Prism Volume Calculator

Compute the exact internal 3D cubic capacity and fluid volume across any right prism shape. Includes automated capacity conversions into Liters, Milliliters, Gallons, and cubic measurements.

Base Geometry Selection

Select Prism Solid Type

Length Unit:

Prism Base Type (Click for Dedicated SEO Page)

Rectangular Cube Triangular Trapezoidal Hexagonal Pentagonal

Base Length (l)cm

Base Width (w)cm

Prism Height (H)cm

Step-by-Step Volume Derivation

3D Volumetric Capacity ModelLiquid Level 70%

Primary Volume (V = B × H)

cm³

Base Area Component (B)

cm²

Equivalent Liquid & Space Capacities

Liters:-- L

Milliliters:-- mL

US Gallons:-- gal

Cubic Feet:-- ft³

Universal Volume Formulas for Prisms

The volume of any right or oblique prism depends solely on the 2D cross-sectional area of the base polygon (B) and the perpendicular height (H). Per Bonaventura Cavalieri’s principle (1635), two prisms having equal heights and equal base areas across all parallel slices share identical internal volume regardless of tilt or curvature.

Rectangular & Cube

V = l \cdot w \cdot h \quad | \quad V = a^3

Multiply the base rectangle dimensions by height. In a cube, all dimensions equal a, yielding a³.

Triangular Prism

V = \left(\frac{1}{2} b h_b\right) H

Half of the triangle base edge times triangle height produces Base Area B, then scaled by prism length H.

Regular Hexagonal

V = \left(\frac{3\sqrt{3}}{2} a^2\right) H

The regular hexagon base comprises six equilateral triangles, generating 2.598076 · a² multiplied by height H.

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 \cdot w \cdot h

Regular Hexahedron→

Cubic Prism Calculator

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

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

Specialized Metrics

Calculate by Geometric Property

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

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

→

Surface Area Calculator

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

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

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Lateral Area Calculator

Wall & sides surface area excluding top/bottom bases.

B = \frac{V}{H}

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Base Area Calculator

Cross-sectional polygonal area forward & inverse solver.

P = \sum e_i

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Perimeter & Skeletal Frame

Base perimeter, total 3D edge length, and Euler check.