The Cylinder Calculator converts radius and height into volume, lateral surface area and total surface area for a right circular cylinder. Bases are congruent circles, and the side wall is a rectangle when unrolled. The page redraws a labelled figure with radius and height marked to the entered values.
Enter radius (or diameter) and height. Answers can appear as decimals or as exact multiples of pi. Related pages cover the Cone Calculator when the solid tapers to a point, the Tube Calculator when the cylinder is hollow, and the Sphere Calculator for the inscribed ball comparison.
Calculate the volume of a cylinder
Volume of a right circular cylinder is base area times height. The Cylinder Calculator multiplies pi r squared by height. Radius and height must be positive. Diameter input halves to radius before volume runs. Units on volume are cube units of the length unit used on radius and height.
V = pi * r^2 * hVolume scales with the square of radius and linearly with height. Doubling radius multiplies volume by four; doubling height multiplies volume by two. When a tank problem gives diameter instead of radius, convert first so the square is applied to the correct length.
For the reference case r = 3 and h = 10:
V = pi * 9 * 10 = 90 * pi approx 282.74Exact form 90 * pi is useful when later steps still need pi. Decimal mode shows approx 282.74. An oblique cylinder with the same base area and perpendicular height has the same volume by Cavalieri's principle, but this page models the right circular case with a vertical axis in the diagram.
If the known quantity is volume plus one of radius or height, rearrange to solve for the missing length. From V and r, height is V / (pi * r^2). From V and h, radius is the positive square root of V / (pi * h).
Calculate lateral and total surface area
Lateral surface area is the curved wall only, equal to the circumference of the base times height. Total surface area adds the two circular ends. The Cylinder Calculator reports both so paint questions that skip the lids differ from closed-can questions that include them.
Lateral SA = 2 * pi * r * h
Total SA = 2 * pi * r * (r + h) = 2 * pi * r^2 + 2 * pi * r * hUnrolling the wall produces a rectangle of width 2 * pi * r and height h, which is why lateral area is that product. Each base contributes pi * r^2. Open pipes that ignore ends use lateral area alone; closed tanks use total area.
For r = 3 and h = 10:
Lateral SA = 2 * pi * 3 * 10 = 60 * pi approx 188.50
Base areas = 2 * pi * 9 = 18 * pi approx 56.55
Total SA = 78 * pi approx 245.04A hollow tube with inner and outer radii needs a different volume formula (annular cross section times length). Use the Tube Calculator for pipe walls. A capsule adds hemispherical caps to a cylinder; use the Capsule Calculator for that compound solid.
Solve a cylinder with radius 3 and height 10
Take r = 3 and h = 10 as the reference cylinder. Volume and surface areas factor cleanly with pi. Diameter is 6. The numbers below are the regression fixtures for the cylinder engine. 1. Diameter
d = 2 * 3 = 62. Volume
V = pi * 9 * 10 = 90 * pi approx 282.743. Lateral surface area
Lateral SA = 2 * pi * 3 * 10 = 60 * pi approx 188.504. Total surface area
Total SA = 2 * pi * 3 * (3 + 10) = 78 * pi approx 245.04Starting from volume 90 * pi with r = 3 recovers h = 10. Starting from the same volume with h = 10 recovers r = 3. Lateral area 60 * pi with r = 3 recovers h = 10 as well when the wall is the known paint area.
Compare with a cone of the same base radius and height: cone volume is one-third of cylinder volume, so (1/3) * 90 * pi = 30 * pi. Compare with a sphere of radius 3: sphere volume is (4/3) * pi * 27 = 36 * pi, smaller than this taller cylinder.
Tank problems sometimes give diameter and height in mixed units (inches of diameter, feet of height). Convert to one length unit before squaring radius. A 6-inch radius is 0.5 ft; using 6 with height in feet multiplies volume by 144 erroneously relative to cubic feet.
Lateral area 60 * pi is the label wrap on a can. Total area 78 * pi adds the top and bottom lids. Net layouts unroll the wall to a rectangle 2*pi*r by h and attach two disks of radius r; those pieces match the surface formulas on this page.
Recover a missing length from volume
If volume and radius are known, height is h = V / (pi * r^2). For V = 90 * pi and r = 3, h = 90 * pi / (9 * pi) = 10. If volume and height are known, radius is r = sqrt(V / (pi * h)).
For the same volume with h = 10, r = sqrt(9) = 3. The Cylinder Calculator accepts radius or diameter on input; diameter mode halves before these rearrangements run.
Lateral paint area can recover height when radius is known: h = (lateral SA) / (2 * pi * r). For lateral SA = 60 * pi and r = 3, h = 10. Closed-can total area needs care because both lids and the wall appear in one sum; prefer lateral area alone when only the curved wall was measured.
Unit note: keep radius and height in the same length unit before squaring. A tank with diameter in inches and height in feet must convert first. After conversion, volume is in cube units of that shared length (cubic feet, cubic metres, and so on).
Frequently asked questions
What is cylinder volume?
Cylinder volume is V = pi * r^2 * h. For r = 3 and h = 10, V = 90 * pi approx 282.74.
What is lateral surface area?
Lateral surface area is 2 * pi * r * h, the curved wall only. For r = 3 and h = 10, lateral SA = 60 * pi approx 188.50.
What is total surface area of a cylinder?
Total surface area is 2 * pi * r * (r + h), which adds both circular bases to the wall. For r = 3 and h = 10, total SA = 78 * pi approx 245.04.
Can the Cylinder Calculator use diameter?
Yes. The Cylinder Calculator converts d to r = d / 2 before volume and surface area run.
How does cylinder volume compare to a cone?
A cone with the same base radius and height has one-third the cylinder volume.
When should ends be included in surface area?
Include both bases for a closed can or tank. Use lateral area alone for an open tube or when lids are omitted from the coating estimate.
What if the cylinder is hollow?
Use the Tube Calculator. Hollow volume uses pi * (R^2 - r^2) * length with outer and inner radii.
What units does the Cylinder Calculator use?
Radius and height share one length unit. Volume uses cube units; surface areas use square units of that length.
Summary
Cylinder Calculator returns volume, lateral surface area and total surface area from radius and height, with substituted arithmetic and a labelled figure. Worked numbers match r = 3 and h = 10: V = 90 * pi and total SA = 78 * pi.
Use the Cone Calculator for a tapering solid, the Tube Calculator for a hollow pipe, and the Capsule Calculator when hemispheres close the ends.