Cylinder Volume Formula Calculator
Enter a radius or diameter and the perpendicular height.
Base area first, then multiply by height.
Exact:
Check my answer
Enter a decimal or an exact coefficient followed by π. Add the cubic unit to check it too.
Find the base area before the cylinder volume
The formula V = πr²h is easier to audit as two steps. First calculate the circular base area, A = πr². Then multiply that area by the perpendicular height: V = A × h. The calculator keeps both checkpoints visible with your own measurements instead of showing only a final number.
Example: radius 5 cm and height 8 cm
The base area is A = π × 5² = 25π cm². Multiply it by the height: V = 25π × 8 = 200π cm³, approximately 628.3185307 cm³. You can leave an exact classroom answer as 200π cm³ or round the decimal as the question requests.
Check an exact π or decimal answer
After calculating, enter a proposed answer such as 200π cm³ or 628.32 cm³. The checker compares the value and, when supplied, its unit. It can flag a likely diameter-as-radius error, a missing multiplication by π, or a length unit that was not cubed. Diagnostic wording says what the result “looks like” because a number alone cannot prove which working method produced it.
Radius, diameter, and the four-times error
Radius runs from the center of the circular base to its edge. Diameter spans the whole circle, so r = d/2. If a diameter is entered as though it were a radius, squaring it produces four times the correct base area. Select Diameter above to make the conversion an explicit part of the calculation receipt.
Scope, units, and numeric limits
This version calculates a solid right circular cylinder using one shared length unit for the base and perpendicular height. The result uses the matching cubic unit. Plain positive decimals with up to six decimal places are converted to exact fractions before the π coefficient is simplified; the displayed decimal uses browser floating-point arithmetic. Hollow cylinders, tilted cylinders, surface area, and horizontal tank fill levels are intentionally outside this page.
Frequently asked questions
What is the cylinder volume formula?
For a right circular cylinder with radius r and perpendicular height h, V = πr²h. First find the circular base area πr², then multiply that area by the height.
Can I use diameter instead of radius?
Yes. Select Diameter and enter it directly. The calculator divides the diameter by 2 before squaring the radius and shows that conversion in the steps.
How can I check my cylinder volume answer?
Calculate with your measurements, then enter your proposed decimal or exact π answer in Check my answer. Add the cubic unit if you want the tool to verify the unit too.
Why is my cylinder volume answer four times too large?
A common cause is using the diameter as the radius. Because the radius is squared, substituting d instead of d/2 makes the calculated base area and volume four times too large.
Why does cylinder volume use cubic units?
Volume measures three-dimensional space. If radius and height are measured in centimeters, the result is cubic centimeters (cm³), not cm or cm².
Does this calculate a hollow or tilted cylinder?
No. This page deliberately solves a solid right circular cylinder so the formula and answer check stay unambiguous. Hollow cylinders and horizontal tank fill levels use different inputs and should be treated as separate problems.