What is a Circular Cylinder Calculator?
A right circular cylinder is a 3D solid with two parallel circular bases joined by a curved side. This calculator computes its volume, total surface area, base area (one circle), and lateral surface area (the curved side) from just two measurements: the base radius and the height.
How to Use It
Enter the radius (\(r\)) of the circular base and the height (\(h\)) of the cylinder in any consistent unit (cm, m, in, etc.). The results are returned in the corresponding squared units for area and cubic units for volume. Click calculate and all four values appear instantly.
The Formulas Explained
The volume is the base area times the height: $$V = \pi r^2 h$$ The base area of one circular end is \(\pi r^2\), and there are two of them. The lateral (side) surface, if you "unrolled" it, is a rectangle of width \(2\pi r\) (the base circumference) and height \(h\), giving \(2\pi r h\). Adding the two bases and the side gives the total surface area: $$A = 2\pi r^2 + 2\pi r h$$
Worked Example
Suppose \(r = 5\) and \(h = 10\). $$V = \pi \times 5^2 \times 10 = \pi \times 250 \approx 785.40 \text{ cubic units}$$ Base area = \(\pi \times 25 \approx 78.54\). Lateral area = \(2\pi \times 5 \times 10 = 100\pi \approx 314.16\). Total surface area = \(2(78.54) + 314.16 \approx 471.24\) square units.
FAQ
Does this work for an oblique cylinder? No — these formulas are for a right circular cylinder where the side is perpendicular to the bases.
What units does it use? Any unit you like, as long as \(r\) and \(h\) share it. Volume comes out in cubic units, areas in square units.
What is the difference between lateral and total surface area? Lateral area is only the curved side (\(2\pi r h\)). Total surface area also includes the top and bottom circles (\(2\pi r^2\)).
