How this calculator works
A cylinder’s volume is its base area times perpendicular height. Lateral area unrolls into a rectangle of width equal to the base circumference. A closed total includes two bases, which must be removed before dividing by the circumference. For an axial diagonal, use a rectangular cross-section through the central axis: its width is 2r and its height is h. The table checks the two squared legs against the squared diagonal. All dimensions describe a right circular cylinder.
Formula
h = V/(πr²) = V/B; h = L/(2πr); h = (S-2πr²)/(2πr); h = sqrt(d²-4r²). Here B is one base area, L is lateral area, S is closed total area and d is the axial diagonal.
Worked example
With radius 2 m and axial diagonal 5 m, the rectangle is 4 m wide. Height = √(25-16)=3 m. The volume is 12π m³, lateral area is 12π m² and closed total area is 20π m².
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Frequently asked questions
Is the diagonal measured across a circular base?
No. It joins opposite corners of a rectangle cut vertically through the axis. Its horizontal span is the cylinder’s full diameter.
Can I use the total area of an open can?
The total-area mode assumes two circular caps. For an open can, first subtract its single base to obtain lateral area, then choose lateral mode.
Can base area replace radius?
Yes. Base-area-and-volume mode divides the volume by one base area and also recovers the matching radius.