Online Prism Calculator

Cubic Prism Calculator

Enter any single parameter (side edge length, volume, total surface area, or space diagonal) to calculate all other dimensions of the cubic prism with real-time 3D isometric projection and step-by-step mathematical proofs.

Input Variable

Solve Cubic Prism by Any Known Value

Material Mass EstimatorMass: --

Step-by-Step Mathematical Proofs

Interactive 3D Cubic PrismWebGL Orbit Controls
Side Edge Lengthaa
--
cm
VolumeV=a3V = a^3
--
cm³
Total Surface AreaS=6a2S = 6a^2
--
cm²
Space Diagonald=a3d = a\sqrt{3}
--
cm
Face Diagonaldf=a2d_f = a\sqrt{2}
--
cm
Inscribed Sphere Radiusr=a2r = \frac{a}{2}
--
cm
Explore Geometry Tools

Solvers by Prism Solid

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

Cuboid→

Rectangular Prism Calculator

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

V=l⋅w⋅hV = l \cdot w \cdot h
3-Sided Prism→

Triangular Prism Calculator

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

V=12bhbHV = \frac{1}{2} b h_b H
4-Sided Prism→

Trapezoidal Prism Calculator

Compute volume and surface area for standard and isosceles trapezoidal troughs and prisms.

V=a+b2htLV = \frac{a + b}{2} h_t L
Specialized Metrics

Calculate by Geometric Property

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

V=B⋅HV = B \cdot H→
Volume Calculator

Compute capacity & liquid volumes across 6 solid prisms.

S=2B+SlatS = 2B + S_{\text{lat}}→
Surface Area Calculator

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

Slat=P⋅HS_{\text{lat}} = P \cdot H→
Lateral Area Calculator

Wall & sides surface area excluding top/bottom bases.

B=VHB = \frac{V}{H}→
Base Area Calculator

Cross-sectional polygonal area forward & inverse solver.