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Cylinder Height from Volume, Curved Area or Axial Diagonal

Cylinder Height from Volume, Curved Area or Axial Diagonal. Convert compatible units, recover unknown dimensions and distinguish curved surfaces, bases and total measures.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Radius (r) 3, Height (h) 4 gives Diagonal (d) 7.2111026, Combined area of both circular ends 56.548668, Lateral surface area 75.398224, Total surface area 131.94689, Volume 113.09734.

h = V/(πr²); h = Alateral/(2πr); h² = d²−4r²

Worked example

Enter these known values and leave the other values blank.

Radius (r)
3 cm
Height (h)
4 cm
Volume
113.0973 cm³
Diagonal (d)
7.2111 cm
Combined area of both circular ends
56.5487 cm²
Lateral surface area
75.3982 cm²
Total surface area
131.947 cm²

Assumptions and limitations

  • This is a closed right circular cylinder. The base-area control means the combined area of both circular ends. The axial diagonal spans a rectangle whose width is the diameter, twice the radius.
  • Select units before entering dimensions. Clear an unknown result before solving backward, and supply enough independent measurements. Display rounding does not represent measurement uncertainty.
  • Calculations use 64 significant digits and full-precision π. Original reference drawings explain dimensions and are not drawn to the entered scale.

Common questions

How long must the axial diagonal be?

It must exceed the diameter and perpendicular height. The axial rectangle uses diameter, not radius, as its width.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor. The cubic international mile uses the cube of the exact 1609.344-meter mile, replacing a rounded reciprocal factor.

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