Prism Volume Calculator
Volume and surface area of a prism whose base is a regular polygon — triangular, square, hexagonal or any other.
Results
Volume
69.2820
m³
Area of the base
6.9282
m²
Perimeter of the base
12.0000
m
Area of the sides
120.0000
m²
Total surface area
133.8564
m²
Apothem of the base
1.1547
m
Volume
69,282.032
L
What this tool does
Every prism obeys one rule: the volume is the base area times the length, however many sides the base has. This page takes the base as a regular polygon, so the same three numbers cover a triangular prism, a square one, a hexagonal one, and everything between. Push the number of sides high enough and the answer creeps towards a cylinder, which is exactly what a prism with infinitely many sides is.
Formula
base = n s² ÷ (4 tan(π ÷ n)) · V = base × length · lateral = n s × length
Variables
| Symbol | Meaning | Unit |
|---|---|---|
n | Sides of the base polygon | — |
s | Length of each base side | m |
len | Length of the prism | m |
V | Volume | m³ |
BA | Area of the base | m² |
BP | Perimeter of the base | m |
LA | Area of the sides | m² |
TA | Total surface area | m² |
AP | Apothem of the base | m |
LI | Volume | L |
Worked example
- Sides of the base polygon3
- Length of each base side4 m
- Length of the prism10 m
- Volume69.2820 m³
- Area of the base6.9282 m²
- Perimeter of the base12.0000 m
- Area of the sides120.0000 m²
- Total surface area133.8564 m²
- Apothem of the base1.1547 m
- Volume69,282.032 L
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.