The formula used throughout:
(Vf - Vi) / Vi × 100 = percentage change
1. Salary raise
Your annual salary goes from $52,000 to $56,160. What is the percentage increase?
Step 1 — identify the values: Vi = 52,000, Vf = 56,160
Step 2 — apply the formula: (56,160 - 52,000) / 52,000 × 100 = 4,160 / 52,000 × 100 = 8
Step 3 — interpret: Your salary increased by 8%.
2. Population growth
A town's population grows from 18,400 to 19,872 residents over one year. What is the percentage growth?
Step 1: Vi = 18,400, Vf = 19,872
Step 2: (19,872 - 18,400) / 18,400 × 100 = 1,472 / 18,400 × 100 = 8
Step 3: The population grew by 8% over the year.
3. Exam score change
A student scored 68 out of 100 on the first test and 59 out of 100 on the second. What is the percentage change in score?
Step 1: Vi = 68, Vf = 59
Step 2: (59 - 68) / 68 × 100 = -9 / 68 × 100 = -13.24
Step 3: The score declined by 13.24%. The negative sign shows a decrease.
4. Fuel price
The price of a gallon of gas rises from $3.10 to $3.42. What is the percentage increase?
Step 1: Vi = 3.10, Vf = 3.42
Step 2: (3.42 - 3.10) / 3.10 × 100 = 0.32 / 3.10 × 100 = 10.32
Step 3: Gas prices rose by 10.32%.
Want the theory behind these steps? Read the percentage change formula explained, or plug in your own numbers with the percentage change calculator.