# Converting Cubic Inches to Cubic Centimeters

## Cubic Inches to CC Worked Unit Conversion Example Problem

Cubic inches (in3) and cubic centimeters (cc or cm3) are common units of volume. Cubic inches is a unit used primarily in the United States, while cubic centimeters is a metric unit. This example problem demonstrates how to convert cubic inches to cubic centimeters.

## Cubic Inches to Cubic Centimeters Problem

Many small car engines have an engine displacement of 151 cubic inches. What is this volume in cubic centimeters?

## Solution

1 inch = 2.54 centimeters

That is a linear measurement, but you need a cubic measurement for volume. You cannot simply multiply this number times three. Instead, form a cube in three dimensions. You may remember the formula for volume is length x width x height. In this case, length, width, and height are all the same. First, convert to cubic measurements:

(1 inch)3 = (2.54 cm)3
1 in3 = 16.387 cm3

Now you have the conversion factor between cubic inches and cubic centimeters, so you're ready to complete the problem. Set up the conversion so the desired unit will be canceled out. In this case, you want cubic centimeters to be the remaining unit:

volume in cm3 = (volume in in3) x (16.387 cm3/1 in3)
volume in cm3 = (151 x 16.387) cm​3
volume in cm3 = 2474.44 cm3

A 151-cubic-inch engine displaces 2474.44 cubic centimeters of space.

## Cubic Centimeters to Cubic Inches

You can reverse the direction of the volume conversion easily enough. The only trick is to make sure the correct units cancel out. Suppose you want to convert a 10 cm3 cube into cubic inches. Use the volume conversion from earlier, where 1 cubic inch = 16.387 cubic centimeters:

volume in cubic inches = 10 cubic centimeters x (1 cubic inch / 16.387 cubic centimeters)
volume in cubic inches = 10 / 16.387 cubic inches
volume = 0.610 cubic inch

The other conversion factor you could have used is:

1 cubic centimeter = 0.061 cubic inch

It does not matter which conversion factor you choose. The answer will come out the same. If you're unsure whether you're doing the problem correctly, work it both ways to check yourself.