How to Calculate Percent Increase and Decrease (Step-by-Step Guide)

To calculate percent increase or decrease, use this formula: Percent change = (New value − Old value) ÷ Old value × 100. First subtract the old number from the new one to find the change, then divide that change by the ORIGINAL number, and finally multiply by 100 to turn it into a percentage. A positive answer means an increase; a negative answer means a decrease.

Percent change shows up everywhere in everyday American life: sale prices, salary raises, gas prices, test scores, and stock values. Yet many students and adults mix up the steps — most commonly by dividing by the wrong number. This guide teaches you three reliable methods, with hand-checked US-dollar examples you can follow line by line. If you’d rather skip the arithmetic, Calcrio’s free percentage increase calculator does it all instantly.

What Is the Percent Increase and Decrease Formula?

The single formula behind every percent-change problem is:

Percent change = (New − Old) ÷ Old × 100

There are three moving parts to understand:

• New value: the later or final number (today’s price, this year’s salary).
• Old value: the starting or original number (yesterday’s price, last year’s salary). This is the base — and it’s the number you always divide by.
• The change: New − Old. Positive means the value went up; negative means it went down.

This is a 7th-grade Common Core standard (7.RP.A.3), which means it is exactly the skill middle-school students are tested on — and the same math adults use for the rest of their lives. The most common error, by far, is dividing by the NEW value instead of the old one. Remember: the question is always “change from what?” — and the answer is always the original.

How Do You Calculate Percent Increase?

Percent increase answers questions like “By what percent did the price go up?” Follow these three steps:

1. Subtract: New value − Old value = amount of increase.
2. Divide: Amount of increase ÷ Old value = decimal change.
3. Multiply by 100: Decimal change × 100 = percent increase.

Worked Example: $30 Video Game → $39

A video game you wanted cost $30 last month. Today the price is $39. What is the percent increase?

1. Subtract: 39 − 30 = 9. The price rose by $9.
2. Divide: 9 ÷ 30 = 0.3. We divide by the original price, $30.
3. Multiply by 100: 0.3 × 100 = 30% increase.

The game costs 30% more than it did. Notice how dividing by 30 (not 39) is the step that keeps the answer correct. If you’d like to check any number pair yourself, try the free percentage increase calculator on Calcrio — it shows each step.

How Do You Calculate Percent Decrease?

The formula doesn’t change at all — the same three steps apply, and the math naturally produces a negative answer:

1. Subtract: New value − Old value (the result is negative).
2. Divide: Result ÷ Old value.
3. Multiply by 100 and read the minus sign as “decrease.”

Worked Example: $90 Sneakers → $72

A pair of sneakers listed at $90 drops to $72 during a sale. What is the percent decrease?

1. Subtract: 72 − 90 = −18. The price fell by $18.
2. Divide: −18 ÷ 90 = −0.2. Again, we divide by the original $90.
3. Multiply by 100: −0.2 × 100 = −20%, which we say as a 20% decrease.

You saved 20% off the original price. Percent decrease is the same math retailers use when they advertise “20% off” — see our guide to how to calculate percent off a sale price for the shopper’s version of this skill.

What Is the Multiplier Method for Percent Change?

The multiplier method is the fastest way to handle percent change once you’re comfortable — it’s also how calculators and spreadsheets do it internally. Instead of subtracting and dividing, you convert the percent into a single multiplier:

• For a percent increase: multiplier = 1 + (percent ÷ 100). A 15% increase → ×1.15.
• For a percent decrease: multiplier = 1 − (percent ÷ 100). A 15% decrease → ×0.85.

Example: a $40 T-shirt marked up 15%. Multiply $40 × 1.15 = $46. Check: 40 × 0.15 = 6, and 40 + 6 = 46. It matches.

Example: a $120 jacket on 25% sale. Multiply $120 × 0.75 = $90. Check: 120 × 0.25 = 30, and 120 − 30 = 90. It matches.

The multiplier method really pays off with repeated changes — like a discount followed by tax, or two discounts in a row. You just multiply the multipliers: 20% off then 10% off is ×0.8 × 0.9. (That one has a famous trap in it; we break it down in our guide to why a 10% increase then a 10% decrease doesn’t get you back to start.)

What Is the Easiest Way to Do Percent Increase in Your Head?

You don’t always need a calculator. The 10% trick handles almost every real-world situation:

• 10% of any number: move the decimal point one place left. 10% of $80 = $8.
• 5%: take half of the 10% value. 5% of $80 = $4.
• 20%: double the 10% value. 20% of $80 = $16.
• 25%: divide by 4. 25% of $80 = $20.
• 50%: divide by 2. 50% of $80 = $40.
• 15%: add 10% and 5%. 15% of $80 = $8 + $4 = $12.

Example: your $12 lunch special rises by about 10%. Ten percent of $12 is $1.20, so the new price is roughly $13.20. Done in seconds, no phone required.

Percent Increase vs Percent Decrease: Quick Comparison

	Percent Increase	Percent Decrease
Formula	(New − Old) ÷ Old × 100	(New − Old) ÷ Old × 100
Sign of answer	Positive (+)	Negative (−), said as “decrease”
Multiplier	Greater than 1 (e.g. ×1.20)	Less than 1 (e.g. ×0.80)
Everyday example	$30 game → $39 = 30% increase	$90 sneakers → $72 = 20% decrease
What you divide by	Always the OLD value	Always the OLD value

What Is the Difference Between Percent Change and Percent of a Number?

This is the #1 source of confusion on tests. They sound alike but answer different questions:

• “What is 20% OF $80?” means find a part of $80: 80 × 0.20 = $16. The answer is a dollar amount.
• “What is the percent increase FROM $80 TO $96?” means compare two values: (96 − 80) ÷ 80 × 100 = 20% increase. The answer is a percentage.

“Percent of” starts from one number; “percent change” always involves two numbers — an old and a new.

What Mistakes Should You Avoid?

• Dividing by the new value. (39 − 30) ÷ 39 gives 23.1% — wrong. Always divide by the old value.
• Forgetting to multiply by 100. An answer of 0.3 is not “0.3%” — it’s 30%. The ×100 step is what turns a decimal into a percentage.
• Misreading the sign. −20% doesn’t mean “negative twenty percent”; it means a 20% decrease.
• Mixing up percent and percentage points. If a tax rate rises from 5% to 8%, that’s a 3 percentage point rise — but a 60% relative increase. Confusing the two is so common it has its own guide: percentage points vs percent.
• Adding percentages together. Two 10% changes in a row never net to 20% — they multiply. A 10% increase followed by a 10% decrease leaves you 1% below where you started.

Where Else Does Percent Change Show Up?

Once you know the formula, you’ll spot it everywhere: your salary raise percentage tells you whether your new pay keeps up with inflation; percent-off math tells you what a sale really saves you; and successive percent changes explain everything from price swings to pay cuts followed by raises. Master this one formula and all four applications come free.

Frequently Asked Questions

What is the formula for percent increase?

Percent increase = (New value − Old value) ÷ Old value × 100. Subtract the old number from the new one, divide by the old number, and multiply by 100.

How do you calculate percent decrease between two numbers?

Use the same formula. The result comes out negative — for example, $90 down to $72 gives −20%, which you read as a 20% decrease.

How do you find the new value after a percent increase?

Multiply the old value by (1 + percent ÷ 100). A $200 salary with a 5% increase becomes $200 × 1.05 = $210.

Can percent increase be more than 100%?

Yes. If something doubles, that’s a 100% increase; if it triples, it’s a 200% increase. There is no upper limit on percent increase.

What is percent change, in one sentence?

Percent change expresses how much a value went up or down relative to its starting value — it’s the change divided by the original, written as a percentage.

Is there a free tool that does this automatically?

Yes — Calcrio’s free percentage increase calculator handles both directions and shows the steps, so you can verify your homework.