Maths6 min readUpdated Mar 25, 2026

Percentage Increase and Decrease Formula: How to Calculate with Examples

The Calculory Team

Content and Research

Master the percentage increase and decrease formulas with step-by-step worked examples. Calculate percentage change for prices, salaries, investments, and growth rates.

Key Takeaways

The percentage increase formula is ((New Value - Old Value) / Old Value) x 100. Always divide by the original value, not the new value.
The percentage decrease formula uses the same structure: ((Old Value - New Value) / Old Value) x 100, or use the general formula and interpret negative results as decreases.
A 50% increase followed by a 50% decrease does NOT return to the starting value. $100 becomes $150 then $75, a net loss of 25%.
Percentage change and percentage difference are different formulas. Change uses the original as denominator; difference uses the average of both values.
Reverse percentage lets you find the original price: divide the final price by (1 + rate) for increases or (1 - rate) for decreases.
Use the free Percentage Increase Calculator to verify your calculations and avoid the most common error: dividing by the wrong value.

What is Percentage Change?

Percentage change measures how much a value has increased or decreased relative to its original amount. It standardizes comparisons across different scales so you can evaluate changes meaningfully.

Why Raw Numbers Are Misleading

Scenario	Dollar Change	Percentage Change	Which Is More Significant?
Stock A: $50 to $55	+$5	+10%	Stock A (10% gain)
Stock B: $500 to $505	+$5	+1%	Stock B barely moved
Rent: $1,200 to $1,350	+$150	+12.5%	Significant increase
Salary: $75,000 to $75,150	+$150	+0.2%	Negligible change

The same dollar amount means completely different things depending on the base. Percentage change solves this by expressing every shift relative to the starting point.

The General Formula

Component	Formula	Notes
Percentage Change	((New Value - Old Value) / Old Value) x 100	Positive = increase, negative = decrease
Old Value	The starting, original, or "before" number	This is ALWAYS the denominator
New Value	The ending, current, or "after" number	This goes in the numerator

Use our Percentage Calculator to compute any percentage change instantly. Enter the old and new values, and the calculator handles the rest.

The Percentage Increase Formula with Worked Examples

The percentage increase formula calculates how much a value has grown relative to its original amount.

Formula

Percentage Increase = ((New Value - Old Value) / Old Value) x 100

Three Worked Examples

Scenario	Old Value	New Value	Difference	Calculation	Result
Salary raise	$52,000	$55,640	$3,640	$3,640 / $52,000 x 100	7%
Rent increase	$1,200	$1,350	$150	$150 / $1,200 x 100	12.5%
Website traffic	4,500	6,300	1,800	1,800 / 4,500 x 100	40%
Investment return	$10,000	$11,500	$1,500	$1,500 / $10,000 x 100	15%
Home value	$320,000	$348,800	$28,800	$28,800 / $320,000 x 100	9%

In each case, the process is identical: subtract the old value from the new value, divide by the old value, and multiply by 100. The formula works with any unit: dollars, people, kilograms, or clicks.

Try it yourself with the Percentage Increase Calculator. Enter your old and new values to verify your manual calculation.

The Percentage Decrease Formula with Worked Examples

The percentage decrease formula works the same way, but the new value is smaller than the old value.

Formula

Percentage Decrease = ((Old Value - New Value) / Old Value) x 100

Three Worked Examples

Scenario	Old Value	New Value	Difference	Calculation	Result
Sale price (jacket)	$120	$84	$36	$36 / $120 x 100	30% off
Stock loss	$45.00	$38.25	$6.75	$6.75 / $45 x 100	15% drop
Weight loss	185 lbs	170.2 lbs	14.8 lbs	14.8 / 185 x 100	8% loss
Workforce reduction	1,250	1,075	175	175 / 1,250 x 100	14% decrease
Laptop discount	$850	$680	$170	$170 / $850 x 100	20% off

You can also use the general percentage change formula for decreases. Plugging in a new value smaller than the old value automatically gives a negative result: ((38.25 - 45) / 45) x 100 = -15%. The negative sign indicates a decrease.

Calculate any discount or decrease with the Percentage Decrease Calculator. Essential for verifying sale prices and financial losses.

Percentage Change vs Percentage Difference

These two concepts sound similar but use different formulas and serve different purposes. Confusing them leads to incorrect conclusions.

Formula Comparison

Metric	Formula	When to Use
Percentage Change	((New - Old) / Old) x 100	Comparing the same thing at two time points
Percentage Difference	(\|A - B\| / ((A + B) / 2)) x 100	Comparing two different things simultaneously

Same Numbers, Different Results

Values	Percentage Change	Percentage Difference	Why They Differ
$10,000 to $12,000	20% (divides by $10K)	18.2% (divides by $11K avg)	Different denominators
$50 to $75	50% (divides by $50)	40% (divides by $62.50 avg)	Larger gap = bigger divergence
100 to 105	5% (divides by 100)	4.88% (divides by 102.5 avg)	Close values = small difference

When to Use Each

Scenario	Use Change	Use Difference
This year's revenue vs last year	Yes
Stock price before and after earnings	Yes
Two students' test scores		Yes
Prices of two competing products		Yes
Your weight in January vs June	Yes

Need to compare two values without a clear before/after relationship? Use the Percentage Difference Calculator for the correct formula.

Five Common Percentage Calculation Mistakes

Mistake 1: Dividing by the Wrong Value

The most frequent error. If a price increased from $80 to $100:

Method	Calculation	Result	Correct?
Divide by OLD value (correct)	$20 / $80 x 100	25%	Yes
Divide by NEW value (wrong)	$20 / $100 x 100	20%	No

Mistake 2: Confusing Percentage Points with Percentage Change

If an interest rate moves from 4% to 5%:

Statement	Value	Meaning
Increased by 1 percentage point	1 pp	The absolute difference between 4% and 5%
Increased by 25%	25%	The percentage change: (5-4)/4 x 100

These are very different claims. In finance and economics, this distinction matters enormously.

Mistake 3: Assuming Percentage Changes Are Reversible

Step	Calculation	Value
Start		$100
50% increase	$100 x 1.50	$150
50% decrease	$150 x 0.50	$75 (not $100)
Net result		-25% loss

A 50% increase followed by a 50% decrease results in a 25% net loss, not break-even.

Mistake 4: Adding Percentages from Different Bases

Year	Return	Portfolio Value	Why Not Simply 30%
Start		$1,000
Year 1	+10%	$1,100	10% of $1,000
Year 2	+20%	$1,320	20% of $1,100 (not $1,000)
Actual total		$1,320	32% gain (not 30%)

Percentages compound. Each year's gain applies to a larger base.

Mistake 5: Ignoring the Sign

A percentage change of -15% is a decrease. Always be explicit: "prices decreased by 15%" not "prices changed by 15%."

Avoid all five mistakes by running your numbers through the Percentage Increase Calculator or Percentage Decrease Calculator before making any decision.

Reverse Percentage Calculations

Sometimes you know the final value and the percentage change, but need to find the original value. This is essential for finding pre-discount prices or pre-tax amounts.

Reverse Percentage Formulas

Situation	Formula	Example
After an increase	Original = New / (1 + Rate/100)	$180 after 20% increase: $180 / 1.20 = $150
After a decrease	Original = New / (1 - Rate/100)	$56 after 30% discount: $56 / 0.70 = $80

Worked Examples

Scenario	Final Value	Change	Calculation	Original Value
Salary after 15% raise	$63,250	+15%	$63,250 / 1.15	$55,000
Laptop after 20% discount	$680	-20%	$680 / 0.80	$850
Price after 8% tax	$54	+8%	$54 / 1.08	$50
Stock after 25% drop	$37.50	-25%	$37.50 / 0.75	$50

The Common Trap

If a $56 shirt is 30% off, do NOT calculate 30% of $56 ($16.80) and add it back to get $72.80. The 30% was applied to the original price, not the sale price. The correct original is $56 / 0.70 = $80. Verify: 30% of $80 = $24, and $80 - $24 = $56.

Use the Percentage Calculator to instantly reverse any percentage calculation. Enter the final value and percentage to find the original.

Real-World Applications of Percentage Change

Percentage change calculations appear in virtually every field. Here are the most common applications with the tools to handle each one.

Where You Use Percentage Change Every Day

Application	What You Calculate	Example	Calculator to Use
Inflation tracking	CPI percentage change year over year	3.2% means prices rose 3.2% from last year	Inflation Impact
Salary negotiations	Raise as percentage of current salary	$5,000 raise on $40,000 = 12.5% vs on $150,000 = 3.3%	Percentage Increase
Investment returns	Portfolio gain or loss as percentage	$10,000 to $11,500 = 15% annual return	Percentage Calculator
Sales and discounts	Price reduction as percentage of original	$120 jacket for $84 = 30% off	Percentage Decrease
Business metrics	Revenue, conversion, or churn rate changes	Email open rate 18% to 22% = 22.2% improvement	Percentage Increase
Real wage growth	Whether your raise beats inflation	4% raise with 3.2% inflation = 0.8% real gain	Salary vs Inflation

Is your salary keeping pace with inflation? Use the Salary vs Inflation Calculator to find out if your raise actually increased your purchasing power or just kept up with rising costs.

Practice Problems with Solutions

Test your understanding with these problems. Try solving each one before reading the solution.

Problems and Solutions

#	Problem	Working	Answer
1	House value: $320,000 to $348,800	$28,800 / $320,000 x 100	9% increase
2	Workforce: 1,250 to 1,075 employees	175 / 1,250 x 100	14% decrease
3	New salary $63,250 after 15% raise. Original?	$63,250 / 1.15	$55,000
4	Laptop costs $680 after 20% discount. Original?	$680 / 0.80	$850

Challenge Problems

#	Problem	Working	Answer
5	Investment: +12% year 1, -8% year 2. Start $5,000	$5,000 x 1.12 = $5,600; $5,600 x 0.92 = $5,152	3.04% gain (not 4%)
6	Price +25%, then -25% discount. Same as original?	$100 x 1.25 = $125; $125 x 0.75 = $93.75	No. 6.25% less than original

Key insight from problems 5 and 6: Percentage changes do not simply add or cancel. A gain followed by an equal loss always results in a net loss. This is why compound returns and sequential discounts require careful calculation, not mental shortcuts.

Verify all your answers with the Percentage Increase Calculator or Percentage Decrease Calculator.

Frequently Asked Questions

How do you calculate percentage increase?

Use the formula: ((New Value - Old Value) / Old Value) x 100. For example, if a product price rises from $80 to $100, the percentage increase is (($100 - $80) / $80) x 100 = 25%.

How do you calculate percentage decrease?

Use the formula: ((Old Value - New Value) / Old Value) x 100. For example, if a stock drops from $150 to $120, the percentage decrease is (($150 - $120) / $150) x 100 = 20%.

What is the difference between percentage change and percentage difference?

Percentage change measures the shift from one specific value to another and requires knowing which is the original (e.g., price went from $50 to $60, a 20% increase). Percentage difference compares two values without a clear original, using their average as the base (e.g., City A costs $50 and City B costs $60, a 18.2% difference).

Why is a 50% decrease followed by a 50% increase not break-even?

Because the base changes. If $100 drops 50% to $50, then increases 50%, you get $75, not $100. The 50% increase applies to the smaller base ($50), so you only gain $25. You actually need a 100% increase to recover from a 50% loss.

How do you reverse a percentage to find the original price?

Divide the final price by (1 + percentage/100) for increases, or (1 - percentage/100) for decreases. If a product costs $120 after a 20% markup, the original price was $120 / 1.20 = $100. If it costs $80 after a 20% discount, the original was $80 / 0.80 = $100.

What is a percentage point vs a percentage change?

A percentage point is the arithmetic difference between two percentages. A percentage change is the relative difference. If interest rates rise from 4% to 5%, that is a 1 percentage point increase but a 25% relative increase (1/4 x 100). Confusing the two is a common error in financial reporting.

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