Prism Calculator
Calculate prism properties including volume, surface area, and lateral surface for any regular polygon base shape.
V = Base Area x HeightPrism Properties
Volume
1200 cm^3
3D Visualization
Prism Input
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
?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.
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.
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."
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.
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.
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.
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).
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.
Last updated: 2025-01-15
Prism Properties
Volume
1200 cm^3