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Closed Cylinder Surface, Volume and Axial Diagonal

Closed Cylinder Surface, Volume and Axial Diagonal. Convert compatible units, recover unknown dimensions and distinguish curved surfaces, bases and total measures.

  • Formula & worked example
  • Private in your browser
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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 Longest diagonal (d) 7.2111026, Combined area of both circular ends 56.548668, Lateral surface area (A_l) 75.398224, Total surface area (A) 131.94689, Volume (V) 113.09734, Surface to volume ratio (A / V) 1.1666667.

V = πr²h; Atotal = 2πr(r+h); d² = 4r²+h²

Worked example

Enter these known values and leave the other values blank.

Radius (r)
3 cm
Height (h)
4 cm
Combined area of both circular ends
56.55 cm²
Lateral surface area (A_l)
75.4 cm²
Total surface area (A)
131.95 cm²
Volume (V)
113.1 cm³
Surface to volume ratio (A / V)
1.1667 1 / cm
Longest diagonal (d)
7.211 cm

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

Why is the surface-to-volume unit inverse length?

Area divided by volume leaves one inverse length. Changing the length unit changes the numeric ratio without changing the physical shape.

References

Require positive physical dimensions and real nondegenerate inverse roots while preserving documented limiting shapes. 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. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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