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Percentage Change Calculator

Measure the percent increase or decrease between two values, raise or lower a value by a percent, or find the original value before a change.

Level: Grade 7

  • Common Core standard 7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Printable worksheet

Percentage Change Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Calculation

Result

Percent change

30%

Going from 50 to 65 is a 30% increase.

Amount of change (new − original)
15
Direction
increase
Multiplier (new ÷ original)
1.3
Percent difference (gap ÷ average of the two)
26.09%
Change needed to get back to the original
-23.08%

See the step-by-step solution ↓

Step-by-step solution

  1. Find how much it changed: subtract the original number from the new one

    65−50=15

  2. Divide by the size of the original, so the change is compared with where you started

    15|50|=0.3

  3. Multiply by 100 to turn it into a percent (positive means an increase)

    0.3×100=30%

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

How to solve this on a calculator

The keys to press to get this page's worked-example answer on an ordinary calculator, with what the display should show after each step.

Scientific calculator

Percent increase from 50 to 65

Problem
A monthly bill rose from $50 to $65. What is the percent increase?
Formula
percent change = (new − original) ÷ original × 100
Example values
original = 50 (the old bill); new = 65 (the new bill). These are the fixed values from the worked example on this page, so the keys stay the same whatever you type into the calculator above.
Why a scientific calculator
Brackets keep the subtraction first, and a scientific calculator shows the whole line so you can check it before pressing =. It also works on a basic calculator, fraction calculator (not on this site yet) or financial calculator.
The whole sequence
(65−50)÷50×100=

Step by step

  1. (65−50)

    Find the change inside brackets: new minus original, 65 − 50. The brackets make it happen first.

    Display: (65−50)

  2. ÷50

    Divide by the original value, 50, to compare the change with where you started.

    Display: (65−50)÷50

  3. ×100

    Multiply by 100 to turn the fraction into a percent.

    Display: (65−50)÷50×100

  4. =

    Press =. The bill went up by 30%.

    Display: 30

If your answer looks wrong

  • Without the brackets, 65 − 50 ÷ 50 × 100 = gives −35, because ÷ and × are done before −.
  • Divide by the original value (50), not the new one. Dividing by 65 gives about 23.08, which is the size of the fall going back from 65 to 50.
  • A negative answer means a decrease: from 65 down to 50 the same keys give −23.0769230769.

How this is checked: an automated test presses these keys on this site's scientific calculator, checks every display along the way, and confirms the answer matches the calculator on this page (last checked 2026-10-19). It has not been checked on any particular brand or model, and real calculators label some keys differently.

What this calculator does

Find out by what percent something went up or down. Percent change compares how much a number moved with where it started. Going from 50 to 65 is a rise of 15. Since 15 is 30% of the starting 50, that's a 30% increase.

The calculator also works the other way around. Give it a starting number and a percent, and it adds or takes away that percent for you. Or give it the number after a change and the percent that was applied. It then works back to the original, which is how you find a price before tax or a markup. For two numbers, it also shows the multiplier (new ÷ original), the percent difference, and the change you'd need to get back to where you started.

Where it's used

Why this math matters outside the classroom:

  • Price increases. A coffee that went from $3.50 to $3.85 rose by 0.35 ÷ 3.50 = 10%.
  • Sales growth. A shop whose monthly sales grew from $40,000 to $46,000 had a 15% increase.
  • Markdowns. An $80 jacket marked down 25% sells for 80 × 0.75 = $60.
  • Original prices. A $54 price after a 10% discount means the original price was 54 ÷ 0.9 = $60.
  • Population change. A town that shrank from 12,500 to 11,875 residents lost 5% of its population.

Grade level and standards: Grade 7; Common Core State Standards for Mathematics 7.RP.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what you want to do. You can find the percent change between two numbers, or raise or lower a number by a percent. You can also find the original number before a change.
  2. For percent change, enter the original number and the new one. To raise or lower a number, enter the starting number and the percent. To find the original, enter the number after the change and the percent that was applied. Use a negative percent for a decrease.
  3. Read the answer, the actual amount it changed by, and the steps shown underneath.

What the inputs mean

Original value
The earlier number, the one you're comparing from. It can't be zero, because the change is measured against it.
New value
The later number you're comparing with the original.
Starting value
The number you want to raise or lower.
Percent
How much to add or take away, out of 100. It can't be negative, so pick the decrease option instead. Percents above 100% are fine.
Value after the change
The number after the percent change was applied, such as a sale price or a price with a markup.
Percent change that was applied
The percent change that gave you the new number. Use a positive number for an increase and a negative one for a decrease. It must be more than −100%.

Formula and method

percent change = (new − original) ÷ |original| × 100
increased value = start + start × percent ÷ 100
decreased value = start − start × percent ÷ 100
original value = new value ÷ (1 + percent ÷ 100)
percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100

In the formulas, "original" and "start" are the number you begin with, and "new" is the number after the change. a and b are the two numbers being compared. The bars, as in |original|, mean "the size of the number, ignoring any minus sign".

The difference between the two numbers is divided by the size of the original. So the answer always compares the change with where you started. A positive answer is an increase, and a negative answer is a decrease.

Because the calculator ignores the original's minus sign, a move from −10 to −5 counts as a 50% increase, not a decrease. That makes sense, since −5 is higher than −10.

To undo a change, divide by the multiplier instead of subtracting the same percent. A 30% increase multiplies by 1.3, so the original is the new number divided by 1.3.

Worked example

A monthly bill rose from $50 to $65, and you want to know the percent increase.

  1. Find the difference: 65 − 50 = 15.
  2. Divide by the original: 15 ÷ 50 = 0.3.
  3. Multiply by 100: 0.3 × 100 = 30.

Result: The bill went up by 30%, a multiplier of 1.3. Going back from 65 to 50 would be a 23.08% decrease. The percent difference between the two amounts is 26.09%.

Understanding the result

Percent change doesn't work the same in both directions, which trips up a lot of people. A rise from 80 to 100 is a 25% increase. But a fall from 100 back to 80 is a 20% decrease, because each one is measured from a different starting point.

For positive numbers, a decrease can never be more than 100%. An increase has no upper limit: going from 1 to 3 is a 200% increase.

Assumptions and limitations

  • The original number is what the change is measured from. Swapping the two numbers gives a different answer.
  • Numbers are worked out exactly. The answer is only rounded when it's shown on screen.
  • Decreasing by more than 100% is allowed and gives a negative result, just as normal arithmetic would.
  • There is no percent change from an original of zero, so the calculator shows an error instead of a number.
  • When the numbers are already percents, such as interest rates, the change in percentage points is a different measure. A rate going from 4% to 5% is a rise of 1 percentage point, but a 25% increase.
  • Comparing numbers on opposite sides of zero, such as a loss turning into a profit, gives percents that are correct but often not very useful.

Frequently asked questions

How do I calculate percent change?

Subtract the old number from the new one. Divide by the old number, then multiply by 100. From 40 to 50: (50 − 40) ÷ 40 × 100 = 25%. A negative answer means a decrease.

Why doesn't a 20% increase followed by a 20% decrease bring me back to the start?

Because the decrease is taken from the bigger, already-increased number. 100 rises to 120, and 20% of 120 is 24. So you end at 96, which is a 4% loss overall.

What is the difference between percent change and percentage points?

When the numbers are already percents, plain subtraction gives percentage points. An interest rate moving from 4% to 5% rose by 1 percentage point. That's a 25% increase in the rate itself.

What is the difference between percent change and percent difference?

Percent change treats one number as the starting point and measures the move away from it. Percent difference compares two numbers without picking a starting point. It divides the gap by their average. For 50 and 65, the percent change is 30%, but the percent difference is 15 ÷ 57.5 = 26.09%. The calculator shows both.

How do I undo a percent increase?

Divide by 1 plus the rate, instead of subtracting the same percent. If a price after a 25% increase is 125, the original is 125 ÷ 1.25 = 100. Use the find-the-original option to do this in one step.

Why can't the original value be zero?

Percent change divides by the original number. Compared with zero, any move at all is endlessly large, so there's no percent to report. The actual amount it changed by still makes sense.

How this calculator is checked

Method: Standard definition of relative change, expressed as a percent; absolute value of the original used as the denominator. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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