Calculator Suite

Geometry Calculator

Calculate area, volume, perimeter, and surface area for 2D and 3D shapes

Shape Selection

Choose your shape type and enter the required dimensions

Quick Geometry Presets

Circle (r=5)Square (10×10)Rectangle (12×8)Sphere (r=3)Cube (6×6×6)Cylinder (r=4, h=10)

Common Dimensions

123510121520

Geometry Formulas

Essential formulas for area, volume, and perimeter calculations

Circle

A = \pi r^2

P = 2\pi r

$A$ = Area, $P$ = Perimeter, $r$ = Radius

Rectangle

A = l \times w

P = 2(l + w)

$l$ = Length, $w$ = Width

Sphere

V = \frac{4}{3}\pi r^3

SA = 4\pi r^2

$V$ = Volume, $SA$ = Surface Area

Cylinder

V = \pi r^2 h

SA = 2\pi r(r + h)

$h$ = Height

Geometry Principles

Scaling Laws

Area scales with the square of linear dimensions, while volume scales with the cube. This explains why larger objects have proportionally less surface area.

Optimization

Circles and spheres are nature's most efficient shapes, maximizing area or volume while minimizing perimeter or surface area.

Real Applications

Geometry is fundamental in architecture, engineering, manufacturing, and design. Understanding these relationships helps optimize materials and space.

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