Area Calculator
Calculate the area and perimeter of 2D shapes including rectangles, circles, triangles, trapezoids, and regular polygons. Choose your shape and enter dimensions.
Formula:A = l × w
Results
Area
60 cm²
Perimeter32 cm
FormulaA = l × w
Select Shape
Enter Dimensions
Calculated Results
Area
60
cm²
Perimeter
32
cm
Formula Used
A = l × w
Area Formulas Reference
| Shape | Area Formula | Perimeter |
|---|---|---|
| Square | A = s² | P = 4s |
| Rectangle | A = lw | P = 2(l + w) |
| Circle | A = πr² | C = 2πr |
| Triangle | A = ½bh | P = a + b + c |
| Trapezoid | A = ½(a+b)h | P = a + b + c + d |
| Parallelogram | A = bh | P = 2(a + b) |
| Ellipse | A = πab | ≈ π(a+b)(1+3h/(10+√(4-3h))) |
| Rhombus | A = ½d₁d₂ | P = 4s |
Results
Area
60 cm²
Perimeter32 cm
FormulaA = l × w
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Practice with 3 problems to test your understanding.
?How to Calculate Area
Area measures the space inside a 2D shape. Rectangle: length x width. Square: side squared. Circle: pi x radius squared. Triangle: (base x height) / 2. Trapezoid: ((base1 + base2) x height) / 2. Area is always expressed in square units (sq ft, sq m, cm squared, etc.).
What is Area?
Area is the measure of the two-dimensional space enclosed within a shape's boundaries. It quantifies how much surface a flat figure covers and is expressed in square units such as square meters, square feet, or square centimeters. Area calculations are fundamental to geometry, construction, real estate, and many practical applications.
Key Facts About Area
- Area is the amount of space inside a 2D shape, measured in square units
- Rectangle area = length x width
- Square area = side squared
- Circle area = pi x r squared (approximately 3.14159 x radius squared)
- Triangle area = (base x height) / 2
- Trapezoid area = ((base1 + base2) x height) / 2
- Parallelogram area = base x height
- Always use consistent units (all cm, all inches, etc.) in your calculations
Quick Answer
Area measures the space inside a 2D shape. Rectangle: length x width. Square: side squared. Circle: pi x radius squared. Triangle: (base x height) / 2. Trapezoid: ((base1 + base2) x height) / 2. Area is always expressed in square units (sq ft, sq m, cm squared, etc.).
Frequently Asked Questions
Area is the amount of two-dimensional space enclosed within a shape. It's measured in square units (like cm², m², or ft²). Area tells you how much surface a shape covers, such as flooring, paint coverage, or land size.
Area measures the space inside a 2D shape (in square units), while perimeter measures the total length around the outside (in linear units). Area tells you how much carpet you need, while perimeter tells you how much fencing.
For irregular shapes, you can: (1) Break it into regular shapes, calculate each area, and add them up; (2) Use the grid method by overlaying squares and counting; (3) Use calculus for curves; (4) Measure using digital tools or planimeters.
Square the linear conversion factor. For example: 1 m² = 10,000 cm² (because 100² = 10,000). 1 ft² = 144 in² (because 12² = 144). 1 acre = 43,560 ft². 1 hectare = 10,000 m².
The basic formula is A = ½ × base × height. You can also use Heron's formula when you know all three sides: A = √(s(s-a)(s-b)(s-c)) where s is the semi-perimeter (a+b+c)/2.
A regular polygon has all sides equal length and all interior angles equal. Examples: equilateral triangle, square, regular pentagon, regular hexagon. Their area formulas involve the side length and special constants.
Last updated: 2025-01-15
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).
Results
Area
60 cm²
Perimeter32 cm
FormulaA = l × w