Cylinder Formulas (Volume, Surface Area)

A cylinder has two parallel circular bases joined by a curved surface. Its volume is V = πr²h, the base area times the height. Its lateral surface is 2πrh and its total surface area is SA = 2πr(r + h).

Cylinder formulas

Volume: $V = \pi r^2 h$
Lateral surface: $LSA = 2\pi r h$
Surface area: $SA = 2\pi r(r + h)$

where r = base radius, h = height, V = volume, SA = total surface area

Volume

V = \pi r^2 h

Worked example

A unit cylinder (r = 1, h = 1) has volume π ≈ 3.14 cubic units.

V = \pi r^2 h = \pi\cdot 1^2\cdot 1 = \pi \approx 3.14

Lateral surface

LSA = 2\pi r h

Surface area

SA = 2\pi r(r + h)

Interactive cylinder explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Radius r

Height h

Volume V 169.65units³

Lateral surface LSA 113.1units²

Surface area SA 169.65units²

Step-by-step substitution

V = πr²h = π · 3² · 6 = 54π ≈ 169.65
LSA = 2πrh = 2π · 3 · 6 = 36π ≈ 113.1
SA = 2πr(r + h) = 2π · 3(3 + 6) = 54π ≈ 169.65

Classroom use: cylinder formulas

Who it's for: Grades 8–12 · Grade 8 students meeting cylinder volume and high-school geometry students arguing for the formula.

Learning objectives

After using this page, students will be able to:

Compute cylinder volume using V = πr²h.
Compute total surface area as two circles plus a rectangular lateral face.
Explain why the lateral surface unrolls to a rectangle of width 2πr.

Suggested classroom activity

Unroll a paper label from a tin, measure it, and compare with the explorer's lateral-area figure. The 2πr width stops being a memorised term the moment students measure it themselves.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`8.G.C.9`	Know and use the formulas for the volumes of cones, cylinders, and spheres.
`HSG.GMD.A.1`	Give an informal argument for circumference, area, and volume formulas.
`HSG.GMD.A.3`	Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

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Frequently asked questions

What is the volume formula for a cylinder?

A cylinder’s volume is V = πr²h, the circular base area πr² times the height h. A cylinder with radius 3 and height 6 has volume 54π ≈ 169.65 cubic units.

What is the surface area of a cylinder?

Total surface area is SA = 2πr(r + h): two circular ends (2πr²) plus the curved side (2πrh). For r = 3, h = 6, SA = 2π·3·9 = 54π.

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