# Cylinder Calculator

Calculate cylinder volume, total surface area, lateral area, and base area from radius and height. Free online cylinder calculator with formulas.

## What this calculates

Calculate the volume, total surface area, lateral surface area, and base area of any cylinder. Enter the radius and height to get instant results.

## Inputs

- **Radius** — The radius of the circular base.
- **Height** — The height (length) of the cylinder.

## Outputs

- **Volume** — The volume of the cylinder (pi x r^2 x h).
- **Total Surface Area** — The total surface area including both bases (2 x pi x r x h + 2 x pi x r^2).
- **Lateral (Side) Surface Area** — The area of the curved side only (2 x pi x r x h).
- **Base Area** — The area of one circular base (pi x r^2).
- **Base Circumference** — The circumference of the circular base (2 x pi x r).

## Details

A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved surface. It is one of the most common shapes in engineering, manufacturing, and everyday life.

Cylinder Formulas

- Volume: V = pi x r^2 x h (base area times height)

- Lateral Surface Area: LSA = 2 x pi x r x h (the curved side)

- Total Surface Area: TSA = 2 x pi x r x h + 2 x pi x r^2 (side plus both bases)

- Base Area: A = pi x r^2

Real-World Applications

Cylinder calculations are essential for determining the capacity of tanks, pipes, cans, and barrels. Engineers use these formulas to calculate material requirements for cylindrical structures, and chemists use them for graduated cylinders and reaction vessels.

## Frequently Asked Questions

**Q: How do I calculate the volume of a cylinder?**

A: Multiply the area of the circular base (pi x r^2) by the height: V = pi x r^2 x h. For a cylinder with radius 4 cm and height 10 cm: V = pi x 16 x 10 = 502.65 cubic centimeters. This formula works because a cylinder is essentially a stack of circles.

**Q: What is lateral surface area?**

A: Lateral surface area is the area of the curved side of the cylinder, excluding the two circular bases. Imagine unrolling the cylinder's side into a flat rectangle; its width is the circumference (2 x pi x r) and its height is h, giving LSA = 2 x pi x r x h. This is useful for calculating the material needed to wrap or label a cylindrical object.

**Q: How do I find the radius from the volume?**

A: Rearrange the volume formula: r = sqrt(V / (pi x h)). For example, if the volume is 500 cubic cm and the height is 10 cm: r = sqrt(500 / (pi x 10)) = sqrt(15.915) = 3.989 cm.

**Q: What is the difference between a cylinder and a prism?**

A: A cylinder has circular bases, while a prism has polygonal bases (triangular, rectangular, hexagonal, etc.). Both are formed by extending a 2D shape along a height. The volume formula is the same concept: base area times height. As the number of sides of a prism's base increases, it approaches a cylinder.

**Q: How much liquid can a cylindrical tank hold?**

A: Calculate the volume using V = pi x r^2 x h with consistent units. The result is in cubic units. To convert: 1 cubic meter = 1000 liters, 1 cubic foot = 7.481 gallons, and 1 liter = 1000 cubic centimeters. For a tank with radius 2 meters and height 3 meters: V = pi x 4 x 3 = 37.7 cubic meters = 37,700 liters.

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Source: https://vastcalc.com/calculators/math/cylinder
Category: Math
Last updated: 2026-04-21