Prism Calculator

Free Online Prism Calculator

This prism calculator helps you instantly find the base area, base perimeter, volume, lateral surface area, and total surface area of any right prism — triangular, square, rectangular, pentagonal, or hexagonal. Just pick a base shape, enter its dimensions along with the prism length, and the calculator solves everything automatically, complete with an extruded 3D diagram and a full step-by-step solution that shows exactly how each formula was applied.

Whether you're a student solving mensuration problems, a teacher preparing worked examples, an engineer estimating material for a structural beam or duct, or simply someone searching for a fast and accurate volume of a prism calculator or surface area of a prism calculator, this tool covers the most common prism shapes you're likely to run into — including a triangular prism calculator, a rectangular prism calculator, a pentagonal prism calculator, and a hexagonal prism calculator, all in one place.

A prism is a three-dimensional solid with two identical, parallel polygon-shaped bases connected by flat rectangular side faces. Because a right prism's volume and surface area depend only on its base shape, base dimensions, and its length (the distance between the two bases), this calculator can solve for every property once you provide those inputs — no manual formula lookup required.

Prism Formulas Used

No matter which base shape you choose, every right prism follows the same core mensuration formulas, built on top of the base shape's own area and perimeter:

• Volume: V = Base Area × Length (the base area multiplied by the distance between the two bases)
• Lateral Surface Area (LSA): Base Perimeter × Length (the combined area of all the rectangular side faces)
• Total Surface Area (TSA): 2 × Base Area + LSA (both bases plus the lateral surface)
• Triangle base area (Heron's formula): A = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2
• Square base area: A = s² • Perimeter: 4s
• Rectangle base area: A = l × w • Perimeter: 2(l + w)
• Regular pentagon base area: A = (1/4)√(5(5+2√5)) × s² • Perimeter: 5s
• Regular hexagon base area: A = (3√3/2) × s² • Perimeter: 6s

How to Use This Prism Calculator

Using this calculator takes just a few simple steps. First, select the base shape of your prism from the dropdown menu — triangular, square, rectangular, pentagonal, or hexagonal. Second, enter the dimensions specific to that base shape: three side lengths for a triangle, one side for a square, pentagon, or hexagon, or a length and width for a rectangle. Third, enter the prism's length — the distance between the two parallel bases. The calculator instantly displays the base area, base perimeter, volume, lateral surface area, and total surface area, along with an extruded 3D diagram and a detailed breakdown of the math behind every number.

This flexible, multi-shape approach means you don't need separate calculators for a triangular prism, a rectangular prism, or a hexagonal prism — this single tool handles Heron's formula for triangles, standard regular-polygon area formulas for pentagons and hexagons, and simple multiplication for squares and rectangles, all behind the scenes.

Worked Example

Suppose you're calculating material for a triangular prism-shaped structural beam with base sides of 5, 6, and 7 units, and a prism length of 10 units. The calculator first finds the base area using Heron's formula: with s = (5+6+7)/2 = 9, the area works out to A = √(9×4×3×2) ≈ 14.7 square units. It then computes the volume as V = A × L ≈ 147 cubic units, the lateral surface area as LSA = Perimeter × L = 18 × 10 = 180 square units, and the total surface area as TSA = 2A + LSA ≈ 209.4 square units.

This same process applies automatically to any of the five supported base shapes, making the tool equally useful as a triangular prism calculator, a square prism calculator, a rectangular prism calculator, a pentagonal prism calculator, or a hexagonal prism calculator.

Understanding the Prism Diagram

The diagram above draws the prism's base shape twice — a solid, shaded front face and a lighter, dashed back face — connected by thin lines that represent the prism's length. This extruded style makes even less-common shapes like pentagonal and hexagonal prisms easy to visualize in 3D, since the eye naturally reads the connected front and back faces as a solid extending into the page. Base side lengths are labeled directly on the front face's edges, and the prism length is labeled along one of the connecting edges, so every key measurement is visible at a glance without needing to check a separate table.

Prism vs. Cylinder and Pyramid: What's the Difference?

A prism has two identical, parallel polygon bases connected by flat rectangular faces, while a cylinder is essentially a prism with a circular base — for that shape, use our Cylinder Calculator instead. A pyramid, by contrast, has only one base and tapers to a single apex point, similar to how a cone relates to a cylinder. If your base shape is a plain rectangle and you already know all three dimensions, our dedicated Cuboid Calculator also works, since a rectangular prism is simply a cuboid.

Where Prism Calculations Are Used

Prism geometry and mensuration formulas show up constantly in real life and across many fields of study and industry:

• Students and teachers use it for geometry and mensuration homework, competitive exams, and lesson planning.
• Engineers and architects use prism volume and surface area when designing structural beams, trusses, ducts, and support columns with polygonal cross-sections.
• Manufacturing industries calculate prism surface area to determine how much material, sheet metal, or coating is needed for hexagonal nuts, pentagonal fittings, and triangular brackets.
• Packaging designers use prism volume formulas to work out the capacity of boxes and containers with non-rectangular cross-sections.
• Construction professionals use prism volume calculations to estimate concrete or material needed for beams and columns with triangular or polygonal profiles.