1) identify the start value (Vi) and end value (Vf),
2) apply the percentage change formula,
3) interpret the result.
Once you see the pattern, you can solve any percentage change problem the same way — or simply use the percentage change calculator to jump straight to the answer.
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.