The Basic Formula for Percentage Increase

Percentage increase tells you how much something has grown as a share of what it started at. The formula is straightforward: subtract the original number from the new number, divide that result by the original number, then multiply by 100.

Written out: ((New Value − Original Value) ÷ Original Value) × 100 = Percentage Increase. That is the entire method. The rest is learning to recognize which number goes where and what the answer means in context.

Key Takeaways

  • Percentage increase uses one formula: divide the change by the original amount, then multiply by 100.
  • The original value always goes in the denominator, even if it is the smaller number.
  • A negative result means the value decreased, not increased.
  • Percentage increase and percentage change are the same calculation — the term "increase" just assumes the result will be positive.

Step 1: Find the Difference Between the Two Numbers

Start by subtracting the original value from the new value. If a shirt cost $20 last month and costs $25 now, the difference is $25 − $20 = $5.

The order matters here. You always subtract the starting point from the ending point. If you reverse it, you will get a negative number, which signals a decrease rather than an increase. Keep the direction correct from the start.

Step 2: Divide the Difference by the Original Value

Take the difference you just found and divide it by the original value. Using the shirt example: $5 ÷ $20 = 0.25.

This decimal tells you the increase as a fraction of the original price. A result of 0.25 means the increase is one-quarter of what you started with. If your result is larger than 1 (like 1.5 or 2), the new value is much larger than the original — the increase is 150 percent or 200 percent.

Step 3: Multiply by 100 to Get the Percentage

Take the decimal from step 2 and multiply it by 100. In the shirt example: 0.25 × 100 = 25. The price increased by 25 percent.

This step converts the decimal into the percentage form people actually use. Without multiplying by 100, you have a decimal that is harder to communicate. With it, you have a number that fits the word "percent" — literally "per hundred."

Real Examples You Can Follow

Example 1: Salary raise. You earned $40,000 last year and $48,000 this year. The difference is $48,000 − $40,000 = $8,000. Divide by the original: $8,000 ÷ $40,000 = 0.2. Multiply by 100: 0.2 × 100 = 20 percent. Your salary increased by 20 percent.

Example 2: Website traffic. Your site had 5,000 visitors last month and 6,500 this month. The difference is 6,500 − 5,000 = 1,500. Divide: 1,500 ÷ 5,000 = 0.3. Multiply by 100: 0.3 × 100 = 30 percent. Traffic grew by 30 percent.

Example 3: A decrease (negative result). A product cost $80 and now costs $60. The difference is $60 − $80 = −$20. Divide: −$20 ÷ $80 = −0.25. Multiply by 100: −0.25 × 100 = −25 percent. The price decreased by 25 percent. The negative sign tells you it is a decrease, not an increase.

Common Mistakes to Avoid

The most frequent error is putting the new value in the denominator instead of the original value. If you divide $5 by $25 instead of by $20, you get 0.2 instead of 0.25, which gives you 20 percent instead of 25 percent. The original value — the starting point — always goes on the bottom of the fraction.

Another mistake is forgetting to multiply by 100. If you stop after step 2, you have a decimal (0.25) instead of a percentage (25). The decimal is mathematically correct but not in the form the question asks for. Always complete the multiplication.

A third pitfall is mixing up which direction you are measuring. Percentage increase from $20 to $25 is not the same as percentage decrease from $25 to $20. The first is 25 percent; the second is 20 percent. The original value changes, so the answer changes.

When to Use Percentage Increase in Real Life

You use this calculation whenever you need to understand how much something has grown relative to where it started. Salary increases, price changes, population growth, test score improvements, and business revenue growth all use the same formula.

The reason percentage is more useful than raw numbers is that it shows proportion. A $5 increase on a $20 item (25 percent) is a bigger change than a $5 increase on a $100 item (5 percent), even though the dollar amount is the same. Percentage tells you the true size of the change.

Frequently Asked Questions

What if the original value is zero?

You cannot divide by zero, so the formula does not work. If something went from zero to any other number, there is no meaningful percentage increase to calculate — the change is infinite in mathematical terms. In practical contexts, people often just describe it as "went from nothing to [amount]" instead.

Can percentage increase be more than 100 percent?

Yes. If something doubles, that is a 100 percent increase. If it triples, that is a 200 percent increase. If a value goes from $10 to $50, the increase is ($50 − $10) ÷ $10 × 100 = 400 percent. There is no upper limit.

Is percentage increase the same as percentage change?

The calculation is identical. "Percentage change" is the neutral term that covers both increases and decreases. "Percentage increase" assumes the result is positive. If you get a negative result, you have a decrease, not an increase.

How do I calculate percentage increase over multiple years?

Use the same formula, but compare the final value to the starting value, not year by year. If something was worth $100 in year one and $144 in year three, the total increase is ($144 − $100) ÷ $100 × 100 = 44 percent over the two-year period. Do not add the yearly percentages together — that gives the wrong answer.