   SEARCH HOME Math Central Quandaries & Queries  Question from Joe, a parent: How do you calculate a percent change between two value ranges - for instance if I project a range for 2007 to be between 100 and 120 and a range for 2008 to be between 120 and 140, how do I calculate the estimated increase between the range? Is it 0% to 40% (taking the two inside values rto calculate the minimum and the two outside values rto calculate the maximum?) Hi Joe,

If you have a number A, say the sales on my shop last month, and a later number B, the sales this month then I can calculate the percentage change in sales as

(B - A)/A × 100.

So this is the change, B - A, relative to the starting value A, and then multiplied by 100 to express this ratio as a percent.

In your case you don't have numbers A and B, you have intervals, 100 to 120 and 120 to 140. I want to look at a slightly different example. Suppose I project a range for 2007 to be between 100 and 120 and a range for 2008 to be between 130 and 140.

There are two numbers you can use to determine an interval, its smallest value or base, and its length. In my example the bases of the two intervals are 100 and 130 and the lengths are 120 - 100 = 20 and 140 - 130 = 10. I could then say that the base of the range has changed

(130 - 100)/100 × 100 = 30%

and the length has changed

(10 - 20)/20 × 100 = -50%

In other words the base of the range has increased by 30% but the length has decreased by 50%.

In your example the base of the range has increased by 20% but the length has remained unchanged.

I hope this helps,
Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.