Percent Increase in Math: Formula & Examples

Definitionnoun phrase

What is percent increase in math?

Percent increase is how much a quantity grew, written as a percent of its original value. Subtract the original from the new value, divide by the original, and multiply by 100: from 80 to 100 is 2080 = 25%. To increase a number by r%, multiply it by 1 + r100, so 80 × 1.25 = 100.

In Spanish: aumento porcentual
Also called: percentage increase, percent growth, markup percent, rate of increase
Grade level: 6-8

Grade 7Grade 8Algebra 1CCSS 7.RP.A.3GEDSATACTASVABTABETEASHiSET

Percent Increase in a picture

The increase is one more quarter of the original, so it is a 25% increase, and the new amount is 125% of the original.

Formal definition and notation

If a quantity grows from an original value O > 0 to a new value N > O, its percent increase is N − OO × 100%. Equivalently, N = O(1 + p), where p is the increase as a decimal; the number 1 + p is the growth factor or multiplier. Percent increase is the positive case of percent change, and it can be more than 100%: doubling is a 100% increase and tripling is a 200% increase.

Symbol	Read it as	Meaning
1 + p	one plus p	the multiplier for an increase of p (as a decimal): a 15% increase multiplies by 1.15

Key facts

Always divide by the original amount. From 80 to 100 is a 25% increase, but from 100 back to 80 is only a 20% decrease.
A percent increase can exceed 100%: going from 30 to 90 is a 200% increase, because the increase, 60, is twice 30.
Multiplying by 1 + p does the increase in one step: a 6% raise on 52,000 dollars is 52,000 × 1.06 = 55,120.
Two increases do not add: 10% then 10% multiplies by 1.1 × 1.1 = 1.21, a 21% increase in all.
To undo an increase, divide by the multiplier: 66 after a 20% increase came from 66 ÷ 1.2 = 55.

Percent increase formula

percent increase = new − originaloriginal × 100

original: the starting value (always the denominator)
new: the value after the increase
new value: = original × ( 1 + r100 ) for an increase of r%

Three questions use the same formula: find the percent (from 40 to 50 is 25%), find the new value (40 up 25% is 50), or find the original (50 after a 25% increase came from 40).

Percent Increase examples, step by step

Example 1: Find the percent increase

Warm-up

A ticket price rose from 40 dollars to 50 dollars. What is the percent increase?

Increase: 50 − 40 = 10 dollars.
Divide by the original: 1040 = 0.25.
As a percent: 0.25 × 100 = 25%.

Answer: The price increased by 25%.

Example 2: Find the new value

Core

A town of 1,200 people grows by 15%. What is the new population?

A 15% increase means the new amount is 115% of the original.
Multiplier: 1 + 0.15 = 1.15.
1200 × 1.15 = 1380.

Answer: The new population is 1,380 people.

Example 3: Work backward to the original

Test-style

After a 20% price increase, a jacket costs 66 dollars. What was the price before the increase?

The new price is 120% of the original: 1.2 × original = 66.
Divide by the multiplier: 66 ÷ 1.2 = 55.
Check: 55 × 1.2 = 66. (Taking 20% off 66 gives 52.80, which is wrong.)

Answer: The original price was 55 dollars.

Common mistakes

✗ MistakeFrom 40 to 50: 1050 = 20% increase.

✓ InsteadDivide by the original: 1040 = 25%.

Percent increase compares the change with where you started. The new value is the wrong base.

✗ MistakeUndoing a 20% increase on 66 dollars by taking 20% off: 66 × 0.8 = 52.80 dollars.

✓ InsteadDivide by the multiplier: 66 ÷ 1.2 = 55 dollars.

The 20% was 20% of the original, which is smaller than 66, so 20% of 66 is too much to remove.

✗ MistakeA 10% raise followed by another 10% raise is a 20% raise.

✓ Instead1.10 × 1.10 = 1.21, a 21% raise.

The second 10% is taken of a bigger number, so the increases compound.

✗ MistakeA price that doubles from 30 to 60 increased by 200%.

✓ InsteadThe increase is 30, and 3030 = 100%.

New is 200% of the original, but the increase is 100%. Subtract the original before dividing.

Not to be confused with

Percent Increasevs.Percent change

Percent change covers both directions and is negative for a decrease; percent increase is the case where the new value is bigger, and is stated as a positive percent.

Percent Increasevs.Percent decrease

Percent decrease divides a drop by the original. From 100 to 80 is a 20% decrease, while from 80 to 100 is a 25% increase.

Percent Increasevs.Percent of a number

“25% of 80” is 20, the size of the increase. “80 increased by 25%” is 100, the new total.

Quick check: 3 questions

Question 1 of 3

A value rises from 60 to 75. What is the percent increase?

Show answer and explanation

Answer: C. Increase 15, divided by the original 60: 1560 = 25%. 20% divides by the new value 75, 15% is the raw increase, and 125% is the new value as a percent of the old.

Question 2 of 3

What is 250 increased by 40%?

Show answer and explanation

Answer: B. 250 × 1.4 = 350. 100 is only the increase, 290 adds 40 instead of 40%, and 140 is 40% of 350.

Question 3 of 3

A quantity doubles. What is the percent increase?

Show answer and explanation

Answer: D. The increase equals the original, so it is xx = 100%. 200% is the new amount as a percent of the original, not the increase.

Percent Increase: frequently asked questions

How do you calculate percent increase?

Subtract the original value from the new value to get the increase, divide that by the original value, and multiply by 100. From 120 to 150: 150 − 120 = 30, 30 ÷ 120 = 0.25, so the increase is 25%. Always put the original value in the denominator.

Can a percent increase be more than 100%?

Yes. Any time the new value is more than double the original, the increase is over 100%. Going from 20 to 70 is an increase of 50, and 5020 = 250%. Percent decrease is different: it cannot go past 100%, because you cannot lose more than everything.

How do you increase a number by a percent?

Multiply by 1 plus the percent written as a decimal. To increase 80 by 15%, multiply by 1.15: 80 × 1.15 = 92. This is the same as finding 15% of 80, which is 12, and adding it to 80, but it takes one step.

Practice and tools

Percent problems practicePractice on Effortless Math Percent Change CalculatorPercent increase or decrease between two values Discount, Tax and Tip CalculatorTax and tip are percent increases on a price

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.RP.A.3

Cite this entry

Effortless Math Team. “Percent Increase.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/percent-increase/

Flashcard

TermPercent Increasegrowth compared with the start

DefinitionThe increase divided by the original, times 100. From 80 to 100: 2080 = 25%. Shortcut: 80 × 1.25 = 100.

Study the full deck

Browse all terms in the Math Dictionary · More ratios and proportions terms · Random term

NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Percent ChangePercent change measures how much a value grew or shrank relative to where it started: the difference divided by the original amount, written as a percent. From 50 to 60 is a 20% increase; from 80 to 60 is a 25% decrease. The original value is always the base, which is the step people get wrong.Ratios and Proportions · Grade 7, Grade 8, Algebra 1PopulationA population in statistics is the whole group of people, animals or objects you want to learn about, such as every student in a school or every bulb a factory makes. Measuring all of them is often too costly, so you study a sample, a part of the population, and use it to draw conclusions about the whole group.Statistics · Grade 7, Statistics, Algebra 1Percent DecreasePercent decrease is how much a quantity went down, written as a percent of its original value. Subtract the new value from the original, divide by the original, and multiply by 100. A price that drops from 80 dollars to 60 dollars has a decrease of 20 dollars, and 2080 = 25%.Ratios and Proportions · Grade 7, Grade 8, Algebra 1PercentA percent is a number out of 100. Percent means per hundred, so 25% means 25 out of 100, or 25100 = 0.25. To find a percent of a quantity, change the percent to a decimal and multiply: 20% of 80 is 0.20 × 80 = 16. The symbol for percent is %.Number System · Grade 5, Grade 6, Grade 7DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6ProportionA proportion is an equation that says two ratios are equal, such as 12 = 36. It is read 1 is to 2 as 3 is to 6. In a true proportion the cross products are equal, which lets you find a missing value. Proportions are often used to solve scale, percent, and rate problems.Ratios and Proportions · Grade 6, Grade 7, Grade 8Unit RateA unit rate is a rate that compares a quantity to one unit of another quantity, such as 50 miles per hour or 4 dollars per notebook. To find it, divide the first quantity by the second: 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour. The word per means for each one.Ratios and Proportions · Grade 6, Grade 7, Grade 8

Percent Increase

What is percent increase in math?

Percent Increase in a picture

Formal definition and notation

Key facts

Percent increase formula

Percent Increase examples, step by step

Example 1: Find the percent increase

Example 2: Find the new value

Example 3: Work backward to the original

Common mistakes

Not to be confused with

Quick check: 3 questions

Percent Increase: frequently asked questions

How do you calculate percent increase?

Can a percent increase be more than 100%?

How do you increase a number by a percent?

Related terms

Practice and tools

Sources

Flashcard

Login

Login and use all of our services.

Register

Register Fast!

Choose your next math review topic