Area Calculator

Calculate the area of rectangles, triangles, circles, trapezoids, and more

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Area of a circle with radius 7
Area of a triangle with base 10 and height 6
Area of a trapezoid with bases 5 and 9 and height 4

What is Area?

Area is the measure of the amount of space enclosed within a two-dimensional shape. It is expressed in square units (e.g., cm2\text{cm}^2, m2\text{m}^2, ft2\text{ft}^2).

Area answers the question: "How much surface does this shape cover?"

Why Area Matters

Area calculations are essential in:

  • Construction: determining material needed for flooring, painting, or roofing
  • Agriculture: measuring land for planting
  • Science: calculating cross-sectional areas, surface areas
  • Everyday life: buying the right amount of carpet, fabric, or tiles

Units of Area

UnitAbbreviationConversion
Square millimetermm2\text{mm}^21 cm2=100 mm21\,\text{cm}^2 = 100\,\text{mm}^2
Square centimetercm2\text{cm}^21 m2=10,000 cm21\,\text{m}^2 = 10{,}000\,\text{cm}^2
Square meterm2\text{m}^21 km2=1,000,000 m21\,\text{km}^2 = 1{,}000{,}000\,\text{m}^2
Square footft2\text{ft}^21 ft2=144 in21\,\text{ft}^2 = 144\,\text{in}^2
Acreac1 ac=43,560 ft21\,\text{ac} = 43{,}560\,\text{ft}^2

How to Calculate Area

Area Formulas for Common Shapes

ShapeFormulaVariables
RectangleA=l×wA = l \times wll = length, ww = width
SquareA=s2A = s^2ss = side length
TriangleA=12bhA = \frac{1}{2} b hbb = base, hh = height
CircleA=πr2A = \pi r^2rr = radius
TrapezoidA=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2) hb1,b2b_1, b_2 = parallel sides, hh = height
ParallelogramA=bhA = b hbb = base, hh = height
EllipseA=πabA = \pi a ba,ba, b = semi-axes

Rectangle

The area of a rectangle is length times width:

A=l×wA = l \times w

Example: A rectangle with l=8l = 8 and w=5w = 5 has area A=8×5=40A = 8 \times 5 = 40 square units.

Triangle

The area of a triangle is half the base times the height:

A=12bhA = \frac{1}{2} b h

If you know all three sides (aa, bb, cc), use Heron's formula:

s=a+b+c2,A=s(s−a)(s−b)(s−c)s = \frac{a + b + c}{2}, \quad A = \sqrt{s(s-a)(s-b)(s-c)}

Circle

The area of a circle with radius rr:

A=πr2A = \pi r^2

If you know the diameter dd: A=πd24A = \frac{\pi d^2}{4}

If you know the circumference CC: A=C24πA = \frac{C^2}{4\pi}

Trapezoid

A trapezoid has two parallel sides (bases) b1b_1 and b2b_2 and height hh:

A=12(b1+b2)⋅hA = \frac{1}{2}(b_1 + b_2) \cdot h

This formula works because the trapezoid's area equals the average of the two bases times the height.

Composite Shapes

For irregular or composite shapes:

  1. Decompose the shape into simpler shapes (rectangles, triangles, etc.)
  2. Calculate the area of each part
  3. Add (or subtract) the areas to get the total

Common Mistakes to Avoid

  • Using diameter instead of radius — the circle formula uses radius rr, not diameter. If given the diameter, divide by 2 first: r=d2r = \frac{d}{2}.
  • Forgetting to halve for triangles — triangle area is 12bh\frac{1}{2}bh, not bhbh. A common error is omitting the 12\frac{1}{2}.
  • Using slant height instead of perpendicular height — for triangles and trapezoids, hh must be the perpendicular distance, not the slant side length.
  • Mixing units — ensure all measurements are in the same unit before calculating. Convert first, then compute.
  • Confusing perimeter with area — perimeter is the total length around a shape (linear units), while area is the enclosed surface (square units).

Examples

Step 1: Use the circle area formula: A=πr2A = \pi r^2
Step 2: Substitute: A=π(7)2=49πA = \pi (7)^2 = 49\pi
Step 3: Calculate: A=49π≈153.94 cm2A = 49\pi \approx 153.94\,\text{cm}^2
Answer: A=49π≈153.94 cm2A = 49\pi \approx 153.94\,\text{cm}^2

Step 1: Use the triangle area formula: A=12bhA = \frac{1}{2} b h
Step 2: Substitute: A=12×10×6A = \frac{1}{2} \times 10 \times 6
Step 3: A=30 cm2A = 30\,\text{cm}^2
Answer: A=30 cm2A = 30\,\text{cm}^2

Step 1: Use the trapezoid formula: A=12(b1+b2)⋅hA = \frac{1}{2}(b_1 + b_2) \cdot h
Step 2: Substitute: A=12(5+9)×4=12(14)×4A = \frac{1}{2}(5 + 9) \times 4 = \frac{1}{2}(14) \times 4
Step 3: A=7×4=28 m2A = 7 \times 4 = 28\,\text{m}^2
Answer: A=28 m2A = 28\,\text{m}^2

Frequently Asked Questions

Area measures the space inside a shape (in square units like square meters), while perimeter measures the total distance around the outside of a shape (in linear units like meters).

Break the irregular shape into simpler shapes like rectangles, triangles, and circles. Calculate the area of each part, then add them together. For shapes that have parts removed, calculate the whole shape and subtract the removed part.

Pi (approximately 3.14159) represents the ratio of a circle's circumference to its diameter. It appears in the area formula because the circle's area can be derived by dividing it into infinitely many thin triangular wedges that, when rearranged, form a rectangle with dimensions pi times r by r.

Area is always in square units. If your measurements are in centimeters, the area is in square centimeters. If in meters, the area is in square meters. Make sure all measurements use the same unit before calculating.

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