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CALCPARK

Cylinder Volume and Surface Area Calculator

Volume and surface area of a cylinder from its radius or diameter and height, with lateral, base and total area, and the volume in litres and US or UK gallons.

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How to use it

  1. Choose whether you are entering the radius or the diameter, and the unit (mm, cm, m, in, ft).
  2. Type the radius or diameter and the height. The volume, capacity in litres and gallons and the three surface areas update live.
  3. Switching between radius and diameter converts the value you typed so the cylinder stays the same.
  4. Copy the summary or share the link.

Example

Radius 3 cm, height 5 cm: base area π × 3² = 28.27 cm²; volume 28.27 × 5 = 141.37 cm³ = 141.37 ml; side 2π × 3 × 5 = 94.25 cm²; total surface 94.25 + 2 × 28.27 = 150.80 cm². A water tank with a 1.2 m diameter (r = 0.6 m) and 1.5 m height: π × 0.36 × 1.5 = 1.696 m³ = 1,696 L = 448 US gallons.

Formulas

V = π r² h
lateral area = 2 π r h        base area = π r²  (two bases)
total surface area = 2 π r h + 2 π r² = 2 π r (r + h)
litres = V[m³] × 1,000;   US gal = L / 3.785411784;   UK gal = L / 4.54609

The formulas are for a right circular cylinder (ends perpendicular to the axis). For a tilted (oblique) cylinder the volume is the same if h is the perpendicular height, but the lateral area is larger. Wall thickness is not subtracted – for the capacity of a pipe or tank enter the inside radius. Partially filled horizontal tanks need a segment calculation, which this tool does not do.

Sources: Wolfram MathWorld – Cylinder, NIST – SI units and conversion factors.

Questions

How many litres does a cylinder hold?
Work in centimetres: volume in cm³ ÷ 1,000 = litres. A 10 cm radius, 31.83 cm tall cylinder is 10,000 cm³ = 10 L. The tool does this conversion for any unit.
What is the lateral surface area?
The curved side only, as if the label were unrolled into a rectangle of width 2πr and height h. Add the two circular ends for the total area – needed for paint, insulation or sheet metal.
Does the order of radius and height matter?
Yes. The radius is squared, so a short wide cylinder holds more than a tall narrow one with the dimensions swapped: r = 5, h = 2 gives 157 cm³, r = 2, h = 5 gives 62.8 cm³.