Online Prism Calculator

Pentagonal Prism Calculator

Determine the volume, surface area, and apothem of a regular pentagonal prism. Derived from the pentagon's golden ratio geometry and Euclidean solid principles.

Input Variable

Solve Pentagonal Prism by Any Known Value

Material Mass EstimatorMass: --

Step-by-Step Mathematical Proofs

Interactive 3D Pentagonal PrismWebGL Orbit Controls
VolumeV=B⋅HV = B \cdot H
--
cm³
Total Surface AreaS=2B+SlatS = 2B + S_{\text{lat}}
--
cm²
Lateral AreaSlatS_{\text{lat}}
--
cm²
Base AreaBB
--
cm²
Base Apothemrinr_{\text{in}}
--
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
Regular Hexahedron→

Cubic Prism Calculator

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

V=a3,  S=6a2V = a^3, \; S = 6a^2
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
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.