Online Prism Calculator

Explore All Prism Calculators

Choose from 48 dedicated high-precision geometry solvers. Filter our collection by 3D solid geometry (shape) or by physical measurement (property).

Direct Solver Matcher

Instant Calculator Finder

Select any prism shape and property to jump straight into the specialized solver.

Launch Rectangular Prism Solver
Matched: /rectangular-prism-calculator
Geometric Classification

1. Choose by Prism Shape

Select a solid geometry to access its comprehensive 3-variable solver and dedicated single-property derivations.

Cuboid

Rectangular Prism

Orthogonal 6-faced solid with 3 distinct dimensions (length, width, height). Essential for shipping boxes, storage capacity, packaging engineering, and room volume.

6 Faces•12 Edges•8 Vertices
V=l⋅w⋅hV = l \cdot w \cdot h
Regular Hexahedron

Cubic Prism

Regular solid where all edges and faces are strictly equal (a = l = w = h). Complete geometric derivations possible from any single known dimension with 3D visualization.

6 Equal Faces•12 Equal Edges•8 Vertices
V=a3S=6a2V = a^3 \quad S = 6a^2
3-Sided Prism

Triangular Prism

A solid bounded by two parallel triangular bases and three rectangular lateral faces. Solves equilateral, isosceles, right-angled, and scalene prisms via base-height or Heron’s theorem.

5 Faces•9 Edges•6 Vertices
V=12bhbHV = \frac{1}{2} b h_b H
Trough & Embankment

Trapezoidal Prism

Prism with trapezoidal cross-sections, widely used in civil engineering, road embankments, irrigation channels, concrete footers, retention basins, and agricultural troughs.

6 Faces•12 Edges•8 Vertices
V=12(a+b)htLV = \frac{1}{2}(a + b) h_t L
Honeycomb Solid

Hexagonal Prism

Solid with regular hexagonal bases, apothem inradius, and 6 rectangular walls. Found across honeycomb structures, quartz crystal prisms, carbon lattices, and fastener bolt heads.

8 Faces•18 Edges•12 Vertices
V=332a2HV = \frac{3\sqrt{3}}{2} a^2 H
5-Sided Solid

Pentagonal Prism

Prism solid bounded by regular pentagons. Evaluates golden-ratio apothem formulas for regular 5-sided polygonal columns, architectural pavilions, and crystal packaging.

7 Faces•15 Edges•10 Vertices
V≈1.7205a2HV \approx 1.7205 a^2 H
Physical Dimension & Quantity

2. Choose by Geometric Property

Select a mathematical quantity to calculate across multiple prism solid geometries simultaneously.

3D Capacity

Volume & Capacity Solver

V=B⋅HV = B \cdot H

Compute internal 3D cubic capacity across all 6 prism solids with real-time liquid volume conversions (Liters, Milliliters, US Gallons, Imperial Gallons, ft³).

  • Supports all 6 prism types
  • Liquid conversions (L, mL, Gal)
  • Material mass calculator
  • Step-by-step proofs
Launch Volume & Capacity Solver
External Area & Net

Total Surface Area Solver

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

Determine total boundary surface area across all prism solids with interactive unfolded 2D nets, material sheet planning, and fabrication waste allowances (+5% to +20%).

  • Interactive 2D net previews
  • Fabrication buffer (+5% to +20%)
  • Sheet metal estimation
  • Two-base sum verification
Launch Total Surface Area Solver
Wall & Perimeter Area

Lateral Surface Area Solver

Slat=P⋅HS_{\text{lat}} = P \cdot H

Calculate the total area of vertical side faces excluding top and bottom bases. Crucial for wrapping labels, wall cladding, paint estimations, and cylindrical duct approximations.

  • Perimeter-height product
  • Excludes top & bottom bases
  • Structural wall cladding
  • Label wrapping dimensions
Launch Lateral Surface Area Solver
2D Cross-Section

Base Area & Cross-Section Solver

B=VHB = \frac{V}{H}

Solve the 2D cross-sectional area of any prism base polygon directly from polygon dimensions, or inversely from known volume and height via Cavalieri’s principle.

  • Direct polygon geometry
  • Inverse derivation (B = V / H)
  • Heron’s triangular formula
  • Regular polygon apothems
Launch Base Area & Cross-Section Solver
Edge Wireframe

Perimeter & Skeletal Frame Solver

Etotal=2P+nHE_{\text{total}} = 2P + nH

Derive base perimeter, total welded skeletal wireframe edge length, and Euler characteristic verification (V - E + F = 2) for rebar, structural framing, and extrusion orders.

  • Base boundary perimeter
  • Total skeletal edge length
  • Welding & frame sizing
  • Euler formula proof
Launch Perimeter & Skeletal Frame Solver
3D Pythagorean

Space Diagonal Calculator

d=l2+w2+h2d = \sqrt{l^2 + w^2 + h^2}

Compute interior 3D corner-to-opposite-corner space diagonals, face diagonals, and internal angles of elevation for shipping crate clearances and structural clearance rays.

  • 3D interior diagonal ray
  • Base & side face diagonals
  • Angle of elevation
  • Longest item fit testing
Launch Space Diagonal Calculator
Inverse Derivation

Prism Height & Inverse Solver

h=VB=SlatPh = \frac{V}{B} = \frac{S_{\text{lat}}}{P}

Calculate perpendicular prism height or length from known volume, total surface area, lateral area, or diagonal ray with step-by-step algebraic isolation.

  • Solve height from Volume
  • Solve height from Lateral Area
  • Solve height from Total Area
  • Solve height from Diagonal
Launch Prism Height & Inverse Solver
Full Cross-Reference Index

3. Complete Shape × Property Index

Direct access table linking all 48 specialized calculator tools in our library.

Prism SolidFull SolverVolumeSurface AreaLateral AreaBase AreaPerimeterDiagonal
Rectangular PrismFull Solver →VolumeSurfaceLateralBase AreaPerimeterDiagonal
Cubic Prism (Cube)Full Solver →VolumeSurfaceLateralBase AreaPerimeterDiagonal
Triangular PrismFull Solver →VolumeSurfaceLateralBase AreaPerimeterN/A
Trapezoidal PrismFull Solver →VolumeSurfaceLateralBase AreaPerimeterN/A
Hexagonal PrismFull Solver →VolumeSurfaceLateralBase AreaPerimeterDiagonal
Pentagonal PrismFull Solver →VolumeSurfaceLateralBase AreaPerimeterN/A