How to use the cylinder calculator
- Measure the radius from the centre of a circular base to its edge. If you measured the full diameter, divide it by 2 before entering the radius.
- Enter the perpendicular height between the parallel bases. Radius and height use the same selected length unit.
- Choose one length unit. Length, square-area, and cubic-volume results all follow that unit.
- Select Calculate or press Enter. Copy results if needed. Editing either value or its input unit immediately removes the old answer and disables copying until you calculate again. Clear removes values and results but keeps your unit choices.
Cylinder formulas and result meanings
Volume: space inside the cylinder
For a right circular cylinder, V = πr²h. The base area πr² is multiplied by the perpendicular height h. Volume uses cubic units, such as cm³ or ft³. This result describes a solid cylinder or the theoretical capacity of a closed cylindrical shape; it does not subtract wall thickness.
Lateral surface area: curved side only
The lateral area is L = 2πrh. Imagine cutting the curved wall vertically and laying it flat: its width is the base circumference 2πr and its height is h. This result excludes both circular ends.
Total surface area: curved side plus two bases
The total area is A = 2πrh + 2πr² = 2πr(h + r). It includes the curved side and both complete circular bases. Use this label only for a closed right cylinder; an open container would need a different combination.
Units and rounding
Each input is converted to metres for calculation, then converted to the selected result unit. Length, area, and volume therefore scale differently: changing metres to centimetres multiplies a length by 100, an area by 10,000, and a volume by 1,000,000. Rounding happens only for display.
Worked examples
Cylinder with radius 3 cm and height 10 cm
V = π × 3² × 10 = 90π ≈ 282.74 cm³. The curved side is 2π × 3 × 10 = 60π ≈ 188.5 cm². Adding two bases gives 60π + 18π = 78π ≈ 245.04 cm² total surface area.
Radius 2 in and height 12 in
Volume = 48π ≈ 150.8 in³, lateral area = 48π ≈ 150.8 in², and total surface area = 56π ≈ 175.93 in².
When these results are useful
- Use volume for a solid geometry exercise or to estimate the ideal internal space of a simple closed cylinder. Real containers may hold less because of wall thickness, rounded seams, or an unfilled top.
- Use lateral area for a label or wrap that covers only the curved wall. Use total surface area for a closed model that includes two complete circular ends. Add allowances separately when cutting or overlapping material.
- The diagram helps distinguish radius from height, but it is not drawn to scale. Measure the real object and use perpendicular height, not a diagonal side length.
Input limits and common errors
- Enter positive finite decimal values. Fractions, formulas, commas, and unit symbols are not accepted in the number fields. Use a period for the decimal point and choose the unit from the menu.
- This page covers a full, right circular cylinder only. It does not calculate hollow pipes, wall thickness, horizontal tank fill, liquid depth, mass, density, or purchasing quantities.
- The total-area result always includes two bases. For an open-top or open-ended object, combine the displayed lateral area with the number of base areas your project actually uses.
Frequently asked questions
Does total surface area include the top and bottom?
Yes. It includes the curved side and two complete circular bases. The lateral result excludes both bases.
Can radius and height use different units?
Use one common unit, as in the sphere and cuboid calculators. Convert either measurement first if they were recorded in different units.
Can I enter a diameter?
The input expects radius. Divide the diameter by 2 first; a 10 cm diameter means a 5 cm radius.
Why did the result disappear when I edited an input?
The previous answer no longer matches the current dimensions. It is removed immediately so it cannot be copied by mistake; calculate again to confirm the new values.
Is this a tank fill or pipe calculator?
No. It calculates the complete geometry of a solid right cylinder. It does not model partial liquid levels, a horizontal tank, hollow walls, or material weight.