Cylinder Volume Calculator
Calculate the volume and lateral surface area of a cylinder.
Did this tool answer your question?
Thanks — this helps us improve the tool.
How to use this tool
- Enter radius and height in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your volume and the full breakdown beneath it.
Calculate cylinder volume (π × r² × h) and lateral surface area (2 × π × r × h).
Formula
Volume = π r2 h
Lateral surface area = 2 π r h
volume = Math.PI * r * r * h surface_area = 2 * Math.PI * r * h
How it works
This calculator finds the volume and lateral (curved) surface area of a right circular cylinder given its radius and height. The volume is the area of the circular cross-section multiplied by the height. The lateral surface area covers only the curved side wall, not the top and bottom circular caps; add 2πr² separately if you need the total closed surface area.
Worked example
- Enter radius r = 2 and height h = 5.
- Volume = π × 2² × 5 = π × 4 × 5 = 20π ≈ 62.8318.
- Lateral surface area = 2 × π × 2 × 5 = 20π ≈ 62.8318.
- For these dimensions, volume and lateral surface area are numerically equal (both 20π).
Volume ≈ 62.8318 cubic units; Lateral surface area ≈ 62.8318 square units.
Common mistakes to avoid
- Using diameter instead of radius; squaring the diameter instead of the radius multiplies the volume by 4.
- Confusing lateral surface area (2πrh, the side only) with total surface area (2πrh + 2πr², including both circular caps).
- Mixing up radius and height when entering values if the cylinder is oriented horizontally.
Key terms
- Radius (r)
- The distance from the central axis of the cylinder to its curved outer wall.
- Height (h)
- The perpendicular distance between the two circular bases of the cylinder.
- Lateral surface area
- The area of the curved side wall only, excluding the top and bottom circular faces.
- Right circular cylinder
- A cylinder whose axis is perpendicular to its circular bases — the most common form assumed in standard formulas.
Frequently asked questions
- How do you find the volume of a cylinder?
- Volume = π × r² × h where r is the radius and h is the height.