How To Do Percent Increase And Decrease | Percent Change Fix

Percent increase and percent decrease show up in homework, shopping receipts, lab data, sports stats, and pay stubs. When the numbers get messy, many people default to guesswork. You don’t need to.

This page gives you one clean setup, then uses it in real situations.

Percent Change Starts With One Question

Before you touch a calculator, ask: “Compared to what?” Percent change is always measured against the original amount. That original amount is the denominator.

If you keep the denominator tied to the starting value, percent increase and percent decrease stop feeling like two topics. They become one pattern with two signs.

Know The Three Numbers In Every Percent Change

• Original value: the starting amount you’re comparing against.
• New value: the amount after the change.
• Change: new minus original. This can be positive or negative.

Use This Core Formula Every Time

Percent change is the change divided by the original value, then multiplied by 100.

Percent change = (New − Original) ÷ Original × 100%

If the result is positive, it’s a percent increase. If it’s negative, it’s a percent decrease. The math is the same.

How To Do Percent Increase And Decrease With One Formula

This section is the full workflow. You can run it on any problem, even when the problem is written in words.

Step 1: Circle The Original Value

Look for the number that comes first in time, the price before the sale, the score before the update, or the population before the change. That number goes on the bottom of the fraction.

Step 2: Find The Change

Subtract original from new. Keep the sign. A negative change is fine; it’s telling you the direction.

Step 3: Divide By The Original

This turns a raw change into a relative change. A $5 change means something different on a $10 item than on a $500 item.

Step 4: Multiply By 100 And Label It

Multiply by 100 to convert to percent. Then label it as increase or decrease based on the sign.

Percent Increase In Plain Steps

Percent increase is used when the new value is larger than the original value. The change is positive, so the percent change is positive.

Worked Example: Price Goes Up

A notebook costs $8 and later costs $10. The change is 10 − 8 = 2. Divide by the original: 2 ÷ 8 = 0.25. Multiply by 100: 25%. That’s a 25% increase.

Quick Check That Catches Most Errors

If something increased, the new value must be bigger than the original. If your percent is negative, you swapped numbers in the subtraction. If your percent is huge and the new value barely moved, you probably divided by the wrong number.

Percent Decrease Without Any New Tricks

Percent decrease is used when the new value is smaller than the original value. The change is negative, so the percent change comes out negative.

Worked Example: Score Drops

A score falls from 92 to 85. The change is 85 − 92 = −7. Divide by the original: −7 ÷ 92 = −0.0761. Multiply by 100: −7.61%. Report it as a 7.61% decrease.

When To Report The Minus Sign

In many classes, you write “7.61% decrease” instead of writing a minus sign. In science and data work, you may keep the sign, since it carries direction. Either way, the calculation is identical.

Want a second explanation and extra practice problems? Khan Academy’s lesson on percent change walks through the same pattern with more examples.

Table Of Common Percent Change Setups

This table shows the most common percent increase and percent decrease situations and how to set them up. Focus on the denominator column. That’s where most mistakes start.

Situation	What Counts As “Original”	Setup Tip
Price change at a store	Price before the change	Use new − old for the change
Test score change	Earlier score	Keep points as change, then convert
Population growth	Starting population	Use totals, not the difference between rates
Discount from a listed price	Listed price	Discount percent is off the listed price
Markup on cost	Cost to the seller	Markup percent is not based on selling price
Tax added at checkout	Pre-tax subtotal	Tax percent is based on the subtotal
Tip on a meal	Meal total before tip	Tip percent uses the pre-tip total
Data value changes over time	Earlier data point	Percent change compares to the earlier value
Rent raised each year	Rent before the raise	Compute each year separately, not from memory

Percent Increase Or Decrease With Multipliers

Sometimes you don’t want the percent change. You want the new value after a percent increase or percent decrease. In that case, a multiplier can save steps.

Turn A Percent Into A Multiplier

• Increase by p%: multiply by (1 + p/100).
• Decrease by p%: multiply by (1 − p/100).

Example: Increase By 18%

A subscription is $25 and increases by 18%. Convert 18% to 0.18, then add 1: 1.18. Multiply: 25 × 1.18 = 29.5. The new price is $29.50.

Example: Decrease By 30%

A jacket is $60 and gets a 30% discount. Convert 30% to 0.30, then subtract from 1: 0.70. Multiply: 60 × 0.70 = 42. The sale price is $42.

Why Multipliers Beat Subtracting The Discount

Subtracting “30%” from a price without converting to dollars mixes units. The multiplier keeps units consistent, so the final number stays in dollars, points, grams, or whatever the quantity is.

Reverse Percent Problems

Reverse percent problems ask you to find the original amount when you only know the new amount and the percent change. These can feel tricky until you stick to the multiplier idea.

Find The Original After A Decrease

A phone case costs $14 after a 20% discount. A 20% decrease means the new value is 80% of the original, so the multiplier is 0.80. Solve: Original × 0.80 = 14, so Original = 14 ÷ 0.80 = 17.5. The original price was $17.50.

Find The Original After An Increase

A lab sample weighs 54 grams after a 12% increase. The multiplier is 1.12. Solve: Original × 1.12 = 54, so Original = 54 ÷ 1.12 = 48.2142857… Round based on the context and rules you’re given.

If you want a textbook-style rundown of percent applications, OpenStax has a free section on percent applications that includes reverse-percent setups.

Table Of Worked Percent Increase And Decrease Examples

These examples show both methods: the percent change fraction and the multiplier method. Use the approach that matches the question being asked.

Scenario	Numbers	Result
Raise on hourly pay	$16 to $18	(18−16)/16×100 = 12.5% increase
Battery level drop	100% to 72%	(72−100)/100×100 = 28% decrease
Recipe scaled up	2 cups to 2.5 cups	(2.5−2)/2×100 = 25% increase
Sale price found	$80 with 15% off	80×0.85 = $68
Original price found	$51 after 15% off	51÷0.85 = $60
Class size change	28 students to 21	(21−28)/28×100 = 25% decrease
Data spike	40 to 58	(58−40)/40×100 = 45% increase
Weight loss	150 lb to 138 lb	(138−150)/150×100 = 8% decrease

Common Mistakes And How To Fix Them

Using The New Value As The Denominator

This flips the meaning. Percent change compares to where you started. If you divide by the new value, you answer a different question.

Dropping Units Midway

Write the change in the same units as the original: dollars with dollars, points with points. Then the division cancels units and you get a clean percent.

Mixing Percent Change With Percentage Points

If a rate goes from 10% to 12%, the change is 2 percentage points. The percent increase is (12−10)/10×100 = 20%. Those are two different statements.

Rounding Too Early

Keep extra decimals until the end, then round once. Early rounding can move a final answer enough to miss an answer choice.

Word Problems: A Reliable Translation

Word problems get simpler when you translate each sentence into the three numbers: original, new, and change.

Spot The Original In Words

• “Was” and “used to be” usually point to the original value.
• “Now” and “after” usually point to the new value.
• “Increased by” and “decreased by” may describe a percent, a raw amount, or both, so read the units.

Two Mini Problems

A store had 240 items in stock and now has 300. The change is 60 and the original is 240, so 60÷240×100 = 25% increase.

A tank held 50 liters and now holds 38 liters. The change is −12 and the original is 50, so −12÷50×100 = −24%. Report it as a 24% decrease.

Fast Mental Checks

• Benchmarks: 10% is one tenth, 25% is one quarter, 50% is one half.
• Direction: increase means new > original, decrease means new < original.

Percent Change With A Calculator Or Spreadsheet

Tools are fine, as long as you still feed them the right numbers.

Calculator Steps

Compute (New − Original) first, then divide by Original, then multiply by 100. Treat the % button as formatting, not magic.

Spreadsheet Formulas

In a spreadsheet, if A2 is the original and B2 is the new value, the percent change formula is:

(B2-A2)/A2

Then format the cell as a percent. That keeps the calculation clean and avoids double-multiplying by 100.

Practice Set With Answers

Try these without peeking. Then check your work.

1. A backpack price moves from $45 to $54. What percent increase is that?
2. A temperature reading falls from 75 to 66. What percent decrease is that?
3. A snack is $2.40 after a 20% discount. What was the original price?
4. A class average rises from 68 to 74. What percent increase is that?
5. A bill is $96 after an 8% tax was added. What was the pre-tax subtotal?

Answer List

• 1) (54−45)/45×100 = 20% increase
• 2) (66−75)/75×100 = 12% decrease
• 3) 2.40 ÷ 0.80 = $3.00
• 4) (74−68)/68×100 = 8.82% increase
• 5) 96 ÷ 1.08 = $88.89

One Last Checklist Before You Submit An Answer

• Did you put the starting value on the bottom?
• Did you compute new minus original for the change?
• Did you label increase or decrease based on the sign and the story?
• Did you round at the end, based on the class rule?