How to Use the Cylinder Calculator

This calculator allows you to find various measurements of a right cylinder given two or more known values.

To compute the surface area and volume of a cylinder in terms of it's radius and height, click the 'Dimensions' button and enter the known values. The surface area and volume will appear in the both the cylinder preview and the math area, where the formulae used to make the calculations are shown. To save either the calculated surface area or volume, click the button that shows the resulting value and it will be copied to the clipboard, or click the 'Save' button to store the entire calculation in the calculator tape for later reference.

To find a cylinder's dimensions in terms of its area, you can click the 'Area' button and supply this value and then one of the remaining critical dimensions (either the cylinder's radius or the cylinder's height). The calculator will also display buttons with the calculated dimensions and volume that can be used to copy these values to the clipboard.

Finally, to find the dimensions in terms of a cylinder's volume, click the 'Volume' button and enter the known dimensions.

What are Cylinders?

A cylinder is a three dimensional object that starts from a circular base defined by a radius and rises through a known height. This definition of a cylinder is more technically a description of a right circular cylinder, however more generally cylinders can also have non-circular bases (such as an ellipse in the base of an elliptical cylinder). Additionally, an oblique cylinder is where the center point of a cylinder's base and a cylinder's apex do not form a line that is orthogonal (i.e., a right angle) to the cylinder's base.

The cylinder calculator on this page shows right circular cylinders in its preview. However, the volume of an oblique circular cylinder is equivalent to the volume of a corresponding right circular cylinder, so the results returned by this caluclator for cylinder volume can be used regardless of a cylinder's angular deflection. However, calculating the surface area of an oblique cylinder is somewhat more complicated and requires trigonometric functions to solve. For this reason, you should not use this calculator to compute the area of an oblique cylinder.

Because cylinders approximate the shapes of many common objects, you can use this cylinder calculator to compute rough volumes or dimensions for many objects. Many tanks as roughly cylinder shaped, and it is also common to treat tubing or piping as cylinders for estimating the volume the hold in an apparatus. In fact, because of it's utility in measuring small changes in volume precisely, a graduated cylinder is a common peice of laboratory equipment used to measure relatively small volumes of liquids.

Mathematical Properties of Cylinders

Cylinders are related to circles in many respects and correspondingly a cylinder's geometry related to the constant pi (π). The equation for the volume of a cylinder is easily arrived at if we already know the area of the cylinder's base. Simply extending that two dimensional area into the third dimension (the cylinder's height) calculates its three dimensional volume...

Equation for Area of a Circle

$$A_{\mathrm{circle}}=\pi r^2$$

Equation for Volume of a Cylinder

$$V_{\mathrm{cylinder}}=\pi r^{2}h$$

It should also be clear that if can give the cylinder calculator virtually anything about the circle (the circle's radius, diameter, circumference, or area) we have exactly half the information needed for deriving anything else about the cylinder. Some other information is necessary to get the cylinder height. This cylinder calculator can work backwards from the cylinder volume or area to determine the cylinder height, provided the radius of the cylinder's base is known.

Calculating the area of a cylinder involves determine the area of the two base surfaces, as well as the area of the lateral surface. The two bases are trivially circles, so calculating their area is straightforward. The cylinder's lateral surface area is more interesting, but again still related to a circle's geometry. Thinking about this surface it's easy to see this value is calculated by multiplying the circumference of the cylinder base times the height of the cylinder. This cylinder calculator first determines the base area, and then adds that value twice to the cylinder's lateral area as shown in the equations below...

Equation for Area of a Cylinder

$$A_{\mathrm{base}}=\pi r^2$$ $$A_{\mathrm{lateral}}=2\pi rh$$ $$A_{\mathrm{total}}=A_{\mathrm{base}}+A_{\mathrm{base}}+A_{\mathrm{lateral}}$$

Cylinder Calculator Definitions

Cylinder

A cylinder is a three dimensional object that is defined from a circular base (defined by a radius) rises through a height dimension to an equivalent circular base. Depending on context, a cylinder can be regarded as a solid object, including all of the points that fall within its volume, or merely as a surface that includes only the points that fall on it's bases and lateral dimension.

Base

In the context of a cylinder, the base is the circle or ellipse that makes up the bottom flat surface. This cylinder calculator assumes circular cylinders. You can see the area of a base identified as a separate value in the cylinder calculator preview area.

Circular Cylinder

A cylinder whose base is a circle. This is the traditional shape of a cylinder. This calculator computes volume of circular cylinders, and surface area of right circular cylinders.

Elliptical Cylinder

A cylinder whose base is an ellipse instead of a circle; this calculator does not calculate the volume or area of elliptical cylinders.

Lateral Surface

The outer (and traditionally vertical) surface of a cylinder. It does not include the cylinder's top or bottom base. This cylinder calculator computes the lateral surface area of right circular cylinders.

Oblique Cylinder

If a cylinder is not a right cylinder, it's sides will be assymetrical. In these cases, the volume is equal to that of a similar right cylinder, but calculating the lateral surface area is more complicated. This calculator does not calculate the surface area of oblique cylinders.

Right Cylinder

When the center of a cylinder's base and the apex of a cylinder form a line segment that is orthogonal (at a right angle) to the cylinder's base, the cylinder is a right cylinder. This is typically what you think of as the traditional symmetric shape of a cylinder. This calculator will find volume and surface area for right cylinders.

Tube

The lateral surface of a cylinder (that is, the surface not inclusive of the top and bottom bases of the cylinder) is referred to as a tube.

Cylinder Calculator Updates

3 September 2018

Initial version of the cylinder calculator.