Area Calculator

Calculate Area by Shape

Choose the shape first so only the dimensions needed for that formula are shown.

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Area result

Area Choose a shape The formula and dimensions will update after calculation.

What is Area?

Area is the amount of space inside the boundary of a two-dimensional shape. It measures the size of a surface and is expressed in square units such as square meters (mΒ²), square feet (ftΒ²), or square centimeters (cmΒ²).

Different shapes have different formulas for calculating area. The most common shapes include rectangles, circles, and triangles, each with their own specific calculation method.

How Area Calculations Work

Follow these detailed steps:

  1. Step 1: Identify the Shape
    Determine if your area is a rectangle, circle, triangle, or combination. Complex shapes can often be broken into simpler ones.
  2. Step 2: Measure Dimensions
    For rectangles: length and width. For circles: radius or diameter. For triangles: base and height (perpendicular).
  3. Step 3: Apply the Formula
    Rectangle: A = l Γ— w. Circle: A = Ο€rΒ². Triangle: A = Β½ Γ— b Γ— h. Add areas for combined shapes.

Area Formulas

Rectangle Area: A = length Γ— width

Circle Area: A = Ο€ Γ— rΒ² (where r is the radius)

Triangle Area: A = (base Γ— height) / 2

Examples

Rectangle Example

Problem: Calculate the area of a rectangle with length 10 meters and width 5 meters.

Solution: A = 10 Γ— 5 = 50 mΒ²

Circle Example

Problem: Calculate the area of a circle with radius 7 cm.

Solution: A = Ο€ Γ— 7Β² = Ο€ Γ— 49 β‰ˆ 153.94 cmΒ²

Triangle Example

Problem: Calculate the area of a triangle with base 12 inches and height 8 inches.

Solution: A = (12 Γ— 8) / 2 = 96 / 2 = 48 inΒ²

Quick Calculation Tips

  • For irregular shapes, break into rectangles and triangles
  • Always use the same units for all measurements
  • Square footage is typically measured to the nearest foot
  • For circles, measure diameter across the center for accuracy

Common Mistakes to Avoid

  • Mixing units
    Don't mix feet and inches. Convert all to same unit first: 6 feet 3 inches = 6.25 feet.
  • Using diameter instead of radius
    Circle area uses radius (half of diameter). For diameter 10, use r = 5 in the formula.

Frequently Asked Questions

What is the difference between area and perimeter?

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

Why is the area of a triangle divided by 2?

A triangle is essentially half of a rectangle or parallelogram with the same base and height. Dividing by 2 gives you exactly half that area.

What value of pi should I use?

For most practical calculations, use Ο€ β‰ˆ 3.14159. Our calculator uses a more precise value for accurate results.

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