Cylinder Volume Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
A cylinder's volume is calculated with π × radius² × height, and its total surface area with 2 × π × radius × (radius + height). For a radius of 2 cm and a height of 10 cm, the volume is about 125.66 cm³.
Explanation
A cylinder is made of two identical circular bases connected by a curved surface, like a can or a tube. Its volume equals the area of its circular base (π × radius²) multiplied by the height, exactly like a prism: the same cross-section repeats along the whole height. Its total surface area adds the area of the two bases (2 × π × radius²) to that of the lateral surface unrolled into a rectangle (2 × π × radius × height), which factors into 2 × π × radius × (radius + height). If the height is zero, the cylinder flattens into a plain disk: the volume becomes zero but the total surface area stays positive, since the disk's two faces remain (see the edge case tested below). For the circle that forms its base, see our circle area and perimeter calculator; for another solid derived from the circle, the sphere volume calculator.
Example: a cylinder with a 2 cm radius and 10 cm height
Inputs
Radius: 2 cm. Height: 10 cm.
Calculation
Volume: π × 2² × 10 = π × 4 × 10 = 40π ≈ 125.66 cm³. Total area: 2 × π × 2 × (2 + 10) = 4π × 12 = 48π ≈ 150.80 cm².
Result
This cylinder has a volume of about 125.66 cm³ and a total surface area of about 150.80 cm².
Frequently asked questions
Why does the total surface area stay positive when the height is zero?
Because a cylinder with zero height flattens into a flat disk, but keeps its two faces (front and back). The area of these two faces (2 × π × radius²) doesn't disappear, even though the volume becomes zero for lack of thickness.
Does the formula change for a cylinder lying on its side?
No: a cylinder's volume and surface area depend only on its radius and height, not on its orientation in space.
How do I calculate just the lateral surface, without the two bases?
The lateral surface alone (the curved side of the cylinder, without the top or bottom) is calculated with 2 × π × radius × height — that's the part of the total-area formula that doesn't involve the two base disks.
Does this formula work for estimating capacity in liters?
Yes, as long as you convert: a volume in cm³ corresponds exactly to milliliters (1 cm³ = 1 mL), so 1,000 cm³ equals 1 liter.