Cylinder Calculator

What is a Cylinder?

A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved surface. The most common type is the right circular cylinder, where the axis is perpendicular to the bases. Cylinders are fundamental geometric shapes found in everyday objects such as cans, pipes, tanks, and columns. For other geometric calculations, try our Cone Calculator, Volume Calculator, and Tank Volume Calculator.

This cylinder calculator helps you compute all essential properties of a right circular cylinder: radius (r), height (h), volume (V), lateral surface area (L), top surface area (T), base surface area (B), and total surface area (A). You can enter any two known values and the tool will automatically calculate the remaining properties.

How to Use the Cylinder Calculator

Using this cylinder geometry calculator is straightforward:

Select Known Values: Choose which two cylinder properties you know from the dropdown menu (radius & height, radius & volume, radius & lateral area, height & volume, height & lateral area, or radius & total area).
Choose Unit: Select your preferred unit of measurement (mm, cm, m, km, in, ft, yd, or none).
Enter Values: Input the two known values into the calculator.
Adjust Precision: Set the number of significant figures for the results.

All results update in real-time as you type. The calculator also displays values in terms of pi for exact mathematical representation.

Cylinder Formulas

The following formulas are used to calculate the properties of a right circular cylinder where r is the radius and h is the height:

V = πr²h

Volume of a cylinder

L = 2πrh

Lateral (curved) surface area

T = B = πr²

Top and bottom (base) surface area

A = L + T + B = 2πr(h + r)

Total surface area (lateral + top + bottom)

How to Derive Other Values

If you know the radius and volume, the height can be found as h = V / (πr²). From the radius and lateral area, h = L / (2πr). From the height and volume, r = √(V / (πh)). From the height and lateral area, r = L / (2πh). From the radius and total area, h = A / (2πr) - r.

Example Calculation

Example: Find the volume and surface area of a cylinder with radius r = 5 cm and height h = 10 cm.

Volume: V = π x 5² x 10 = 250π = 785.398 cm³
Lateral Area: L = 2π x 5 x 10 = 100π = 314.159 cm²
Base Area: B = π x 5² = 25π = 78.540 cm²
Total Area: A = 2π x 5 x (10 + 5) = 150π = 471.239 cm²

Simply select "Radius & Height" from the dropdown, enter 5 and 10, and choose cm as the unit. All results will be displayed instantly.

Frequently Asked Questions

What is the difference between lateral surface area and total surface area of a cylinder?

The lateral surface area (L) is the area of the curved surface of the cylinder, excluding the top and bottom. The total surface area (A) includes the lateral surface area plus the areas of both circular bases. The total surface area formula is A = 2πrh + 2πr² = 2πr(h + r).

Can I calculate the cylinder properties if I only know the volume and radius?

Yes. If you know the volume (V) and radius (r), you can find the height using h = V / (πr²). Once the height is determined, all other properties (lateral area, base area, total area) can be calculated using the standard formulas.

What does "in terms of pi" mean in the results?

The "In Terms of Pi" section shows the exact mathematical values expressed as multiples of pi (π). For example, a volume of 785.398 cm³ is shown as 250π cm³. This representation is useful for mathematical analysis and exact calculations without decimal approximations.

What is the volume of a cylinder with radius 10 cm and height 20 cm?

The volume is V = π x 10² x 20 = 2,000π = 6,283.19 cubic centimeters (cm³). The total surface area would be A = 2π x 10 x (20 + 10) = 600π = 1,884.96 cm².

What units does the cylinder calculator support?

The calculator supports millimeters (mm), centimeters (cm), meters (m), kilometers (km), inches (in), feet (ft), yards (yd), and a "None" option for unitless calculations. Area results use squared units and volume results use cubic units of the selected measurement.

How many faces, edges, and vertices does a cylinder have?

A cylinder has 2 faces (the two circular bases), 1 curved surface, 2 edges (the circular boundaries of the bases), and 0 vertices. Unlike polyhedra, a cylinder is not a polyhedron because it has a curved surface rather than flat polygonal faces.

Report