Cylinder Calculator
A cylinder with a radius of 3 and a height of 5 has a volume of about 141.37 cubic units and a total surface area of about 150.80 square units. This cylinder calculator works out volume, total surface area, lateral surface area, and base area from the radius and the height. Enter both measurements in the same unit and read the four results below.
Quick answer
Volume measures the space inside the cylinder.
What this tells you
- •Volume measures the space inside the cylinder.
- •Total surface area covers both circular ends plus the curved side.
- •Lateral surface area is the curved side only, without the two ends.
- •Base area is the area of one circular end.
How to Use
- 1Enter the radius of the cylinder.
- 2Enter the height of the cylinder.
- 3Use the same unit for both values, for example centimeters for radius and height.
- 4Click Calculate to see the volume, total surface area, lateral surface area, and base area.
How It Works
Formula
Volume: V = pi x r^2 x h. Total surface area: A = 2 x pi x r x (r + h). Lateral surface area: L = 2 x pi x r x h. Base area: B = pi x r^2.Here r is the radius of the circular end and h is the height of the cylinder. The volume multiplies the base area (pi x r^2) by the height. The total surface area adds the two circular ends (2 x pi x r^2) to the curved side (2 x pi x r x h), which factors to 2 x pi x r x (r + h). The lateral surface area is the curved side on its own.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Volume of a cylinder with radius 3 and height 5
The base area is pi x 3^2 = 28.2743. Multiply by the height: 28.2743 x 5 = 141.3717. The total surface area is 2 x pi x 3 x (3 + 5) = 150.7964.
Cylinder with radius 2 and height 5
The base area is pi x 2^2 = 12.5664. Volume is 12.5664 x 5 = 62.8319. Total surface area is 2 x pi x 2 x (2 + 5) = 87.9646.
Cylinder Volume and Surface Area
Sample volume and total surface area values for common radius and height pairs, rounded to 2 decimals.
| Radius (r) | Height (h) | Volume | Total Surface Area |
|---|---|---|---|
| 1 | 1 | 3.14 | 12.57 |
| 2 | 5 | 62.83 | 87.96 |
| 3 | 10 | 282.74 | 245.04 |
| 5 | 10 | 785.40 | 471.24 |
Values use pi as 3.14159 and assume radius and height share the same unit.
Choosing the correct cylinder measurement
Radius is the distance from the center of a circular end to its edge. Diameter runs across the full circle through the center and is twice the radius. Circumference is the distance around the edge. If a drawing or measurement gives diameter, divide by two before entering it. Do not enter circumference as radius.
Height is the perpendicular distance between the two parallel circular bases. For an upright right cylinder, that is the straight vertical height. A pipe or tank lying on its side still uses the end-to-end distance along its central axis. The calculator does not accept a slanted side measurement for an oblique solid.
Volume uses one base area times height. If radius and height are centimeters, the result is cubic centimeters. If both are inches, the result is cubic inches. The form does not attach a unit or convert the result into liters, gallons, or another capacity unit. Make that conversion separately after identifying the cubic unit.
Total surface area includes the curved side and both circular ends. Lateral area includes only the curved side, which is useful for a label wrapped around a can. Base area is one end. An open-top container would use lateral area plus one base, while a tube with no end caps would use lateral area for its outside wall before thickness is considered.
Real containers need dimensional adjustments. An outside radius calculates outside volume, while usable capacity depends on inside radius and internal height. Wall thickness, rounded corners, domed ends, seams, fittings, fill limits, and displacement reduce or change capacity. A hollow tube also needs inner and outer radii rather than one solid-cylinder radius.
All outputs use JavaScript's value of pi and round to four decimal places. The page's reference note says 3.14159 as a readable approximation, but the calculation itself uses greater internal precision. Keep symbolic pi or unrounded values when an exercise asks for an exact answer or when later calculations need more precision.
Measurements also carry uncertainty. Because radius is squared, a radius error can have a larger effect on volume than the same absolute height error. Use suitable instruments and tolerances for manufacturing, laboratory, or engineering work. A geometry result alone does not verify a part's capacity, pressure rating, strength, or compliance.
Common mistakes
- Using the diameter instead of the radius. The radius is half the diameter, so divide the diameter by 2 before entering it.
- Forgetting to square the radius. The base area uses r^2, not r, so a radius of 3 gives 9 inside the formula.
- Mixing length units. Keep the radius and the height in the same unit, otherwise the volume and area results are wrong.
- Using slanted edge length as height. A right cylinder uses the perpendicular distance between its circular ends.
- Using total surface area when a container has no top or when only the curved label area is needed.
- Reading a cubic-unit volume as though it were square-unit surface area.
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