Cube Diagonal Calculator

Compute the interior 3D space diagonal ( $d_{\text{space}} = a\sqrt{3}$ ) and 2D face diagonal ( $d_{\text{face}} = a\sqrt{2}$ ).

Cube Dimensions

Select Base Cross-Section

Unit:

Base Polygon

Cube Edge Length (a)cm

3D Cube Diagonal RayCorner to Corner

3D Space Diagonal

d = a\sqrt{3}

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cm

2D Face Diagonal

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cm

Explore Geometry Tools

Select a 3D prism shape to calculate volume, surface area, and step-by-step formulas.

Solve for volume, surface area, diagonal, and missing dimensions with 3-variable solver.

V = l \cdot w \cdot h

Calculate cubic prism edge, volume, total area, and space diagonal given any single parameter.

V = a^3, \; S = 6a^2

Solve equilateral, right-angled, and scalene prisms via base-height or Heron’s theorem.

V = \frac{1}{2} b h_b H

Specialized Metrics

Solve directly for a specific property across multiple prism types simultaneously.

V = B \cdot H

Compute capacity & liquid volumes across 6 solid prisms.

S = 2B + S_{\text{lat}}

Total outer surface with 2D net and scrap margin estimation.

S_{\text{lat}} = P \cdot H

Wall & sides surface area excluding top/bottom bases.

B = \frac{V}{H}

Cross-sectional polygonal area forward & inverse solver.