What is a Triangular Prism?

A triangular prism is a three-dimensional geometric shape characterized by two identical triangular bases connected by three rectangular lateral faces. This polyhedron has 5 faces, 9 edges, and 6 vertices, and appears frequently in architecture, packaging, and engineering applications from roof trusses to optical prisms.

What is a Triangular Prism Calculator?

A triangular prism calculator is a digital tool that automatically computes key measurements of a triangular prism, including surface area, volume, base area, and lateral surface area. These calculators eliminate complex manual calculations and provide instant, accurate results for students, engineers, architects, and DIY enthusiasts.

How to Use the Triangular Prism Calculator

1. Select Your Triangle Type: Choose from the four available options based on the known measurements of your triangular base
2. Input Your Dimensions: Enter the required values in the appropriate fields
3. Select Units: Choose consistent measurement units for all inputs
4. View Results: The calculator automatically displays the total surface area, volume, base area, and lateral surface area.

The Four Calculation Methods

• ◣ Right Triangle: Use when you know two perpendicular sides of the right triangular base
• ▲ 3 Sides: Use when you know all three side lengths of the triangular base (uses Heron’s formula)
• ▲ 2 Sides + Angle Between: Use when you know two sides and the included angle
• ▲ 2 Angles + Side Between: Use when you know two angles and the side between them.

Key Formulas Behind the Calculations

Surface Area Formulas

The total surface area of a triangular prism is the sum of the areas of all its faces:

Total Surface Area = 2 × Base Area + Lateral Surface Area 

Where:

• Base Area varies based on available measurements
• Lateral Surface Area = Perimeter of Base × Height of Prism 

Base Area Calculations by Triangle Type

Triangle Type	Formula
Right Triangle	Base Area = (a × b) / 2
Three Sides (SSS)	Base Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2 (Heron’s formula)
Two Sides + Included Angle (SAS)	Base Area = (1/2) × a × b × sin(γ)
Two Angles + Side Between (ASA)	Base Area = a² × sin(β) × sin(γ) / (2 × sin(β + γ))

Volume Formula

Volume = Base Area × Height of Prism 

This formula applies regardless of the triangle type, as volume represents the three-dimensional space occupied by the prism.

Parameter Help Section

Input Parameters

• Side Lengths (a, b, c): The lengths of the triangle’s sides; for right triangles, sides a and b are the legs (perpendicular sides)
• Prism Length (L): The distance between the two triangular bases (also called height or depth of the prism) 
• Angles (β, γ): Interior angles of the triangular base measured in degrees or radians
• Right Angle: 90° angle between sides a and b in the right triangle mode.

Output Parameters

• Total Surface Area: The combined area of all five faces (two triangles + three rectangles) 
• Lateral Surface Area: The area of the three rectangular sides only (excludes the triangular bases) 
• Base Area: The area of one triangular base (both bases have equal area) 
• Volume: The three-dimensional space enclosed by the prism, measured in cubic units.

FAQ

Q1. What if I don’t know all three sides of the triangle?

A: Our calculator solves this exact problem! Use the “2 sides + angle between” or “2 angles + side between” options when you have incomplete information about the triangular base. 

Q2. Can I use different units for different measurements?

A: For accurate results, use consistent units throughout your calculations. The calculator includes unit conversion for outputs, but inputs should maintain the same unit system.

Q3. What’s the difference between lateral and total surface area?

A: Lateral surface area includes only the three rectangular sides, while total surface area includes both triangular bases plus all three rectangular sides. 

Q4. How accurate are the calculations?

A: The calculator provides high-precision results based on the exact values you input. For practical applications, round your results to an appropriate number of significant figures based on measurement precision.