How cylinder volume and surface area are found
A cylinder's volume is the area of its circular base times its height. The surface area adds the two circular caps to the curved side wall, which unrolls into a rectangle of width equal to the base's circumference.
- r — base radius — center to edge
- h — height between the two circular bases
- π — ≈ 3.14159 (circumference ÷ diameter)
More detail
Why the two terms in surface area
2·π·r² covers the top and bottom circular caps (two circles of area π·r² each). 2·π·r·h covers the curved side: unrolled flat, it's a rectangle whose width is the base's circumference (2·π·r) and whose height is the cylinder's height h.
Volume scales with r², not r
Doubling the radius quadruples the volume (since it depends on r²), while doubling the height only doubles it. For the same proportional change, increasing the radius adds far more volume than increasing the height.
Working with diameter. If you measured the diameter instead of the radius, halve it first (r = diameter ÷ 2) before entering it above. Keep radius and height in the same unit so the volume and surface area come out consistent.
Frequently asked questions
What is the volume of a cylinder with radius 3 and height 5?
Volume = π · r² · h = π · 3² · 5 = π · 45 ≈ 141.3717 cubic units. Enter r = 3, h = 5 above to see the volume together with the surface area of ≈ 150.7964.
How do you find the surface area of a cylinder?
Surface area = 2·π·r² + 2·π·r·h — the two circular caps (2·π·r²) plus the curved side unrolled into a rectangle (2·π·r·h). Both terms use the same radius r and the cylinder's height h.
Why does volume grow faster than surface area when the radius increases?
Volume depends on r² (from the circular base), so doubling the radius quadruples it. The 2·π·r² term in surface area also depends on r², but the 2·π·r·h term only depends on r linearly — so overall surface area grows more slowly than volume as radius increases.
What happens if radius or height is 0 or negative?
No cylinder exists without a positive radius and a positive height, so both volume and surface area show "—".
Does this work for any cylinder shape?
This calculator assumes a right circular cylinder — a circular base with sides perpendicular to it, like a soda can. Oblique (slanted) cylinders or elliptical bases need different formulas.