Calculating Percent Variation

Usually, percentages are used to compare the size or proportion of a part to a whole. For example, you might say that 4 percent of students in your class have red hair, or 10 percent of them are left-handed. But you can also use percentages to compare the difference between two values that represent the same sort of thing – for example, if Suzy Girl Scout sells $300 of cookies one day and $500 of cookies the next day, what is the percent variation between the two sales amounts? A few simple calculations are all it takes to find out.

TL;DR (Too Long; Didn’t Read)

​**TL;DR (Too Long; Didn’t Read)**​

Divide the difference of the two amounts by the original or benchmark value, then multiply the result by 100:

(​_difference_​ ÷ ​_benchmark_​) × 100

1. Find the Difference

Find the difference, or the amount of change, between the two values. Subtract the benchmark or original value from the newer value being compared to it. In this case, the difference between Suzy’s two days of sales is:

($500 – $300 = $200)

2. Divide by the Benchmark

Divide the difference from Step 1 by the benchmark value. If there’s a time difference between the values, the benchmark is usually the original or older value. So in this example, the benchmark is Suzy’s first day of sales, in which she made $300:

(frac{$200}{$300} = 0.67)

3. Convert to Percentage

Multiply the result from Step 3 by 100 to convert it into percentage form:

(0.67 × 100 = 67%)

So the percentage variation from day one of Suzy’s sales to day two is 67 percent.

Another Example Calculation

Imagine that Sam is training for a marathon. By the end of the first month, he’s run 100 miles. He decides that he needs to try harder and during the second month, he runs 175 miles. What is the percent of variation between his total mileage from month one and his mileage from month two?

1. Find the Difference

Subtract the two values to find the difference between them. Since the benchmark value is Sam’s first month in which he logged 100 miles, you have:

(175 text{ miles} – 100 text{ miles} = 75 text{ miles})

2. Divide by the Benchmark

Divide the result from Step 2 by your benchmark value. This gives you:

(frac{75 text{ miles}}{100 text{ miles}}= 0.75)

3. Convert to Percentage

Multiply the result from Step 3 by 100 to convert it to a percentage. So, you have:

(0.75 × 100 = 75%)

So, the variance between Sam’s first month and his second month is 75 percent.