Converting Cubic Inches to Liters

This example problem demonstrates how to convert cubic inches to liters, using the real-life scenario of engine displacement, which is the combined swept displacement of all of the machine's pistons in their cylinders. When someone describes the power of a car, that person might say that it has a 3.3-liter engine or some such example.

Problem

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

Working the Solution

1 inch = 2.54 centimeters

First, convert the measurements to cubic measurements.

(1 inch)³ = (2.54 cm)³

1 in³ = 16.387 cm³

Second, convert to cubic centimeters.

Set up the conversion so that the desired unit will be canceled out. In this case, we 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) cm³

volume in cm³ = 2,474.45 cm³

Third, convert to liters.

1 L = 1,000 cm³

Set up the conversion so that the desired unit will be canceled out. In this case, we want liters to be the remaining unit.

volume in L = (volume in cm³) x (1 L/1,000 cm³)

volume in L = (2,474.45/1,000) L

volume in L = 2.474 L

Answer

A 151–cubic inch engine displaces 2.474 liters of space (or air).