Geometric Reference Guide
Volume Formulas & Mathematical Derivations
Standard reference equations, surface area formulas, and diagrams for regular three-dimensional geometric solids. Click any shape to open its dedicated interactive calculator.
Cube
3D GeometryVolume Formula:V = a³
Surface Area:A = 6a²
Variables: a = edge length
Rectangular Prism (Box)
3D GeometryVolume Formula:V = l × w × h
Surface Area:A = 2(lw + lh + wh)
Variables: l = length, w = width, h = height
Cylinder
3D GeometryVolume Formula:V = π × r² × h
Surface Area:A = 2πrh + 2πr²
Variables: r = radius, h = height
Sphere
3D GeometryVolume Formula:V = ⁴⁄₃ × π × r³
Surface Area:A = 4 × π × r²
Variables: r = radius
Cone
3D GeometryVolume Formula:V = ⅓ × π × r² × h
Surface Area:A = πr(r + s) where s = √(r² + h²)
Variables: r = base radius, h = height, s = slant height
Pipe (Fluid Bore)
3D GeometryVolume Formula:V = π × (ID / 2)² × L
Surface Area:Internal Surface = π × ID × L
Variables: ID = inside diameter, L = length