8 + 5) = 2 × 13 = 26
d = √(8² + 5²) = √(64 + 25) = √89 ≈ 9.434
The area is 40 ft² and the perimeter is 26 ft. To convert square meters to square feet, use the square meters to square feet calculator.
Example 2: A circle with radius 3.5
A circular flower bed has a radius of 3.5 ft. We use π ≈ 3.14159:
A = π × r² = π × 3.5² = π × 12.25 ≈ 38.48
C = 2 × π × r = 2 × π × 3.5 ≈ 21.99
The area is 38.48 ft² and the circumference is 21.99 ft. The diameter is 7 ft.
Example 3: A triangle with sides 13, 14 and 15
We know all three sides, so we use Heron's formula. First we check that 13 + 14 is greater than 15, and it is:
s = (13 + 14 + 15) ÷ 2 = 42 ÷ 2 = 21
A = √[21 × (21 - 13) × (21 - 14) × (21 - 15)] = √[21 × 8 × 7 × 6] = √7056 = 84
P = 13 + 14 + 15 = 42
The area is 84 and the perimeter is 42.
Example 4: A trapezoid with bases 10 and 6, height 4 and slanted sides of 5
A = (B + b) × h ÷ 2 = (10 + 6) × 4 ÷ 2 = 16 × 4 ÷ 2 = 32
P = 10 + 6 + 5 + 5 = 26
The area is 32, the perimeter is 26 and the midsegment is 8.
Regular polygons table
For a regular polygon with side 1, this table gives the area, the apothem and the interior angle. For another side s, multiply the area by s² and the apothem by s. The interior angle does not change.
| Sides (n) | Polygon | Area (side 1) | Apothem | Interior angle |
|---|---|---|---|---|
| 3 | Equilateral triangle | 0.433 | 0.2887 | 60° |
| 4 | Square | 1 | 0.5 | 90° |
| 5 | Pentagon | 1.72 | 0.6882 | 108° |
| 6 | Hexagon | 2.598 | 0.866 | 120° |
| 7 | Heptagon | 3.634 | 1.038 | 128.57° |
| 8 | Octagon | 4.828 | 1.207 | 135° |
| 9 | Nonagon | 6.182 | 1.374 | 140° |
| 10 | Decagon | 7.694 | 1.539 | 144° |
| 11 | Hendecagon | 9.366 | 1.703 | 147.27° |
| 12 | Dodecagon | 11.2 | 1.866 | 150° |
Frequently asked questions
How do I find the area of a triangle when I know the three sides?
Use Heron's formula: find the semiperimeter s = (a + b + c) ÷ 2, and the area is √[s(s - a)(s - b)(s - c)]. For sides 6, 8 and 10: s = 12 and the area is 24.
What is the difference between area and perimeter?
The perimeter is the distance around a shape and the area is the surface inside it. A rectangle that is 8 by 5 has a perimeter of 26 and an area of 40. The units differ too: ft for the perimeter and ft² for the area.
How do I find the area of a circle from its diameter?
Divide the diameter by 2 to get the radius, then use A = πr². With a diameter of 10, the radius is 5 and the area is 78.54.
How do I find the area of a regular hexagon?
Use the regular polygon formula: A = n × s² ÷ (4 × tan(180° ÷ n)). For a hexagon with side 6, the apothem is 5.196 and the area is 93.53.
Why does the calculator say my sides do not make a triangle?
Because the two shorter sides do not add up to more than the longest side. With sides 2, 3 and 6: 5 is not greater than 6, so that triangle cannot exist.
Learn more
- Area and perimeter of geometric figures
- Area of a circle
- Area of a trapezoid
- Perimeter and area of a triangle
- Area of regular polygons
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