How to Calculate Percentage Increase and Decrease

Percentages show up in prices, grades, savings, discounts and news headlines. Once you know three simple formulas, you can solve nearly any everyday percentage problem. This guide uses easy examples, walks through a few problems step by step and ends with common mistakes to avoid.

1. Find a percentage of a number

Formula: number x (percentage / 100)

Example: What is 15% of 80? 80 x 0.15 = 12. This is useful for tips and discounts.

Another example: A restaurant bill is $64 and you want to leave an 18% tip. 64 x 0.18 = $11.52, so the total is $75.52.

2. Find what percent one number is of another

Formula: (part / whole) x 100

Example: You scored 42 out of 50. (42 / 50) x 100 = 84%.

Another example: You got 17 questions right on a 20-question quiz. 17 / 20 = 0.85, so your score is 85%.

3. Calculate percentage increase

Formula: ((new value - old value) / old value) x 100

Example: Your rent goes from $1,200 to $1,320. The change is $120. $120 / $1,200 = 0.10, so the rent increased by 10%.

Step-by-step walkthrough

Suppose your town grew from 8,000 residents to 8,600 and you want the percentage growth.

Subtract the old value from the new value: 8,600 - 8,000 = 600.
Divide that change by the old value: 600 / 8,000 = 0.075.
Multiply by 100: 0.075 x 100 = 7.5%.

The same steps work for a raise. If your salary goes from $52,000 to $54,600, the change is $2,600, and 2,600 / 52,000 = 0.05, so you received a 5% raise.

4. Calculate percentage decrease

Use the same formula. If the result is negative, it is a decrease.

Example: A jacket drops from $80 to $60. (60 - 80) / 80 = -0.25, so the price decreased by 25%.

Discounts and sales tax

Price after a discount: price x (1 - discount%). A $60 item with 30% off costs 60 x 0.70 = $42.
Price with sales tax: price x (1 + tax%). A $42 item with 8% tax costs 42 x 1.08 = $45.36.

Sales tax rates vary by state and city, so check the rate where you are buying. On a $25 item with 7% tax, the tax is 25 x 0.07 = $1.75 and the total is $26.75.

Working backward to the original price

Sometimes you know the sale price and want to find the original. Say a coat costs $45 after 25% off. You are paying 75% of the original price, so divide by 0.75: 45 / 0.75 = $60. Check it: 60 x 0.75 = 45. A common error is to add 25% to $45, which gives $56.25 and the wrong answer, because the 25% was taken from the original price, not from the sale price.

Why increases and decreases are not symmetrical

If a stock falls 50% and then rises 50%, you are not back to where you started. Start at $100: down 50% is $50, up 50% is $75. To get back to $100, you need a 100% increase. The base number changes each time, so percentage changes cannot simply be added or subtracted.

The jacket works the same way. After a 25% price cut from $80 to $60, the store would need a 33.3% increase to return to $80, because $20 is one third of $60.

Stacked discounts

A store offers 20% off, and then an extra 10% off the sale price. That is not 30% off. On a $100 item, 20% off gives $80, and 10% off $80 gives $72. The total saving is $28, or 28%. The second discount applies to a smaller number, so it is worth less than the first.

Percentage points vs percent

If an interest rate goes from 4% to 6%, it increased by 2 percentage points, but the rate itself increased by 50 percent (2 / 4). News stories sometimes mix these up, so look carefully at what is being compared.

Which number is the base?

Comparing two numbers gives different percentages depending on which one you treat as the starting point. A $50 plan costs 25% more than a $40 plan (10 / 40), but the $40 plan costs only 20% less than the $50 plan (10 / 50). Neither answer is wrong; they answer different questions. Always ask what you are comparing against.

Quick mental math tricks

10% of a number: move the decimal one place left. 10% of 85 is 8.5.
5%: half of 10%. 5% of 85 is 4.25.
15% tip: add 10% and 5%. On $85, that is 8.50 + 4.25 = $12.75.
25%: divide by 4.

Common mistakes

Dividing by the new value instead of the old value when calculating change.
Adding two successive percentage changes together.
Forgetting to convert the percentage to a decimal (15% is 0.15, not 15).
Adding a percentage to a sale price when you really need to divide to find the original.
Confusing percentage points with percent when comparing rates.

Quick takeaways

For a change, always divide by the starting value.
Convert percentages to decimals before multiplying (30% becomes 0.30).
A 50% drop needs a 100% rise to recover.
Two discounts in a row are worth less than their sum.
Check your answer by working it backward.

Frequently asked questions

Can a percentage be more than 100%?

Yes. If something grows from 20 to 50, the change is 30, and 30 / 20 = 1.5, so it increased by 150%. A decrease cannot exceed 100% for a quantity that cannot go below zero, because a 100% decrease already means nothing is left.

How do I calculate a percentage change if the old value is zero?

You cannot, because the formula divides by the old value and division by zero is undefined. In that case, report the raw change instead, such as "went from 0 to 25 sales".

Is percent change the same as percent difference?

Not always. Percent change compares a new value to an old one and depends on which is the starting point. Some fields use a "percent difference" formula that compares two numbers to their average, which treats both equally. If you are comparing a before and after, use percent change.

What is the fastest way to find a 20% discount?

Find 10% by moving the decimal one place left, then double it. For a $65 item, 10% is $6.50, so 20% is $13.00 and the sale price is $52.

Use the calculator

Our free Percentage Calculator handles percent of, what-percent and percentage change in one place. For shopping and bills, the Sales Tax Calculator and Tip and Bill Split Calculator use the same ideas.