Calculate cube volume, total surface area, lateral surface area, space diagonal, and inradius from side length with step-by-step steps.
Did this calculation save you time?
Student ProjectHi! I'm a student developer building Calculat in my spare time. I was tired of searching for basic math tools and having to click through 10 spammy popups, loan ads, and cookie trackers.
I keep this website 100% free, private, and ad-free. If this helped you with your homework, project, or finances today, bookmarking this page or telling a friend helps me keep building more free tools!
A cube is a regular three-dimensional hexahedron bounded by six square faces, with three faces meeting at each of its eight vertices. It is one of the five Platonic solids.
V = s^3, \quad A_{\text{total}} = 6s^2, \quad A_{\text{lat}} = 4s^2, \quad d_{\text{space}} = s\sqrt{3}Volume is side cubed. Total surface area is 6 times side squared (six faces). Space diagonal connects opposite corners through the interior.
Scenario: Find volume and surface area of a cube with side s = 5 cm
Volume: V = 5³ = 125 cm³
Total Surface Area: A = 6 × 5² = 6 × 25 = 150 cm²
Lateral Surface Area: A_lat = 4 × 25 = 100 cm²
Space diagonal: d = 5√3 ≈ 8.6603 cm
A cube has 6 square faces, 12 straight edges of equal length, and 8 vertices.
The space diagonal connects opposite opposite vertices passing through the center: d = √(s² + s² + s²) = s√3.
Total surface area includes all 6 faces (6s²). Lateral surface area includes only the 4 vertical side faces (4s²), excluding top and bottom bases.
The circumscribed sphere touches all 8 vertices, with radius equal to half the space diagonal: R = (s√3) / 2.
Calculate cuboid (rectangular prism) volume, total surface area, lateral area, and space diagonal from length, width, and height.
Calculate square area, perimeter, diagonal, inradius, and circumradius from side length with step-by-step formulas.
Calculate sphere volume, surface area, diameter, and great circle circumference from radius with step-by-step mathematical deduction.