Calculate volume, surface area, and dimensions of cylinders
Last updated: April 2026 | By Patchworkr Team
Distance from center to edge
Length of the cylinder
V = πr²h
Where r is radius and h is height
A = 2πr² + 2πrh
Two circular bases plus lateral (side) area
A_b = πr²
Area of one circular end
A_l = 2πrh
Area of the curved side surface
C = 2πr = πd
Perimeter of the circular base
A cylinder is a three-dimensional geometric solid consisting of two parallel circular bases connected by a curved surface. In a right circular cylinder (the most common type), the axis connecting the centers of the two bases is perpendicular to the base planes, creating straight sides. The distance between the bases is the height, and the distance from the center to the edge of the circular base is the radius.
Cylinders are one of the most common shapes in everyday life and engineering. Pipes, cans, tanks, columns, pistons, wheels, and countless other objects are cylindrical. The cylinder's simple geometry makes it easy to manufacture, and its circular cross-section provides uniform strength in all radial directions, making it ideal for containing pressure (like in pipes and tanks) or transmitting force (like in hydraulic cylinders).
Understanding cylinder volume is essential for calculating capacities of tanks, determining material quantities for manufacturing, sizing HVAC ducts, computing engine displacement, and countless other applications. The relationship V = πr²h shows that volume increases with the square of the radius, meaning doubling the radius quadruples the volume (if height stays constant).
Step 1: Choose your input method. Select "Use Radius" if you know the distance from the center to the edge, or "Use Diameter" if you know the distance across the full circle through the center.
Step 2: Enter the radius or diameter value. If you have diameter but selected radius mode, divide your diameter by 2. If you have radius but selected diameter mode, multiply your radius by 2.
Step 3: Enter the height (or length) of the cylinder. This is the distance between the two circular ends, measured perpendicular to the bases.
Technical Details: The calculator computes multiple properties: Volume (space inside), total surface area (all outer surfaces including both ends), base area (one circular end), lateral surface area (just the curved side), and circumference (perimeter of the circular base). Use consistent units throughout—if radius is in inches, height must be in inches, and results will be in cubic inches and square inches.
Scenario: A manufacturing company needs to determine the capacity of a cylindrical water storage tank. The tank has a diameter of 6 feet and a height of 12 feet.
Radius: 3 feet (diameter ÷ 2)
Volume: 339.29 cubic feet
Capacity: 2,538 gallons (339.29 ft³ × 7.48 gal/ft³)
Surface Area: 282.74 square feet (useful for painting/coating calculations)
Material: For a 1/4-inch steel wall, approximately 70.7 ft² of steel needed (lateral area only)
Knowing the precise volume allows the company to spec the right tank size for their needs, calculate water weight (about 21,200 pounds when full), determine structural support requirements, and estimate coating/painting costs based on the surface area.
Radius is the distance from the center to the edge (halfway across). Diameter is the distance all the way across through the center (twice the radius). d = 2r, or r = d/2.
Volume is base area (πr²) times height (h), giving πr²h. The formula 2πrh is for lateral surface area (the curved side), not volume. Don't confuse the two!
For a pipe or tube, calculate the volume with the outer radius, then subtract the volume with the inner radius: V = π(R² - r²)h, where R is outer radius and r is inner radius.
Yes, if the tank is completely full. For partially full horizontal cylinders, the calculation is more complex and requires trigonometry based on the fill level. Use specialized tank volume calculators for that.
Water tanks, fuel tanks, silos, pipes, engine cylinders, cans, drums, columns, pistons, and any cylindrical container or structure. Also used in calculating engine displacement in automotive engineering.
Since volume = πr²h, doubling the radius quadruples the volume (2² = 4). Tripling the radius increases volume ninefold (3² = 9). Volume increases with the square of radius.
Rearrange the formula: r = √(V/πh) to find radius from volume and height, or h = V/(πr²) to find height from volume and radius. You need to know at least two of the three values.
Total surface area (2πr² + 2πrh) includes both circular ends. For open containers or pipes, use only lateral area (2πrh). Add one base (πr²) for containers with one end open.
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