Cylinder calculator
Find the volume, surface area, radius, diameter, or height of any cylinder. Enter the two values you know — the calculator solves for everything else, in the units you need.
V = π × r² × h = π × 5² × 12
How to calculate the volume of a cylinder
A cylinder's volume is the area of its circular base multiplied by its height. Because the base is a circle, that area is π times the radius squared — so the full formula is:
Here, r is the radius of the circular base and h is the perpendicular height — the straight-line distance between the two circular faces, not the slanted side length if the cylinder leans.
A water tank has a radius of 5 cm and a height of 12 cm. What's its volume?
V = π × 5² × 12 = π × 25 × 12 = 942.48 cm³
That's also about 0.94 liters, or 0.25 US gallons.
If you only know the diameter
Measuring across a cylinder (the diameter) is usually easier than measuring to its center (the radius). Since the diameter is always twice the radius, substitute d/2 for r:
How to calculate the surface area of a cylinder
A cylinder's surface has three parts: the curved side wall, plus the two flat circular ends. Imagine peeling the label off a can — it unrolls into a flat rectangle. That rectangle's height is the cylinder's height, and its width is the circumference of the base (2πr). That gives the lateral surface area:
Add the two circular ends (each π × r²) to get the total surface area:
Using the same tank — radius 5 cm, height 12 cm:
Lateral area = 2 × π × 5 × 12 = 376.99 cm²
Two circular ends = 2 × π × 5² = 157.08 cm²
Total surface area = 376.99 + 157.08 = 534.07 cm²
How to find the radius, diameter, or height when you know the volume
Sometimes you're working backward — you know how much a cylindrical container needs to hold, and you need to figure out its dimensions. Rearranging the volume formula gives you each one directly. Use the calculator above (switch to a "Volume & ..." mode) to do this instantly, or use these formulas by hand. For a deeper walkthrough with more worked examples, see our full guide to reverse-solving cylinder dimensions.
| You know | Solve for | Formula |
|---|---|---|
| V and h | radius | r = √(V / (π × h)) |
| V and r | height | h = V / (π × r²) |
| radius | diameter | d = 2 × r |
| diameter | radius | r = d / 2 |
Is there a "perimeter" of a cylinder?
Strictly speaking, no — perimeter is a 2D concept, the distance around a flat shape's edge. A cylinder is a 3D solid, so it doesn't have a single perimeter. When people search for this, they usually mean one of two things:
- The circumference of the circular base — the distance around one of the circular ends, calculated as 2πr. This is what you'd measure if you wrapped a tape measure around the can's top or bottom.
- The total surface area — if what you actually want is "how much material covers the outside," that's surface area (above), not a perimeter at all.
If you're trying to find the circumference, the calculator above shows it automatically as "base circumference" alongside the surface area breakdown.
Cylinder volume in gallons and liters
For tanks, drums, and storage cylinders, volume in cubic units isn't always the most useful number — you usually want gallons or liters. The calculator converts automatically, but here's the math if you're doing it by hand:
| Conversion | Multiply cubic result by |
|---|---|
| cm³ → liters | 0.001 |
| in³ → US gallons | 0.004329 |
| ft³ → US gallons | 7.48052 |
| liters → US gallons | 0.264172 |
| liters → UK (imperial) gallons | 0.219969 |