Cylinder Calculator
Find the volume and surface area of a right circular cylinder from the radius and height, or recover r or h from a known volume. The formulas are V = πr²h, lateral area 2πrh, and total surface 2πr(r + h).
Lateral 94.2477796077 · total S = 150.796447372
- The base is a circle of area πr² = 3.14159265359 × 3² = 28.2743338823.
- Volume V = πr²h = 28.2743338823 × 5 = 141.371669412.
- Lateral area = 2πrh = 94.2477796077. Total surface = 2πr(r + h) = 150.796447372.
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How to Use the Cylinder Calculator
From r and h (or d and h) grows a right circular cylinder. From V and h recovers the radius. From V and r recovers the height.
- Choose the pair you know.
- Enter non-negative lengths. When solving for r or h from volume, the other length must be positive.
- Read the volume (or the missing length), the lateral area, and the total surface.
A solid ball belongs on the Sphere Calculator. The circular base alone belongs on the Circle Calculator. A party hat with the same r and h belongs on the Cone Calculator (V = (1/3)πr²h, one-third of this can). A rectangular box belongs on the Rectangular Prism Calculator (V = LWh). Converting cubic units belongs on the Volume Converter. Oblique cylinders are later solids.
Volume and Surface
The volume is the base area times the height: stack circles of area πr² up through height h. The lateral area is the unrolled label — a rectangle of width 2πr (the circumference) and height h. The total surface adds the two lids: each lid is πr², so S = 2πrh + 2πr² = 2πr(r + h).
Solving for r from a known volume takes a square root: r = √(V / (πh)). Solving for h is a division: h = V / (πr²). The height must be perpendicular to the base. An oblique “leaning” cylinder has the same volume formula with perpendicular height, but its lateral area is not 2πrh; that case is out of scope here.
Cylinder Calculator Examples
Radius 3, height 5
V = 45π ≈ 141.371669412. Lateral = 30π ≈ 94.2477796077. Total = 48π ≈ 150.796447372.
Radius 2, height 10
V = 40π ≈ 125.663706144. A taller, thinner can can hold less than the 3-by-5 can even though 2 + 10 = 12 is larger than 3 + 5 = 8. Volume cares about r²h, not r + h.
Diameter 6, height 5
r = 3, the same cylinder as the first example.
Volume of the 3-by-5 can, known height
Entering V ≈ 141.371669412 and h = 5 returns r = 3.
Height 0
V = 0 and the lateral area is 0. Total surface is two coincident lids: 2πr². A can crushed to zero height is a disk, not a tank.
A negative radius
A length cannot be negative. The calculator rejects −1.
The Label and the Lids
Homework often asks only for the label: that is the lateral area 2πrh, not the total surface. Including both circular bases is the total S. A soup-can net is a rectangle plus two circles. Do not use the sphere formulas (4/3)πr³ or 4πr² on a can — those belong on the Sphere Calculator.
Common Cylinder Mistakes
Using (4/3)πr³ for a can
That is a sphere. A cylinder is V = πr²h.
Using (1/3)πr²h for a can
That is a cone, on the Cone Calculator. A cylinder is the full πr²h, three times the matching cone.
Using diameter as radius
d = 6 means r = 3. Plugging 6 into πr²h quadruples the volume.
Reporting lateral area as the total surface
The label omits the lids. Add 2πr², or use 2πr(r + h).
Adding r and h in the volume
Volume is πr² times h, not π(r + h). The 2-by-10 can vs the 3-by-5 can shows the difference.
Converting liters on this page
V is already in the cube of your input unit. Use the Volume Converter for liters and gallons.
Cylinder Calculator FAQs
What is the volume of a cylinder?
V = πr²h. For r = 3 and h = 5, V = 45π ≈ 141.371669412 cubic units.
What is the surface area of a cylinder?
Lateral (the label) is 2πrh. Total surface, including both bases, is 2πr(r + h).
How do you find the radius from the volume?
r = √(V / (πh)). The height must be positive.
Is a cylinder the same as a sphere, a circle, or a cone?
No. A circle is the base. A sphere is a ball. A cone with the same r and h has one-third this volume, on the Cone Calculator. This page is a right circular can.
Does this convert liters or treat an oblique cylinder?
No. Use the Volume Converter for units. Oblique cans are out of scope. A dome belongs on the Hemisphere Calculator.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
Sources
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.