How to Calculate Volume in a Wire

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Even though you can bend and twist it into various shapes, a wire is basically a cylinder. It has a circular cross-section with a specific radius and has a particular length. That's all you need to calculate its volume, using the standard expression:

V=\pi r^2 L

where "r" is the wire radius and "L" is its length. Since diameter (d) is more often mentioned in the wire specifications than radius, you can rewrite this equality in terms of this quantity. Remembering that radius is half of diameter, the expression becomes:

V=\frac{\pi d^2 L}{4}

Keep Units Consistent

The diameter of a wire is orders of magnitude smaller than its length in most cases. You'll probably want to measure the diameter in inches or centimeters while you measure the length in feet or meters. Remember to convert your units before calculating volume, or the calculation will be meaningless. It's usually better to convert the length to the units you used to measure diameter rather than the other way around. This produces a large number for length, but it's easier to work with than the extremely small number you'll get for diameter if you convert it to meters or feet.

Sample Calculations

1. What is the volume of a 2-foot length of 12-gauge electrical wire?

Looking up the diameter of 12-gauge wire in a table, you find it to be 0.081 inches. You now have enough information to calculate the wire volume. First convert the length to inches: 2 feet = 24 inches. Now use the appropriate equation:

V=\frac{\pi d^2 L}{4}=\frac{\pi (0.081)^2 24}{4}=0.124\text{ in}^3

1. An electrician has 5 cubic centimeters of space left in an electrical box. Can he fit a 1-foot length of 4-gauge wire in the box?

The diameter of 4-gauge wire is 5.19 millimeters. That's 0.519 centimeters. Simplify the calculation by using the wire radius, which is half the diameter. The radius is 0.2595 centimeters. The length of the wire is 1 foot = 12 inches = (12 x 2.54) = 30.48 centimeters. The volume of the wire is given by:

V=\pi r^2 L=\pi (0.2595)^2 30.48=6.45\text{ cm}^3

The electrician doesn't have enough room in the box to install the wire. He either needs to use smaller wire, if codes allow, or a bigger box.

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