Sometimes you report a change as an absolute change, such as the Dow Jones dropping by 44.05 points. Other times you report a percentage change, such as the Dow Jones dropping by 0.26 percent. The percentage change shows how big the change is relative to the initial value. The word “delta” comes from the Greek letter delta, which is represented as a triangle and is commonly used to symbolize a change. Delta X, or the change in X, is equivalent to X(final) - X(initial). You can calculate the percentage change in X in two ways.

## Method 1

Calculate the percentage change using the equation [X(final) - X(initial)] / X(initial) * 100.

Suppose the cargo space is 34.2 in the old model of a car and 32.6 cubic feet in the new model. Subtract the new value from the old value. 32.6 cubic feet - 34.2 cubic feet = -1.6 cubic feet.

Divide by the old value: -1.6 cubic feet / 34.2 cubic feet = -0.0468.

Convert to a percent: -0.0468 * 100 = -4.68 percent. The cargo space dropped by 4.68 percent.

## Method 2

Calculate the percentage change using the equation [X(final) / X(initial) * 100] - 100 percent.

Use the same cargo space example of 34.2 in the old model of a car and 32.6 cubic feet in the new model. Divide the new value by the old value: 32.6 cubic feet / 34.2 cubic feet = 0.953.

Convert to a percentage: 0.953 * 100 = 95.3 percent.

Subtract 100 percent. 95.3 percent - 100 percent = -4.7 percent. The difference between Method 1 and Method 2 comes from the difference in rounding.

References

About the Author

Ariel Balter started out writing, editing and typesetting, changed gears for a stint in the building trades, then returned to school and earned a PhD in physics. Since that time, Balter has been a professional scientist and teacher. He has a vast area of expertise including cooking, organic gardening, green living, green building trades and many areas of science and technology.