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Area Calculator
Pick a shape, type its dimensions in any unit, and get the area instantly with the formula worked out step by step. The perimeter, a labeled diagram and the area in other units (m², ft², acres, hectares…) are shown too.
Triangle: what do you know?
Perpendicular height to the base
Half the diameter
Perpendicular height, not the slanted side
Add it to also get the perimeter
°
Enter your values to see the result.
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How to use the Area Calculator
- Choose the shape from the list.
- Pick the unit your measurements are in.
- Enter the dimensions shown for that shape. Results update as you type.
- Read the area in square units, plus the perimeter and other values.
- Check the steps and the conversion table, or copy the results.
Area formulas for common shapes
Every result on this page comes from one of the standard geometry formulas below. Lengths must be in the same unit; the area comes out in that unit squared.
| Shape | Area formula | Perimeter | Example |
|---|---|---|---|
| Square | A = s² | 4s | s = 5 → A = 25 |
| Rectangle | A = l × w | 2(l + w) | 12 × 8 → A = 96 |
| Triangle | A = ½ × b × h | a + b + c | b = 10, h = 6 → A = 30 |
| Triangle (3 sides) | A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 | a + b + c | 3, 4, 5 → A = 6 |
| Circle | A = πr² | 2πr | r = 4 → A ≈ 50.27 |
| Trapezoid | A = (a + b) ÷ 2 × h | a + b + both legs | 6, 10, h = 5 → A = 40 |
| Parallelogram | A = b × h | 2(b + side) | b = 9, h = 4 → A = 36 |
| Ellipse | A = πab | ≈ Ramanujan approximation | a = 6, b = 3 → A ≈ 56.55 |
| Circle sector | A = (θ/360) × πr² | arc + 2r | r = 5, θ = 60° → A ≈ 13.09 |
Converting square units
Because area is length × length, the conversion factor is squared. One meter is 3.2808 feet, so one square meter is 3.2808² ≈ 10.764 square feet. The table lists exact or standard factors.
| Unit | Equals |
|---|---|
| 1 square meter (m²) | 10,000 cm² · 10.7639 ft² · 1.19599 yd² |
| 1 square foot (ft²) | 144 in² · 0.092903 m² |
| 1 square yard (yd²) | 9 ft² · 0.836127 m² |
| 1 acre | 43,560 ft² · 4,046.86 m² |
| 1 hectare (ha) | 10,000 m² · 2.47105 acres |
| 1 square mile (mi²) | 640 acres · 2.58999 km² |
Tip: for irregular shapes, split the outline into rectangles, triangles and circle parts, find each area separately, then add them (or subtract cut-outs).
Frequently asked questions
How do you calculate area?
Area is the amount of flat space inside a shape, measured in square units. Each shape has its own formula: a rectangle is length × width, a triangle is ½ × base × height, a circle is π × r², and a trapezoid is (a + b) ÷ 2 × height.
How do I find the area of a triangle with three sides?
Use Heron's formula. Compute the semi-perimeter s = (a + b + c) ÷ 2, then area = √(s(s − a)(s − b)(s − c)). For sides 3, 4 and 5, s = 6 and the area is √(6 × 3 × 2 × 1) = 6.
Why is the area in square units?
Area multiplies two lengths together, so the unit is squared too. Measuring in feet gives square feet (ft²), measuring in meters gives square meters (m²). Converting is not linear: 1 m = 3.28 ft, but 1 m² = 10.76 ft².
What height do I use for a triangle or parallelogram?
Use the perpendicular height: the straight-line distance from the base to the opposite vertex or side, at a right angle to the base. The slanted side length is not the height unless the shape has a right angle.
How accurate is the ellipse perimeter?
The area of an ellipse (π × a × b) is exact, but its perimeter has no simple formula. The calculator uses Ramanujan's second approximation, which is accurate to a tiny fraction of a percent for almost every ellipse.
How do I find the area of a circle sector?
Multiply the full circle area by the fraction of the circle the sector covers: area = (θ ÷ 360) × π × r², where θ is the central angle in degrees. A 90° sector is a quarter of the circle.
Can I use this for room or floor area?
Yes. Measure the room in feet or meters and use the rectangle shape. For L-shaped rooms, split the floor into rectangles, calculate each one and add them up. For flooring or paint, add 5–10% extra for waste.
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