Percentage increase vs percentage decrease explained

Percentage increase and percentage decrease both compare a change to the original number. They answer questions like:

• How much did the price go up?
• How much did the bill go down?
• What percentage raise did I get?
• How large was the discount?
• Did traffic grow by 12% or fall by 12%?

The key word is original. Percentage change is normally measured against the starting value, not the final value.

The formula for percentage increase

Use percentage increase when the new number is larger than the original number:

percentage increase = (new value - original value) ÷ original value × 100

Example: a price rises from $50 to $65.

65 - 50 = 15
15 ÷ 50 × 100 = 30%

The price increased by 30%.

The formula for percentage decrease

Use percentage decrease when the new number is smaller than the original number:

percentage decrease = (original value - new value) ÷ original value × 100

Example: a price falls from $80 to $60.

80 - 60 = 20
20 ÷ 80 × 100 = 25%

The price decreased by 25%.

Both formulas follow the same idea:

change ÷ original value × 100

The only difference is how you find the change.

Increase example: salary raise

Suppose a salary changes from $40,000 to $44,000.

44,000 - 40,000 = 4,000
4,000 ÷ 40,000 × 100 = 10%

That is a 10% increase.

This example is simple because the raise is measured against the old salary. If someone says “I got a 10% raise,” they normally mean 10% of the salary before the raise.

Decrease example: sale discount

Suppose a bag was $120 and is now $90.

120 - 90 = 30
30 ÷ 120 × 100 = 25%

The price decreased by 25%.

If the sale label says “25% off,” the discount should be based on the original price.

Why a 50% increase and a 50% decrease do not cancel out

This is a common surprise.

Start with 100. Increase by 50%:

100 + 50% = 150

Now decrease 150 by 50%:

150 - 50% = 75

You do not return to 100. You end at 75.

That happens because the second percentage is based on a different original value. The increase used 100 as the base. The decrease used 150 as the base.

This matters when reading investment returns, price changes, discounts, traffic reports, and statistics.

Percentage change vs percentage points

Percentage change and percentage points are not the same thing.

If an interest rate moves from 4% to 5%, it rose by 1 percentage point.

But the relative percentage increase is:

1 ÷ 4 × 100 = 25%

So it rose by 1 percentage point, or by 25% relative to the old rate.

When the values are already percentages, be careful with wording.

Quick table of examples

Original	New	Change	Result
100	120	+20	20% increase
100	80	-20	20% decrease
50	65	+15	30% increase
80	60	-20	25% decrease
200	250	+50	25% increase
200	150	-50	25% decrease

The arithmetic is small, but the wording can change the answer.

Common mistakes to avoid

Using the new value as the base

If a price goes from $80 to $100, the increase is $20. The base is $80:

20 ÷ 80 × 100 = 25%

If you divide by $100 instead, you get 20%, which answers a different question.

Ignoring negative change

If your calculation gives a negative number, it usually means the new value is lower than the original value. You can say “20% decrease” instead of “-20% increase” when writing for normal readers.

Comparing two percentages incorrectly

A move from 30% to 40% is +10 percentage points, not simply “10% more.” Relative to 30%, it is a 33.3% increase.

When to use a calculator

Use a calculator when the numbers are not clean, when decimals are involved, or when you need to compare several changes quickly.

The ToolSnap percentage calculator can help with increase, decrease, and “what percent of” questions without making you rewrite the formula each time.

Simple rule to remember

Percentage increase and decrease both ask:

How large is the change compared with the original value?

Find the change, divide it by the original value, and multiply by 100.