About

Miscalculating cylinder volume leads to material waste in manufacturing, incorrect fluid capacity in tank engineering, and dosage errors in pharmaceutical filling. This calculator computes V, total surface area A, lateral surface area A_lat, and base area A_base from radius r and height h using exact closed-form solutions. Results are produced in the unit system you select. The tool assumes a right circular cylinder with uniform cross-section. It does not account for wall thickness, oblique angles, or truncation.

Pro tip: for pipes and hollow cylinders, compute the outer cylinder volume and subtract the inner cylinder volume separately. If you only know the diameter, the tool derives r automatically. All intermediate values are displayed so you can cross-check against engineering drawings or CAD models.

Formulas

The volume of a right circular cylinder is the product of its base area and height.

V = π ⋅ r² ⋅ h

Total surface area includes both circular bases and the lateral (side) surface.

A_total = 2 ⋅ π ⋅ r ⋅ (r + h)

The lateral surface area is the area of the rectangular sheet that wraps around the cylinder.

A_lat = 2 ⋅ π ⋅ r ⋅ h

Each circular base has an area of:

A_base = π ⋅ r²

Where r = radius of the circular base, h = height (length) of the cylinder, π ≈ 3.14159265. If only diameter d is known: r = d2.

Reference Data

Object	Typical Radius	Typical Height	Approx. Volume	Use Case
Soda Can (355 mL)	3.3 cm	12.2 cm	417 cm³	Beverage packaging
Paint Can (1 gal)	7.8 cm	19.0 cm	3,632 cm³	Paint storage
Oil Drum (55 gal)	28.6 cm	88.9 cm	228,500 cm³	Industrial storage
Water Pipe (4 in)	5.08 cm	100 cm	8,107 cm³	Plumbing
Grain Silo (small)	3.0 m	10.0 m	282.7 m³	Agriculture
Concrete Column	0.3 m	3.0 m	0.848 m³	Structural engineering
Coffee Mug	4.0 cm	9.5 cm	477 cm³	Household
Swimming Pool (round)	3.0 m	1.5 m	42.4 m³	Residential pool
Fuel Tank (truck)	30.0 cm	120 cm	339,292 cm³	Vehicle fuel storage
AA Battery	0.7 cm	5.0 cm	7.7 cm³	Electronics
Water Tower	5.0 m	8.0 m	628.3 m³	Municipal water
Wine Barrel	29.0 cm	90.0 cm	237,793 cm³	Viticulture
Telescope Tube	15.0 cm	120 cm	84,823 cm³	Optics housing
Hydraulic Piston	5.0 cm	30.0 cm	2,356 cm³	Mechanical engineering
Chemical Reactor	1.0 m	3.0 m	9.42 m³	Process engineering

Frequently Asked Questions

You can toggle between radius and diameter input mode. When diameter is selected, the tool internally divides by 2 to obtain the radius before applying the volume formula V = π·r²·h. This prevents the common error of plugging diameter directly into the radius variable, which would overestimate volume by a factor of 4.

Volume units are the cube of the selected linear unit. If you enter radius and height in centimeters, volume is in cubic centimeters (cm³). 1 cubic meter = 1,000,000 cm³. 1 liter = 1,000 cm³. The results panel shows conversions to liters and gallons automatically for practical reference.

Not directly. A hollow cylinder (annular cylinder) requires computing two volumes: V_outer = π·R²·h and V_inner = π·r²·h, then subtracting. Use this tool twice with the outer and inner radii, then manually subtract. The formula for a hollow cylinder is V = π·h·(R² − r²).

Yes. Cavalieri's principle states that an oblique cylinder has the same volume as a right cylinder with identical base area and perpendicular height. However, the surface area formulas shown here apply only to right circular cylinders. For oblique cylinders, the lateral surface area calculation requires integration along the slant.

1 liter = 1,000 cm³ exactly. 1 US gallon = 3,785.41 cm³. 1 imperial gallon = 4,546.09 cm³. The calculator provides automatic conversions in the results section. For industrial tank sizing, always confirm whether US or imperial gallons are specified in your engineering documents.

All calculations use IEEE 754 double-precision floating point (approximately 15-17 significant digits). Results are displayed rounded to 4 decimal places by default. The value of π used is Math.PI in JavaScript, which is 3.141592653589793. For most engineering applications, this exceeds required precision.

Surface area determines material cost for fabrication (sheet metal, plastic molding), heat transfer rate in thermal engineering (Q = h·A·ΔT), and coating or painting requirements. A cylinder with the same volume but different aspect ratio (r/h) will have vastly different surface areas. Minimizing surface area for a given volume occurs when h = 2r.