Triangle type
▲ base and height
Triangular prism with a known base and height of its face





Base (b)
in
Height (h)
in
Prism length (L)
in
Prism volume
cu in
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Volume of a Triangular Prism Calculator

By Łucja Zaborowska
Last updated: Sep 21, 2020
Table of contents:

Our volume of a triangular prism calculator is a simple tool that can solve all your queries connected to the topic - using one of the 6 available methods with 6 different sets of data. 📐

Take a look at our article below - you will not only discover what the formula is for the volume of a triangular prism, we will also explain the mathematical laws that make it possible.

Get ready - we'll help you finally understand how to find the volume of a triangular prism all by yourself. 🤓

How to use the volume of a triangular prism calculator?

So, how do you find the volume of a triangular prism with the help of our tool? It's as easy as it seems - you're just seconds away from your result!

  1. Select the type of triangle face calculation

    Think about what you already know about the triangle present in the prism, and find out which values are given:

    • ▲ Base and height - you already know the length of the base and the triangle's height;
    • ◣ Right triangle - your triangle has a right angle (90°) between two of its arms. You know the lengths of these arms (this option serves as the volume of a right triangular prism calculator);
    • ▲ 3 sides - you know the lengths of all three sides of the triangle;
    • ▲ 2 sides + angle between - you know the lengths of two sides and the value of the angle between them;
    • ▲ 2 angles + side between - you know the value of two angles of the triangle and the length of the side that lies between them; and
    • ▲ Area of triangular face - the perfect option if you're one step ahead and you have already calculated the area of a triangular face of your prism.

  2. Enter all the data given in your query

    You can choose from 11 different units - don't hesitate to mix them!

  3. Your results are here 🎉

It was that bad, was it? How about trying our other prism calculators:

🔺 Triangular:

♦️ Rectangular:

How to calculate the volume of a triangular prism?

As we've already mentioned, there are 6 ways to find out what is the volume of a triangular prism in our calculator. Let's quickly browse all of them.

  1. ▲ Base and height

    This is the basic volume equation of a triangular prism:

    Volume = 0.5 * Base * Height * Length

    Where:

    • Base and Height are the values of the triangular face of the prism; and
    • Length means the length of the entire prism, i.e., the distance between two faces.

  2. ◣ Right triangle

    Probably the most popular type of prism!

    The right triangular prism formula looks as follows:

    Volume = Length * ((a * b) / 2)

    Where:

    • a and b are the sides of the triangle that touch the right angle; and
    • Length means the length of the entire prism, i.e., distance between two faces.

    In order to calculate the c side, use the Pythagorean theorem.

  3. ▲ 3 sides

    Volume = 0.25 * √( (a+b+c) * (-a+b+c) * (a-b+c) * (a+b-c) ) * Length

    Where:

    • √ - means the square root of all the multiplied sums of the triangle sides (x² = y, √y = x);
    • a, b, and c are sides of the triangular face; and
    • Length means the length of the entire prism, i.e., distance between two faces.
💡 Remember that for three lines to form a triangle, the sum of lengths of any two sides must be greater than the length of the third side!

  1. ▲ 2 sides + angle between

    Volume = 0.5 * a * b * sin(Angle γ) * Length

    Where:

    • sin - sine of the Angle γ (use the sines tables and our law of sines calculator to understand the basis of this equation);
    • a and b are the sides of the triangle that touch the Angle γ;
    • Angle γ - its value must be between 0 and 180 degrees; and
    • Length means the length of the entire prism, i.e., distance between two faces

  2. ▲ 2 angles + side between

    Volume = 0.5 * a *((a * sin(Angle β))/ sin(Angle β + Angle γ)) * sin(Angle γ) * Length

    Where:

    • sin - sine of a given angle. Found with the sines tables, based on the law of sines (as mentioned above);
    • a is the side of a triangle that touches both Angle γ and Angle β;
    • Angle γ - its value must be between 0 and 180 degrees;
    • Angle β - its value must be between 0 and 180 degrees; and
    • Length means the length of the entire prism, i.e., distance between two faces
💡 Sum of Angle γ and Angle β also can't exceed 180 degrees (Angle β + Angle γ < 180°).

  1. ▲ Area of triangular face

    The best solution if you already know the triangular face.

    Volume = Triangle base area * Length

    Where:

    • Triangle base area is given in area unit e.g., square inches (in²), square meters (m²), or square miles (mi²); and
    • Length means the length of the entire prism, i.e., distance between two faces
Łucja Zaborowska