Choose a guided mode for common tasks, or use Any two values for radius/diameter, height, total surface area, lateral surface area, or volume.
Given r = 5 cm and h = 12 cm: V = πr²h = π × 5² × 12 = 942.48 cm³.
Given d = 10 cm and h = 12 cm, use r = d/2 = 5 cm. S = 2πr(r + h) = 534.07 cm².
Given V = 942.48 cm³ and r = 5 cm: h = V/(πr²) = 942.48/(π × 25) = 12 cm.
A cylinder with r = 5 cm and h = 12 cm has 942.48 cm³. Since 1 L = 1000 cm³, capacity is 0.94 L.
Calculations use standard right circular cylinder formulas. The default pi value is JavaScript Math.PI (about 3.141592653589793), results are rounded to the selected decimal places for display, and internal checks use a small numerical tolerance. Last reviewed: June 9, 2026.
A right circular cylinder is defined by its radius r and height h. From those, the key measures are:
B = πr²C = 2πrL = 2πrhS = L + 2πr² = 2πr(r + h)V = πr²hS/VProvide any two values—such as r & h, r & S, h & V, L & V, or S & L. The tool solves for r and h (using exact formulas or a quick numerical method when needed), then derives the rest. If you enter more than two values, it checks for consistency within a small numerical tolerance.
Units: r, d, and h use a length unit (e.g., cm); L, S, and base areas use squared units (e.g., cm²); V can be entered or displayed as cubic units, liters, milliliters, US gallons, or cubic yards. Choose decimal places and π precision to match classroom, lab, or real-world capacity work.
| Given | Find | Formula |
|---|---|---|
r, h | Volume | V = πr²h |
r, h | Lateral area | L = 2πrh |
r, h | Total surface area | S = 2πr(r + h) |
r | Base, top, or bottom area | B = πr² |
r | Base circumference | C = 2πr |
V, h | Radius | r = √(V/(πh)) |
V, r | Height | h = V/(πr²) |
S, r | Height | h = S/(2πr) - r |
S, V | Radius and height | 2πr² + 2V/r - S = 0, then h = V/(πr²) |
When only total surface area and volume are known, two different right circular cylinders can sometimes satisfy both measurements: a wider, shorter cylinder and a narrower, taller cylinder. The calculator shows both real solutions when they exist. Choose the one that matches the physical object or the intended radius-to-height shape. If no solution appears, the entered surface area is too small for that volume.
Unroll a cylinder’s side and you get a rectangle of width 2πr and height h. That’s why L = 2πrh is just “perimeter × height.”
Double the radius and volume jumps by 4×; double the height and volume doubles. Radius changes dominate because of the r² term.
Using π = 22/7 overshoots true π by ~0.04%. On a 10 cm radius, that’s about 0.25 cm² error in area—tiny for homework, big for machining.
A soap film spanning two circles forms a “catenoid,” not a cylinder. Cylinders have constant radius; catenoids shrink in the middle to minimize surface area.
A pill shape is a cylinder plus two hemispheres. Its volume is πr²h + 4/3 πr³—useful for bottle or tank capacity estimates.
Use V = πr²h. Enter the radius or diameter and the height, then choose the volume from radius and height mode to calculate the cylinder volume.
Total surface area is S = 2πr(r + h). Enter radius or diameter and height to calculate total surface area, lateral surface area, base area, top area, and bottom area.
Rearrange the volume formula as h = V/(πr²). Enter volume and radius, then choose the height from volume and radius mode.
Set the length unit for radius and height, then choose liters as the volume unit. The calculator converts the computed cubic volume to liters automatically.
Lateral surface area is the curved side area only. It does not include the top and bottom circles. The formula is L = 2πrh.
Radius is the distance from the center of the circular base to its edge. Diameter is the full width across the circle, so d = 2r.
Use a guided mode for common tasks, or choose any two values to solve from radius or diameter, height, total surface area, lateral surface area, or volume. More values are checked for consistency.
Yes. The same total surface area and volume can describe two real right circular cylinders: one wider and shorter, and one narrower and taller. Compare radius and height to choose the intended shape.