The Basic Formula for Percentage Increase

To find a percentage increase, subtract the starting number from the ending number, divide that result by the starting number, then multiply by 100. The formula is: ((New Value − Old Value) ÷ Old Value) × 100 = Percentage Increase.

The order matters. You always divide by the starting number, not the ending number. This tells you how much the original amount grew relative to itself. If you reverse the division, you will get the wrong answer.

Key Takeaways

  • Percentage increase uses the formula ((New Value − Old Value) ÷ Old Value) × 100, and you must divide by the starting number, not the ending one.
  • A common mistake is dividing by the new value instead of the old value, which gives you a percentage decrease rather than an increase.
  • Negative results mean the value went down, not up—this is a percentage decrease, and the formula still works the same way.
  • Real-world examples include salary raises, price changes, and population growth, where the starting point is always the baseline you compare against.

Working Through a Real Example Step by Step

Say your hourly wage was $15 and it increased to $18. Subtract: $18 − $15 = $3. Divide by the starting wage: $3 ÷ $15 = 0.2. Multiply by 100: 0.2 × 100 = 20%. Your wage increased by 20%.

The decimal step (0.2) is the key. That decimal tells you the increase as a fraction of the original. Multiplying by 100 converts it to a percentage. If you skip the multiplication by 100, you have the answer in decimal form (0.2 = 20%), but percentages are easier to read and compare.

Try another: a product cost $50 last year and costs $65 this year. Subtract: $65 − $50 = $15. Divide: $15 ÷ $50 = 0.3. Multiply by 100: 0.3 × 100 = 30%. The price went up 30%.

What to Do When the Result Is Negative

If your new value is smaller than your old value, the formula still works—but the result will be negative. A negative percentage means the value decreased, not increased. For example, if attendance at an event dropped from 200 people to 150 people, the calculation is ((150 − 200) ÷ 200) × 100 = (−50 ÷ 200) × 100 = −25%. Attendance fell by 25%.

Some people call this a "percentage decrease" to be clear about direction. The math is identical; the negative sign tells you which way the change went. Do not drop the negative sign or convert it to positive—it carries important information about whether something grew or shrank.

Common Mistakes and How to Avoid Them

The most frequent error is dividing by the new value instead of the old value. If you calculated ($18 − $15) ÷ $18 × 100, you would get 16.67%, which is wrong. You divided by the ending wage, not the starting wage. Always ask yourself: "What am I measuring this change against?" The answer is always the starting point.

Another mistake is forgetting to multiply by 100. If you stop at 0.2, you have the decimal form, which is correct mathematically but not a percentage. Percentages are always out of 100, so that final multiplication is required to express your answer in the format people expect.

A third error is mixing up which number goes where in the subtraction. The formula is (New − Old), not (Old − New). If you reverse it, you will get a negative result when you should get positive, or vice versa. Write out the words "new" and "old" next to your numbers if you are unsure.

Using Percentage Increase in Real Situations

Salary increases are the most common use. If you earned $40,000 last year and $44,000 this year, your raise is ((44,000 − 40,000) ÷ 40,000) × 100 = 10%. You can use this to compare raises across years or to negotiate based on inflation or market rates.

Price changes work the same way. If a gallon of milk cost $3.50 last month and $3.85 this month, the increase is ((3.85 − 3.50) ÷ 3.50) × 100 = 10%. Retailers and shoppers use this to track inflation and compare value across time.

Population or business growth also uses this formula. If a town had 50,000 residents in 2020 and 55,000 in 2024, the growth is ((55,000 − 50,000) ÷ 50,000) × 100 = 10%. Planners use this to forecast infrastructure needs and understand trends.

Checking Your Work

A quick way to verify your answer is to work backward. If you calculated a 20% increase on $15, multiply $15 by 1.20 (which is 100% plus 20%). You should get $18. This reverse check catches most arithmetic errors.

To use this method, add your percentage increase to 100, divide by 100 to get a decimal, then multiply by the original value. For a 30% increase on $50: (100 + 30) ÷ 100 = 1.30, then $50 × 1.30 = $65. If this matches your new value, your percentage calculation was correct.

Frequently Asked Questions

Can I use this formula for decreases too?

Yes. The formula works for both increases and decreases. If the new value is smaller, you will get a negative percentage. For example, if sales dropped from 1,000 units to 800 units, the change is ((800 − 1,000) ÷ 1,000) × 100 = −20%. The negative sign shows it is a decrease.

What if the old value is zero?

You cannot divide by zero, so the formula breaks down. If you are starting from zero (no prior value to compare to), a percentage increase is not meaningful. You would need a different approach, such as describing the absolute change instead.

Do I always multiply by 100?

Yes, if you want the answer as a percentage. If you stop before multiplying by 100, you have the decimal form (0.2 instead of 20%), which is mathematically correct but not in percentage format. Multiply by 100 to express it the way most people expect.

What is the difference between percentage increase and percentage point increase?

Percentage increase uses the formula described here and is relative to the starting value. A percentage point is an absolute difference. If interest rates rise from 2% to 5%, that is a 3 percentage point increase, but a 150% percentage increase (because (5 − 2) ÷ 2 × 100 = 150%). The context determines which one matters.