Volume from radius and height
Given r = 5 cm and h = 12 cm: V = πr²h = π × 5² × 12 = 942.48 cm³.
Cylinder Calculator
Calculate Using
Enter radius or diameter plus height for the most common volume workflow.
Length from center to edge.
Full width across the circular base.
Distance between the circular bases.
Uses the selected volume unit.
Top, bottom, and curved side.
Curved side only.
Choose a guided mode for common tasks, or use Any two values for radius/diameter, height, total surface area, lateral surface area, or volume.
Diagram
Results
Worked Examples
Total surface area from diameter and height
Given d = 10 cm and h = 12 cm, use r = d/2 = 5 cm. S = 2πr(r + h) = 534.07 cm².
Height from volume and radius
Given V = 942.48 cm³ and r = 5 cm: h = V/(πr²) = 942.48/(π × 25) = 12 cm.
Capacity in liters
A cylinder with r = 5 cm and h = 12 cm has 942.48 cm³. Since 1 L = 1000 cm³, capacity is 0.94 L.
Methodology & Accuracy
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.
How the Cylinder Calculator Works
A right circular cylinder is defined by its radius r and height h. From those, the key measures are:
- Base area:
B = πr² - Base circumference:
C = 2πr - Lateral surface area (side):
L = 2πrh - Total surface area:
S = L + 2πr² = 2πr(r + h) - Volume:
V = πr²h - Surface-area-to-volume ratio:
S/V
Provide 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.
Formula Reference
| 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) |
Ambiguous Surface Area and Volume Cases
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.
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5 Fun Facts about Cylinders
Lateral area is a rectangle
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.”
Unwrap trick
Volume scales fast
Double the radius and volume jumps by 4×; double the height and volume doubles. Radius changes dominate because of the r² term.
Scaling intuition
Pi choice matters
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.
Precision check
Soap-film minimal
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.
Physics twist
Capsule math
A pill shape is a cylinder plus two hemispheres. Its volume is πr²h + 4/3 πr³—useful for bottle or tank capacity estimates.
Beyond basic
Cylinder Calculator: FAQs
How do I calculate cylinder volume?
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.
How do I find cylinder surface area?
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.
How do I find height from volume?
Rearrange the volume formula as h = V/(πr²). Enter volume and radius, then choose the height from volume and radius mode.
How do I convert cylinder volume to liters?
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.
What is lateral surface area?
Lateral surface area is the curved side area only. It does not include the top and bottom circles. The formula is L = 2πrh.
What is the difference between radius and diameter?
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.
Which inputs are valid?
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.
Can surface area and volume give two cylinder answers?
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.