Direct answer

What are the main cylinder formulas?

The main cylinder formulas are volume $V = π r^{2} h$ , lateral surface area $L S A = 2 π r h$ , total surface area $T S A = 2 π r (r + h)$ , and base area $B = π r^{2}$ . Use radius and height, not diameter, in these formulas.

Short answer

Cylinder formulas at a glance

Volume: $V = π r^{2} h$ Lateral surface area: $L S A = 2 π r h$ Total surface area: $T S A = 2 π r (r + h)$

Definition

What is a cylinder?

A cylinder is a 3D solid with two congruent circular bases connected by a curved surface.

Diagram

Cylinder diagram

Cylinder variables: radius r and height h.

Quick formula table

Cylinder Formulas quick table

Formula	Equation	Variables
Base area	$B = π r^{2}$	r = radius
Volume	$V = π r^{2} h$	h = height
Lateral surface area	$L S A = 2 π r h$	Curved side only
Total surface area	$T S A = 2 π r (r + h)$	Includes both bases

Formula explanation

How to use these formulas

The cylinder volume formula is base area times height. Surface area includes the curved side plus two circular bases.

Calculator

Cylinder Calculator

Enter measurements to get the result, unit, formula, and calculation steps.

Examples

Step-by-step examples

Find volume

Given r = 3 cm and h = 10 cm.
Use $V = π r^{2} h$ .
$V = 90 π \approx 282.74 c m^{3}$ .

Find lateral surface area

Given r = 3 cm and h = 10 cm.
Use $L S A = 2 π r h$ .
$L S A = 60 π \approx 188.50 c m^{2}$ .

Find total surface area

Given r = 3 cm and h = 10 cm.
Use $T S A = 2 π r (r + h)$ .
$T S A = 78 π \approx 245.04 c m^{2}$ .

Find height from volume

Given V = 144π cm³ and r = 6 cm.
Use $h = V / (π r^{2})$ .
$h = 144 π /36 π = 4 c m$ .

Real-world cylinder problem

A can has r = 4 cm and h = 12 cm.
Use $V = π r^{2} h$ .
$V = 192 π \approx 603.19 c m^{3}$ .

Reverse calculations

Solve backwards from known values

Task	Formula	When to use it
Find height from volume	$h = V / (π r^{2})$	Use when volume and radius are known.
Find radius from volume	$r = V / π h$	Use when volume and height are known.
Find height from lateral area	$h = L S A /2 π r$	Use when lateral surface area and radius are known.

Common mistakes

Using diameter as radius.
Forgetting the two circular bases in total surface area.
Writing volume in square units instead of cubic units.

Practice

Practice problems with answers

1. Find volume when r = 5 cm and h = 8 cm.

$V = 200 π \approx 628.32 c m^{3}$ .

2. Find total surface area when r = 5 cm and h = 8 cm.

$T S A = 2 π \times 5 (5 + 8) = 130 π \approx 408.41 c m^{2}$ .

3. Find height when V = 75π m³ and r = 5 m.

$h = 75 π /25 π = 3 m$ .

4. Find base area when r = 6 in.

$B = 36 π \approx 113.10 i n^{2}$ .

5. Find lateral surface area when r = 2 ft and h = 9 ft.

$L S A = 36 π \approx 113.10 f t^{2}$ .

Related formulas

FAQ

Cylinder Formulas FAQ

What is the cylinder volume formula?

The formula is $V = π r^{2} h$ .

What is cylinder lateral surface area?

Lateral surface area is the curved side area: $L S A = 2 π r h$ .

What is total surface area of a cylinder?

Total surface area is $T S A = 2 π r (r + h)$ .