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  1. Home
  2. Math Calculators
  3. Prism Calculator

Prism Calculator

Calculate prism properties including volume, surface area, and lateral surface for any regular polygon base shape.

Formula:V = Base Area × Height

Prism Properties

Volume

1200 cm^3

Base Area80 cm^2
Lateral Surface540 cm^2
Total Surface700 cm^2

3D Visualization

lh
Base Side (a):10 cm
Base Width (b):8 cm
Height (h):15 cm
Base Perimeter:36 cm

Prism Input

cm
cm
cm

The distance between the two parallel bases

Real-World Prism Examples

Quick-start with common scenarios

All Prism Properties

Volume (V)

1200 cm^3

V = Base x h

Base Area

80 cm^2

Base Perimeter

36 cm

Lateral Surface Area

540 cm^2

= Perimeter x h

Total Surface Area

700 cm^2

= 2 x Base + Lateral

Geometric Properties

6

Faces

12

Edges

8

Vertices

Euler's Formula: For any convex polyhedron, Vertices - Edges + Faces = 2. Check: 8 - 12 + 6 = 2

Prism vs Pyramid Comparison

This Prism

1200 cm^3

Equivalent Pyramid

400 cm^3

(Same base & height)

A prism always has 3 times the volume of a pyramid with the same base and height. This relationship was proven by ancient mathematicians.

Prism Formulas

Volume Formulas

  • Any prism: V = Base Area x h
  • Rectangular: V = l x w x h
  • Triangular: V = (1/2)bh_base x H
  • Hexagonal: V = (3sqrt(3)/2)s^2 x h

Surface Area Formulas

  • Total SA = 2 x Base + Lateral
  • Lateral SA = Perimeter x Height
  • Rectangular: 2(lw + lh + wh)

Prism Properties

Volume

1200 cm^3

Base Area80 cm^2
Total Surface700 cm^2

?How to Calculate Prism Properties

Prism formulas: Volume = Base Area x Height. For any prism, multiply the area of the base polygon by the height (length) of the prism. Total Surface Area = 2 x Base Area + Lateral Surface Area. Lateral Surface Area = Base Perimeter x Height. A triangular prism has 5 faces, a rectangular prism has 6 faces.

What is a Prism?

A prism is a three-dimensional solid with two parallel, congruent polygonal bases connected by rectangular lateral faces. Prisms are named by their base shape: triangular prism, rectangular prism (also called cuboid or box), pentagonal prism, hexagonal prism, etc. The height (or length) of a prism is the perpendicular distance between the two bases.

Key Facts About Prisms

  • Volume = Base Area x Height for ALL prisms
  • Lateral Surface Area = Perimeter x Height
  • Total Surface Area = 2 x Base + Lateral
  • A prism has 3x the volume of a pyramid with the same base and height
  • Rectangular prism (cuboid) V = length x width x height
  • Triangular prism has 5 faces, 9 edges, and 6 vertices
  • The two bases of a prism are congruent parallel polygons
  • A right prism has lateral edges perpendicular to the base

Quick Answer

Prism formulas: Volume = Base Area x Height. For any prism, multiply the area of the base polygon by the height (length) of the prism. Total Surface Area = 2 x Base Area + Lateral Surface Area. Lateral Surface Area = Base Perimeter x Height. A triangular prism has 5 faces, a rectangular prism has 6 faces.

Practice Prism Problems

Test your skills with practice problems

Practice with 4 problems to test your understanding.

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Frequently Asked Questions

The volume of any prism is V = Base Area x Height. For a rectangular prism (box): V = length x width x height. For a triangular prism: V = (1/2) x base x height_of_triangle x prism_length. The key is to first calculate the area of the base polygon, then multiply by the height.

V = Base Area x Height. Works for all prism types.

Total Surface Area = 2 x Base Area + Lateral Surface Area. The lateral surface area is the sum of all rectangular side faces, which equals the perimeter of the base times the height of the prism.

Total SA = 2 x Base Area + (Perimeter x Height).

A prism has a polygon base (triangle, rectangle, hexagon, etc.) while a cylinder has a circular base. Both have the same volume formula concept: Base Area x Height. A cylinder is sometimes called a "circular prism."

Prism has polygon base; cylinder has circular base. Same volume formula.

A triangular prism has 5 faces: 2 triangular bases and 3 rectangular lateral faces. It also has 9 edges and 6 vertices. In general, an n-sided prism has n+2 faces, 3n edges, and 2n vertices.

5 faces: 2 triangular bases + 3 rectangular sides.

A right prism has lateral edges perpendicular to the base, making the side faces rectangles. An oblique prism has lateral edges at an angle to the base, making parallelogram-shaped side faces. Both have the same volume formula.

Right prism: edges perpendicular to base. Oblique: edges at an angle.

Height = Volume / Base Area. First calculate the area of the base polygon, then divide the known volume by that area to find the height (length) of the prism.

Height = Volume / Base Area.

A rectangular prism (also called a cuboid or box) is a prism with rectangular bases. It has 6 rectangular faces, 12 edges, and 8 vertices. Volume = length x width x height. Surface Area = 2(lw + lh + wh).

A box shape with 6 rectangular faces. V = l x w x h.

For a regular hexagonal prism: Base Area = (3sqrt(3)/2) x s^2, where s is the side length. Volume = Base Area x Height. The perimeter is 6s, so Lateral Surface Area = 6s x h.

Base Area = (3sqrt(3)/2)s^2. Then V = Base Area x h.

Last updated: 2025-01-15

Prism Properties

Volume

1200 cm^3

Base Area80 cm^2
Lateral Surface540 cm^2
Total Surface700 cm^2