About

Determining the height of a cylinder is a frequent requirement in manufacturing, fluid dynamics, and packaging design. Whether you are sizing a storage tank to hold a specific volume of liquid or designing a label that must fit a specific surface area, the relationship between radius, height, and capacity is governed by fundamental stereometry.

This tool solves for the height dimension (h) by isolating it from the standard Volume or Total Surface Area formulas. It is particularly useful for reverse-engineering container dimensions when material constraints (surface area) or capacity requirements (volume) are fixed. A dynamic visual model updates to reflect the aspect ratio (tall/thin vs. short/wide) of your calculated cylinder.

Formulas

When the Volume V is known, height is derived by dividing volume by the area of the circular base:

h = Vπ⋅r²

When the Total Surface Area A is known (which includes the top and bottom circles), the formula rearranges to:

h = A − 2πr²2πr

Reference Data

Object Type	Radius (r)	Volume (V)	Height (h)	Ratio (h/r)
Std. Soda Can	3.3 cm	355 ml	10.4 cm	~3.1
Oil Barrel (US)	28.5 cm	159 L	86 cm	~3.0
AA Battery	7.25 mm	8.3 cm³	50.5 mm	~6.9
Hockey Puck	3.8 cm	115 cm³	2.54 cm	~0.6
Coin (Quarter)	12.13 mm	808 mm³	1.75 mm	~0.14

Frequently Asked Questions

If you are calculating the length (height) of a pipe based on the total volume of material, No. If you are calculating based on the *internal* volume (capacity) of liquid it can hold, Yes—just use the inner radius. For surface area, pipes usually ignore the end caps, so the formula differs.

This occurs if the Surface Area you input is too small for the given Radius. Even a cylinder with zero height consists of two circles (top and bottom). If your input A is less than 2πr², a cylinder cannot physically exist.

Yes, consistency is key. If Radius is in meters (m), Volume must be in cubic meters (m³). If you mix units (e.g., radius in inches, volume in gallons), you must convert them to a common system before using this calculator.