Area Calculator
Calculate the area of common 2D shapes.
Rectangle
Circle
Triangle
Trapezoid
Quick Examples
Area Formulas
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = l x w | l=10, w=5: A=50 |
| Circle | A = pi r^2 | r=7: A=153.94 |
| Triangle | A = (1/2) b h | b=10, h=8: A=40 |
| Square | A = s^2 | s=6: A=36 |
| Trapezoid | A = (1/2)(a+b)h | a=8, b=12, h=5: A=50 |
What is Area?
Area is the amount of two-dimensional space inside a shape. It's measured in square units like square meters (m2), square feet (ft2), or square centimeters (cm2).
How to Use This Area Calculator
- Choose the shape: click Rectangle, Circle, Triangle, or Trapezoid at the top of the tool.
- Enter the measurements: type the dimensions the shape asks for — length and width for a rectangle, radius for a circle, base and height for a triangle, or the two bases and height for a trapezoid.
- Keep units consistent: enter every measurement in the same unit (all centimeters, all feet, and so on).
- Click "Calculate Area": the result appears instantly, together with the formula the tool used.
Area of a Rectangle
Multiply length by width:
Worked example: A bedroom floor measures 4 m by 5 m. A = 4 × 5 = 20 m². If you are buying tiles that each cover 0.25 m², you need 20 ÷ 0.25 = 80 tiles; add 10% for cutting waste (80 × 1.10 = 88) and buy 88 tiles.
Area of a Triangle
Take half the product of the base and the perpendicular height (the height measured at right angles to the base, not the slanted side):
Worked example: A triangle with base 10 cm and height 8 cm has area A = ½ × 10 × 8 = 40 cm². When you know all three sides instead of the height, Heron's formula gives the same answer without measuring any height.
Area of a Circle
A circle with radius r covers π times the square of the radius:
Worked example: A circular lawn with radius 7 m has area A = π × 49 ≈ 153.94 m². If you only know the diameter, halve it first: a 10 m diameter gives r = 5 m and A = π × 25 ≈ 78.54 m².
Area of a Trapezoid
Average the two parallel sides and multiply by the height:
Worked example: A garden bed shaped like a trapezoid has parallel sides 8 m and 12 m and a height of 5 m. A = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 m².
More Shapes: Ellipse, Parallelogram, Rhombus, Sector
Several other flat shapes appear often in homework and DIY projects:
- Ellipse: A = π × a × b, where a and b are the semi-major and semi-minor axes. An ellipse with a = 5 and b = 3 has A = π × 15 ≈ 47.12 square units.
- Parallelogram: A = base × height, using the perpendicular height. A 12 cm by 5 cm parallelogram has A = 60 cm².
- Rhombus / Kite: A = ½ × d₁ × d₂, using the two diagonals. Diagonals of 8 and 6 give A = ½ × 8 × 6 = 24 square units.
- Circular sector: A = (θ/360) × πr², where θ is the central angle in degrees. A 90° slice of a circle with radius 10 has A = (90/360) × π × 100 ≈ 78.54 square units.
Measuring Irregular Shapes
Real rooms and plots are rarely perfect rectangles. The standard method is to split the shape into simple parts, calculate each part's area, and add the results.
Worked example: An L-shaped patio is a 6 m × 4 m rectangle plus a right triangle with base 6 m and height 3 m. Rectangle: 6 × 4 = 24 m². Triangle: ½ × 6 × 3 = 9 m². Total: 24 + 9 = 33 m².
Why Area Scales with the Square
If you double every side of a shape, the area becomes four times as large, not twice. A 2 m square covers 4 m², but a 4 m square covers 16 m². That is why a pizza that is twice as wide holds about four times the pizza — and why small measurement errors in length turn into larger errors in area.
Square Units and Conversions
Area always carries square units — the unit of your measurements, squared. Feet become square feet (ft²), meters become square meters (m²).
| Conversion | Value |
|---|---|
| 1 m² | 10.7639 ft² |
| 1 ft² | 0.0929 m² |
| 1 yd² | 9 ft² |
| 1 acre | 43,560 ft² |
| 1 hectare | 10,000 m² |
Area vs Perimeter
Area and perimeter answer different questions: area measures the surface inside a shape, perimeter measures the distance around it. Painting a wall needs area; fencing a yard needs perimeter.
| Property | What it measures | Units | Example: 8 m × 5 m rectangle |
|---|---|---|---|
| Area | Space enclosed | Square units | A = 8 × 5 = 40 m² |
| Perimeter | Boundary length | Linear units | P = 2 × (8 + 5) = 26 m |
Common Mistakes
- Using the slanted side as the height: in triangle and trapezoid formulas, height must be the perpendicular distance. A slanted side is longer and gives the wrong answer.
- Mixing units: entering length in meters and width in centimeters produces a meaningless number. Convert everything to one unit first.
- Entering the diameter as the radius: the circle formula needs r, so halve the diameter before squaring.
- Reporting area in plain units: writing "40 m" when you mean 40 m² confuses area with length — always keep the squared unit.
Tip: when measuring a room, measure twice — once along each wall — and subtract doorways and built-in fixtures from the total so you buy exactly the right amount of flooring or paint.
Area in Everyday Projects
Flooring
A 4 m × 5 m room has 20 m² of floor. Flooring sold in boxes covering 2 m² each means 10 boxes, plus one spare for mistakes: buy 11 boxes.
Paint
A wall 3 m wide and 4 m tall has area 12 m². If one liter of paint covers 10 m², one coat needs 1.2 liters — buy 1.5 liters, and double it for two coats.
Lawn seed
A 200 m² lawn with seed bags covering 50 m² each needs exactly 4 bags.
Area Formula Quick Reference
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = l × w | 10 × 5: A = 50 |
| Square | A = s² | s = 6: A = 36 |
| Triangle | A = ½bh (or Heron's) | b = 10, h = 8: A = 40 |
| Circle | A = πr² | r = 7: A ≈ 153.94 |
| Trapezoid | A = ½(a + b)h | a = 8, b = 12, h = 5: A = 50 |
| Parallelogram | A = b × h | b = 12, h = 5: A = 60 |
| Ellipse | A = πab | a = 5, b = 3: A ≈ 47.12 |
| Sector | A = (θ/360)πr² | r = 10, θ = 90°: A ≈ 78.54 |