Area Calculator Online
Calculate surface area and perimeter for circle, rectangle, triangle, trapezoid, and ellipse.
Input Parameters
Live Result
Details
Steps
Shape: Circle (Radius r = 5)
Area Formula: A = π × r²
Substitute: π × (5)² = π × 25 ≈ 78.5398
Circumference Formula: C = 2 × π × r = 2 × π × 5 ≈ 31.4159
Diameter: d = 2r = 10
Quick Answer & Understanding Your Result
An Area Calculator computes the two-dimensional surface space occupied by geometric shapes: Formulas vary by geometry, from Circle (A = πr²) and Rectangle (A = l × w) to Triangle (A = ½ × b × h) and Trapezoid (A = ½(a + b)h). It also computes boundary perimeter and circumference.
The 8 Geometric Shape Formulas
- Circle: Area = π × r², Circumference = 2 × π × r.
- Rectangle: Area = length × width, Perimeter = 2(l + w).
- Triangle: Area = ½ × base × height.
- Square: Area = side², Perimeter = 4 × side.
- Trapezoid: Area = ½ × (base_a + base_b) × height.
- Parallelogram: Area = base × height.
- Ellipse: Area = π × a × b.
- Circle Sector: Area = (θ / 360) × π × r².
Unit Scaling & Conversions
- Area Units: Expressed in squared units (m², ft², in², cm², acres, hectares).
- Conversion Factor: 1 m² = 10.7639 sq ft, 1 acre = 43,560 sq ft.
Select your shape and enter dimensions above to calculate exact surface area and boundary perimeter instantly.
Formula & Calculation Logic
Mathematical FormulaArea measures the amount of 2D surface enclosed within boundary perimeters, scaled in square units.
Step-by-Step Guide
Select Shape
Choose circle, rectangle, triangle, square, trapezoid, parallelogram, ellipse, or sector.
Enter Dimensions
Input radius, length, width, or heights based on selected shape.
Compute Area
Click calculate to apply the shape's geometric formula.
Review Perimeter
View surface area, boundary perimeter, and diagonal dimensions.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Circle with Radius r = 5 | A = π × 5² = 25π ≈ 78.5398. | ||
| Rectangle 12 × 8 | A = 12 × 8 = 96. P = 2(12 + 8) = 40. | ||
| Triangle: Base 10, Height 6 | A = 0.5 × 10 × 6 = 30. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
Wolfram MathWorld - Area
NIST Reference on Constants, Units, and Uncertainty
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: Circle: A = π × r²
Last Reviewed: August 21, 2026
Primary Source: Wolfram MathWorld - Area
Reference Document: NIST Reference on Constants, Units, and Uncertainty
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.