3D Shape Calculator

Select any of 12 three-dimensional shapes, adjust the dimensions with sliders, and see the surface area and volume calculated instantly with step-by-step formulas. The interactive 3D diagram updates in real time.

Select Shape

Cube

Dimensions

Unit

Side Length (a)

cm

Surface Area

150

cm²

Volume

125

cm³

Surface Area Calculation

SA = 6a^2

SA = 6 \times 5^2

SA = 6 \times 25

SA = 150

Volume Calculation

V = a^3

V = 5^3

V = 125

Real-World Presets

Reference Guide

Surface Area Formulas

Shape	Surface Area
Cube	$6a^2$
Rect. Prism	$2(lw+lh+wh)$
Sphere	$4\pi r^2$
Cylinder	$2\pi r^2+2\pi rh$
Cone	$\pi r^2+\pi rl$
Tri. Prism	$bh_t+2sl+bl$
Pyramid	$a^2+2al$
Hemisphere	$3\pi r^2$
Ellipsoid	$\approx 4\pi\!\left(\frac{a^p b^p\!+\!a^p c^p\!+\!b^p c^p}{3}\right)^{\!1/p}$
Torus	$4\pi^2 Rr$
Hex. Prism	$6ah+3\sqrt{3}a^2$
Pent. Prism	$5ah+\tfrac{\sqrt{25+10\sqrt5}}{2}a^2$

Volume Formulas

Shape	Volume
Cube	$a^3$
Rect. Prism	$lwh$
Sphere	$\tfrac{4}{3}\pi r^3$
Cylinder	$\pi r^2 h$
Cone	$\tfrac{1}{3}\pi r^2 h$
Tri. Prism	$\tfrac{1}{2}bh_t l$
Pyramid	$\tfrac{1}{3}a^2 h$
Hemisphere	$\tfrac{2}{3}\pi r^3$
Ellipsoid	$\tfrac{4}{3}\pi abc$
Torus	$2\pi^2 Rr^2$
Hex. Prism	$\tfrac{3\sqrt{3}}{2}a^2 h$
Pent. Prism	$\tfrac{\sqrt{25+10\sqrt5}}{4}a^2 h$

Units and Conversions

Surface area is measured in square units (cm², m², in², ft²) and volume in cubic units (cm³, m³, in³, ft³).

From	To	Factor
1 m	100 cm	length
1 ft	12 in	length
1 in	2.54 cm	length
1 m²	10,000 cm²	area
1 m³	1,000,000 cm³	volume

To convert area, square the length factor. To convert volume, cube it. For example, 1 ft³ = 12³ in³ = 1,728 in³.

Real-World Applications

Packaging — Surface area determines how much material you need to wrap a box or label a can.
Engineering — Tank volume tells you how much liquid a cylindrical or spherical tank holds.
Architecture — Pyramid and prism volumes help estimate material for roofs, columns, and foundations.
Cooking — Knowing the volume of a hemisphere bowl helps scale recipes to the right serving size.
Sports — A basketball (sphere) has a regulation circumference of 75 cm, meaning r is about 12 cm.

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