$Prism$

Prism

Find the volume, base area, lateral and total surface area of a regular n-gonal prism and a right prism.

What is known:

Regular prism: number of sides, base edge, height

Right prism: base area, base perimeter, height

Any prism: base area and height

Number of base sides n

Base edge a

Height h

Units:

The number of sides is a whole number from 3 to 1000 (3 — triangular prism, 4 — square, 6 — hexagonal).

Test yourself

The prism calculator finds the volume, base area, lateral and total surface area of a regular n-gonal prism and of a right prism with a known base area and perimeter, as well as the volume of any prism.

Prism formulas

Value	Formula
Volume of any prism	V = S_base · h
Lateral area of a right prism	S_lat = P_base · h
Total surface area	S = S_lat + 2S_base
Base of a regular prism	S_base = n · a² / (4 tan(180°/n))

Base area of regular prisms

Prism	Base	S_base
triangular	equilateral triangle	a²√3 / 4
square	square	a²
hexagonal	regular hexagon	3a²√3 / 2

Example. A regular triangular prism, a = 6 cm, h = 10 cm.
S_base = 36√3 / 4 ≈ 15.59 cm², V ≈ 155.88 cm³
S_lat = 18 · 10 = 180 cm², S ≈ 180 + 2 · 15.59 = 211.18 cm².

The volume of an oblique prism is also S_base · h, where h is the height (the distance between the bases), not the lateral edge.