Prism Calculator (Volume and Surface Area)

Calculate the volume ($V$), lateral surface area ($LSA$), and total surface area ($TSA$) for the two most common types of prisms: **Rectangular** and **Triangular**. Select the prism type below to input your dimensions.

Universal Prism Formulas

A prism is a polyhedron whose two bases are parallel, congruent polygons, and whose faces are parallelograms. All calculations stem from the base properties.

1. Volume ($V$)

The volume formula is consistent for all prisms, requiring only the area of the base ($B$) and the height/length of the prism ($L$):

Where $B$ is the area of the polygonal base and $L$ is the distance between the two bases.

2. Surface Area ($TSA$ and $LSA$)

The lateral surface area ($LSA$) is the area of all the sides, excluding the top and bottom bases. The total surface area ($TSA$) includes the bases.

Specific Prism Formulas

Rectangular Prism (Cuboid)

For a rectangular base with length $l$ and width $w$, and prism height $h$:

• **Base Area ($B$):** $B = l \cdot w$
• **Base Perimeter ($P$):** $P = 2l + 2w$
• **Volume ($V$):** $V = l \cdot w \cdot h$
• **Total Area ($TSA$):** $TSA = 2(lw + lh + wh)$

Triangular Prism

For a triangular base with base side $b_{tri}$ and height $h_{tri}$, and prism length $L$:

• **Base Area ($B$):** $B = \frac{1}{2} b_{tri} \cdot h_{tri}$
• **Volume ($V$):** $V = \frac{1}{2} b_{tri} \cdot h_{tri} \cdot L$
• **Total Area ($TSA$):** You must sum the area of the three rectangular sides (Lateral Area) and the two triangular bases.

Frequently Asked Questions (FAQ)

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V = B \cdot L

LSA = P \cdot L \quad (\text{where } P \text{ is the perimeter of the base})

TSA = LSA + 2B = P \cdot L + 2B

TSA = P \cdot L + 2B

B = l \cdot w

Lateral Surface Area ($LSA$): $LSA = P \cdot L \quad (\text{where } P \text{ is the perimeter of the base})$ Total Surface Area ($TSA$): $TSA = LSA + 2B = P \cdot L + 2B$