Area Calculator

Calculate area of various geometric shapes with step-by-step solutions

Area Result
Select a shape and enter dimensions
Step-by-Step Solution
Step 1:
Identify the shape and its dimensions
Recognize the geometric shape and its parameters
Step 2:
Apply the area formula
Use the appropriate formula for the shape
Step 3:
Substitute values
Plug in the given dimensions
Step 4:
Calculate the area
Perform the calculation
Area Formulas
  • Circle: A = πr²
  • Triangle: A = ½bh
  • Rectangle: A = lw
  • Square: A = a²
  • Trapezoid: A = ½(a+b)h
  • Ellipse: A = πab
  • Sector: A = (θ/360)πr²
  • Parallelogram: A = bh
  • Rhombus: A = ½d1d2
  • Regular Polygon: A = (n × a²) / (4 × tan(π/n))
Common Area Calculations
Shape Dimensions Area
Circle r = 5 cm 78.54 cm²
Triangle b = 6 m, h = 4 m 12 m²
Rectangle l = 8 m, w = 5 m 40 m²
Square a = 7 in 49 in²
Trapezoid a = 5 cm, b = 9 cm, h = 4 cm 28 cm²
Ellipse a = 10 m, b = 6 m 188.5 m²
Sector r = 8 cm, θ = 60° 33.51 cm²
Applications of Area Calculation
  • Construction: Flooring, painting, roofing
  • Landscaping: Lawn care, garden planning
  • Agriculture: Field size, crop yield
  • Architecture: Space planning, material estimation
  • Manufacturing: Material usage, cost estimation
  • Real Estate: Property valuation
  • Physics: Pressure, force distribution
  • Geography: Land area measurement

Area Formulas

Common area formulas for geometric shapes:

Shape Formula Variables
Rectangle A=l×w l = length, w = width
Triangle A=12×b×h b = base, h = height
Circle A=πr2 r = radius
Trapezoid A=12×(a+b)×h a, b = parallel sides, h = height
Ellipse A=π×a×b a = semi-major axis, b = semi-minor axis
Regular Polygon A=14×n×s2×cot⁡(πn) n = sides, s = side length
Parallelogram A=b×h b = base, h = height
Rhombus A=d1×d22 d₁, d₂ = diagonals

Note: All measurements must be in the same units. Area will be in square units.

Frequently Asked Questions

Common questions about area calculations:

For irregular shapes:

  • Divide into regular shapes (triangles, rectangles)
  • Calculate area of each component
  • Sum all component areas
  • Use approximation methods like Simpson's rule
  • Use graph paper or digital tools for measurement

Area calculations:

  • Use consistent units for all dimensions
  • Area will be in square units (e.g., m², cm², ft²)
  • Convert units before calculating if necessary
  • Common conversions: 1 m² = 10,000 cm², 1 ft² = 144 in²
  • Use SI units for scientific calculations

Accuracy depends on:

  • Precision of measurements
  • Shape complexity
  • Calculation method
  • Rounding during computation
  • Measurement errors

For practical applications, allow ±5% margin of error.

Generally no, except for specific shapes:

  • Circle: Area = P²/(4π) where P is perimeter
  • Square: Area = (P/4)²
  • Regular polygons: Area = (P² × cot(π/n))/(4n)

For irregular shapes, perimeter alone doesn't determine area.

Area: Measurement of two-dimensional space

Surface Area: Total area of all surfaces of a three-dimensional object

Example:

  • Area of a circle: πr²
  • Surface area of a sphere: 4πr²

Need more help? If your question isn't answered here, please contact our support team or consult our complete user guide.