Area Calculator
Find the area and perimeter of any common shape, with a scale drawing and every step shown. Each box can have its own unit, and the answer comes in any area unit. For rooms and flooring, use the square footage calculator.
Fractions work too, like 1 1/2 or 3/4. Each box can use a different unit.
How your area is worked out
Every shape has its own rule. Your numbers, step by step.
- 1
One unit for all
5 m, 3 mAll in m
- 2
Use the rule
length × width5 m × 3 m
- 3
Work it out
= 15 m²= 161.4587 ft²
- 4
Distance round
2 × (length + width)2 × (5 + 3)= 16 m
Read more: every formula, a worked example and area units
Area is how many unit squares fit inside a shape: a 5 m × 3 m rectangle holds 15 squares that are 1 m on each side, so its area is 15 m². Every shape has its own rule, but all of them need the lengths in one unit first. Perimeter is the distance round the edge, in plain length units.
The formula
rectangle = length × width
square = side × side = diagonal² ÷ 2
triangle = ½ × base × height
triangle from 3 sides (Heron) = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
triangle from 2 sides and the angle between = ½ × a × b × sin C
equilateral triangle = √3 ÷ 4 × side²
circle = π × radius²
semicircle = π × radius² ÷ 2; quarter circle = π × radius² ÷ 4
ellipse = π × a × b (a, b = half the long and short widths)
parallelogram = base × height = a × b × sin(angle)
trapezoid = (top + bottom) ÷ 2 × height
rhombus or kite = diagonal 1 × diagonal 2 ÷ 2
regular polygon = n × side² ÷ (4 × tan(180° ÷ n)) = ½ × perimeter × apothem
sector = π × radius² × angle ÷ 360°
ring = π × (R² − r²)
segment = ½ × radius² × (θ − sin θ), θ in radians
Worked example
A rectangle 5 m long and 3 m wide: area = 5 × 3 = 15 m². Perimeter = 2 × (5 + 3) = 16 m. One square metre is 10.7639 square feet, so the area is 15 × 10.7639 = 161.4587 ft² (161.46 rounded). If the width had been typed as 300 cm, it is turned into 3 m first: 300 ÷ 100 = 3, so the answer is the same 15 m².
A circle with a radius of 3 m: area = π × 3² = 3.1416 × 9 = 28.2743 m², and the circumference is 2 × π × 3 = 18.8496 m. A triangle with sides 3, 4 and 5: s = (3 + 4 + 5) ÷ 2 = 6, so area = √(6 × 3 × 2 × 1) = √36 = 6.
Area units
| Unit | Equals |
|---|---|
| 1 cm² | 100 mm² |
| 1 m² | 10,000 cm² = 10.7639 ft² |
| 1 km² | 1,000,000 m² = 100 hectares |
| 1 in² | 6.4516 cm² |
| 1 ft² | 144 in² = 0.092903 m² |
| 1 yd² | 9 ft² = 0.836127 m² |
| 1 acre | 43,560 ft² = 4,046.86 m² |
| 1 hectare | 10,000 m² = 2.4711 acres |
| 1 mi² | 640 acres = 2.59 km² |
To convert an area, square the length conversion: 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm². 1 ft = 12 in, so 1 ft² = 144 in².
Tips
- The height of a triangle, parallelogram or trapezoid is measured straight up from the base at a right angle, not along a slanted side.
- The radius is half the diameter. If you only know the distance round a circle, divide it by 2π (6.2832) to get the radius.
- For an odd shape, split it into rectangles, triangles and circle parts, work out each one and add them (or take away holes).
- The ellipse perimeter has no simple exact formula; this calculator uses Ramanujan’s, which is extremely close.
- For floors, plots and the cost of flooring, the square footage calculator adds rooms together and allows for waste.
Unit sizes are exact by definition (1 in = 2.54 cm, 1 ft = 0.3048 m, 1 mile = 1,609.344 m). π is used to full computer precision; working lines show it rounded to 3.1416.
Common questions
How do I find the area of a shape?
Use the rule for that shape. A rectangle is length × width, so 5 m by 3 m is 15 m². A triangle is ½ × base × height, a circle is π × radius², and a trapezoid is the average of the two parallel sides × the height. Pick the shape above and the calculator shows the rule with your numbers.
How do I find the area of a triangle with three sides?
Use Heron’s rule. Add the sides and halve it to get s, then area = √(s × (s − a) × (s − b) × (s − c)). For sides 3, 4 and 5, s = 6, so the area is √(6 × 3 × 2 × 1) = √36 = 6. The two shorter sides must add up to more than the longest one.
What is the area of a circle with a radius of 3?
Area = π × radius² = 3.1416 × 3 × 3 = 28.2743 square units. If you know the diameter, halve it first; if you know the circumference, divide it by 2π to get the radius. The distance round (circumference) of the same circle is 2 × π × 3 = 18.8496.
How do I work out area when the sides are in different units?
Turn every length into the same unit first, then use the rule. 5 m by 300 cm is 5 m × 3 m = 15 m², not 5 × 300. Here each box has its own unit, so you can type metres in one and centimetres or feet and inches in another; the calculator converts them for you.
How do I convert square metres to square feet?
One square metre is 10.7639 square feet, so multiply by 10.7639: 15 m² is 161.4587 ft². To go back, divide by 10.7639. One acre is 43,560 ft² (4,046.86 m²) and one hectare is 10,000 m² (2.4711 acres). The table under the answer shows every unit at once.
What is the difference between area and perimeter?
Area is the space inside a shape, measured in square units like m² or ft². Perimeter is the distance round the edge, measured in plain length units like m or ft. A 5 m × 3 m rectangle has an area of 15 m² and a perimeter of 2 × (5 + 3) = 16 m.
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Made by Zulu Calculator, part of AlphaZulu LLC. Formulas are shown in full and rule figures are checked against official sources; see how we build calculators.