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Area Calculator

Math

Calculate the area of rectangles, triangles, circles, trapezoids, parallelograms, ellipses, sectors, and regular polygons with step-by-step formulas and universal unit conversions.

Presets:
RECTANGLE Area (m²)
50 m² Perimeter: 30.0000 m
Length (l) Width (w)

Unit Conversions (Converted from m²)

Square Meters (m²) 50
Square Centimeters (cm²) 500,000
Square Millimeters (mm²) 50,000,000
Square Kilometers (km²) 0.00005
Square Feet (ft²) 538.1955
Square Inches (in²) 77,500.155
Square Yards (yd²) 59.7995
Acres 0.012355
Hectares 0.005

Calculation Steps

1 1. Rectangle Area Formula
A = length × width = 10 m × 5 m = 50 m²

Multiply length by width in the chosen unit.

2 2. Perimeter & Diagonal
P = 2(l + w) = 2(10 + 5) = 30 m | Diagonal d = √(l² + w²) = 11.1803 m

Boundary length and corner-to-corner diagonal distance.

How This Calculator Works

Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina in the plane. It can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape.

📐 Standard Geometric Area Formulas
Rectangle: A = lw | Triangle: A = ½bh | Circle: A = πr² | Trapezoid: A = ½(a + b)h
Parallelogram: A = b · h (base times perpendicular height)
Ellipse: A = π · a · b (semi-major axis times semi-minor axis times π)
Circular Sector: A = (θ / 360°) · πr²
Regular n-gon: A = (n · s²) / [4 · tan(π/n)]

Key Mathematical Rules & Properties

Perpendicular Height Requirement

Always use perpendicular (orthogonal) height, not slant height, when calculating triangle, trapezoid, or parallelogram areas.

Understanding your calculation

Method, example and limitations

How the calculation works

Area describes a two-dimensional surface. Select its shape and use matching length units before applying the corresponding geometric formula.

Example to check

A rectangle 8 m long and 5 m wide has area 40 m². A triangle with base 8 m and perpendicular height 5 m has area 20 m².

Before using the result

Use perpendicular height where required. Square-unit conversions require squaring the length conversion factor.

Calculation methodology · Report a result that needs review