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.
Base is a Rectangle: $V = l \cdot w \cdot h$
Base is a Triangle: $V = \frac{1}{2} b \cdot h_{base} \cdot L$
Side 3 is the Base Side ($b$). For TSA, enter the three sides of the triangular base.
Results
Lateral Surface Area ($LSA$)
Total Surface Area ($TSA$)
Volume ($V$)
Step-by-Step Solution
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.
Lateral Surface Area ($LSA$):
$$LSA = P \cdot L \quad (\text{where } P \text{ is the perimeter of the base})$$Total Surface Area ($TSA$):
$$TSA = LSA + 2B = P \cdot L + 2B$$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.