Cylinder Volume Calculator

Enter a radius (or diameter) and a height and we solve V = πr²h for you, step by step with your numbers. You also get lateral and total surface area, and if you pick a real unit, the answer in gallons and liters too.

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How the cylinder volume formula works

A cylinder is a circle given height. That is the whole idea. The base is a circle with area πr², and the volume is that circular area carried straight up through the height h. So the formula V = πr²h is really just "area of the base times height," the same base-times-height logic you already use for a box.

One consequence worth knowing: height and radius do not pull equal weight. Double the height and the volume doubles. Double the radius and the volume quadruples, because the radius gets squared. If you are sizing a tank and want more capacity, going wider beats going taller.

The formula

V = πr²h

V is the volume, r is the radius of the circular base (half the diameter), and h is the height. If you measured the diameter d instead, use r = d ÷ 2 first, or pick the diameter option above and we do it for you.

Surface area of a cylinder

Two formulas cover it. The lateral surface area is the curved side only: 2πrh, which is what you get if you unroll the side into a flat rectangle (the circumference 2πr wide, h tall). The total surface area adds the two circular ends: 2πrh + 2πr². Use lateral area for wrapping a label around a can; use total area for painting a closed tank. For an open-top container, add just one end: 2πrh + πr².

This is secretly a tank calculator

Half the people searching "volume of a cylinder" are not doing homework. They are standing next to a water tank, a rain barrel, a propane cylinder, a pipe, or a five gallon bucket, and the real question is "how much does this thing hold?" Cubic inches are a terrible answer to that question, so we do not stop there. Pick inches, feet, centimeters, or meters above and the result includes gallons and liters. Measure the inside of the container if you can (walls steal a little capacity), measure across the middle for the diameter, and let the calculator handle the rest. For pools with a shallow and deep end, use our pool volume calculator instead, since depth varies.

Worked example

Find the volume of a cylinder with radius 3 and height 10.

Step 1: square the radius. r² = 3 × 3 = 9.

Step 2: multiply by the height. 9 × 10 = 90.

Step 3: multiply by pi. V = 90π ≈ 282.74 cubic units.

Surface area comes along for free: lateral area = 2πrh = 2π × 3 × 10 = 60π ≈ 188.50, and total area = 60π + 2π(3²) = 78π ≈ 245.04 square units.

The mistake that quadruples your answer

The single most common cylinder error is putting the diameter where the radius belongs. Since the formula squares r, using d instead of r inflates the volume by a factor of exactly 4. If your answer looks suspiciously large, or a "12 inch" bucket seems to hold 47 gallons, check which measurement you took. Measuring across the whole circle gives diameter; the formula wants half of that. This calculator's radius or diameter toggle exists precisely because of this mistake.

Frequently asked questions

How do I find the volume of a cylinder?

Multiply pi times the radius squared times the height: V = πr²h. Square the radius first, multiply by the height, then multiply by pi (about 3.14159). A cylinder with radius 3 and height 10 has volume π × 9 × 10 = 90π, which is about 282.74 cubic units.

What if I only know the diameter, not the radius?

Divide the diameter by 2 to get the radius, then use V = πr²h as usual. This calculator has a diameter option that does the division for you. A common mistake is plugging the diameter straight into the formula, which makes the answer exactly 4 times too big.

How many gallons does a cylinder hold?

Compute the volume in cubic inches, then multiply by 0.004329 to get US gallons. A cylindrical tank 12 inches across (radius 6) and 24 inches tall holds π × 36 × 24 = 2,714.34 cubic inches, which is about 11.75 gallons. Enter your measurements in inches or feet above and we show gallons automatically.

What is the surface area of a cylinder?

Total surface area is 2πrh + 2πr²: the curved side (lateral area) plus the two circular ends. For radius 3 and height 10 that is 188.50 + 56.55 = 245.04 square units. If your cylinder is open on top, like many tanks, drop one end circle and use 2πrh + πr².

Why does the volume formula use the radius squared?

Because the base of a cylinder is a circle, and a circle's area is πr². Volume is just that base area carried up through the height: base times height. That is why doubling the height doubles the volume, but doubling the radius quadruples it.

Does this work for a tank lying on its side?

For total capacity, yes: volume does not care about orientation, so length just takes the place of height. For partial fill it does not. A horizontal tank filled to half its diameter is half full, but any other fill depth needs a circular segment calculation, not a simple ratio.

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