How to Calculate Percentage
Calculate percentages with simple formulas. Learn how to find a percentage of a number, percentage increase, percentage decrease, percentage change, and reverse percentages.
How to Calculate Percentage
A percentage is a way to describe a number out of 100.
The basic formula is:
Percentage = (Part ÷ Whole) × 100
For example, if 18 students out of 30 passed a test:
(18 ÷ 30) × 100 = 60%
So 18 out of 30 is 60%.
The same idea works for grades, discounts, taxes, tips, survey results, price changes, and many everyday calculations.
What Is a Percentage?
The word percent means per hundred.
So:
1% = 1 out of 100
25% = 25 out of 100
50% = 50 out of 100
100% = 100 out of 100
Percentages are useful because they put values on the same scale.
For example:
- 8 out of 10 = 80%
- 40 out of 50 = 80%
- 120 out of 150 = 80%
The numbers are different, but the percentage is the same.
Percentage Formula
To calculate what percent one number is of another, use:
Percentage = (Part ÷ Whole) × 100
Where:
Part= the amount you are comparingWhole= the total amount
Example: 24 Out of 80
Calculate:
What percentage is 24 out of 80?
Use the formula:
(24 ÷ 80) × 100
First divide:
24 ÷ 80 = 0.3
Then multiply by 100:
0.3 × 100 = 30
So:
24 is 30% of 80.
How to Find a Percentage of a Number
To find a percentage of a number, convert the percentage to a decimal and multiply.
Use:
Amount = Number × (Percentage ÷ 100)
Example: What Is 20% of 75?
Convert 20% to a decimal:
20 ÷ 100 = 0.20
Multiply:
75 × 0.20 = 15
So:
20% of 75 is 15.
Example: What Is 12% of 250?
Convert:
12 ÷ 100 = 0.12
Multiply:
250 × 0.12 = 30
So:
12% of 250 is 30.
How to Convert a Percentage to a Decimal
To convert a percentage to a decimal, divide by 100.
Percentage ÷ 100 = Decimal
Examples:
| Percentage | Decimal |
|---|---|
| 5% | 0.05 |
| 10% | 0.10 |
| 25% | 0.25 |
| 50% | 0.50 |
| 75% | 0.75 |
| 100% | 1.00 |
This is why finding 25% of a number is the same as multiplying by 0.25.
How to Convert a Decimal to a Percentage
To convert a decimal to a percentage, multiply by 100.
Decimal × 100 = Percentage
Examples:
| Decimal | Percentage |
|---|---|
| 0.05 | 5% |
| 0.10 | 10% |
| 0.25 | 25% |
| 0.50 | 50% |
| 0.75 | 75% |
| 1.00 | 100% |
For example:
0.375 × 100 = 37.5%
So the decimal 0.375 is equal to 37.5%.
How to Calculate Percentage Increase
Percentage increase shows how much a value went up compared with the starting value.
Use:
Percentage Increase = ((New Value - Old Value) ÷ Old Value) × 100
Example: Price Increases From 40 to 50
Find the difference:
50 - 40 = 10
Divide by the old value:
10 ÷ 40 = 0.25
Multiply by 100:
0.25 × 100 = 25%
So the value increased by:
25%
The old value matters because the increase is measured relative to where you started.
How to Calculate Percentage Decrease
Percentage decrease shows how much a value went down compared with the starting value.
Use:
Percentage Decrease = ((Old Value - New Value) ÷ Old Value) × 100
Example: Price Drops From 80 to 60
Find the decrease:
80 - 60 = 20
Divide by the old value:
20 ÷ 80 = 0.25
Multiply by 100:
0.25 × 100 = 25%
So the value decreased by:
25%
Percentage Change Formula
Percentage change can describe either an increase or a decrease.
Use:
Percentage Change = ((New Value - Old Value) ÷ Old Value) × 100
If the result is positive, the value increased.
If the result is negative, the value decreased.
Example: 120 to 150
((150 - 120) ÷ 120) × 100
(30 ÷ 120) × 100 = 25%
The value increased by 25%.
Example: 150 to 120
((120 - 150) ÷ 150) × 100
(-30 ÷ 150) × 100 = -20%
The value decreased by 20%.
Notice that going from 120 to 150 is a 25% increase, but going from 150 back to 120 is a 20% decrease. The starting value changes the percentage.
How to Calculate a Discount Percentage
To find the discount percentage, compare the discount amount with the original price.
Use:
Discount Percentage = (Discount Amount ÷ Original Price) × 100
Example: $15 Off a $60 Item
(15 ÷ 60) × 100 = 25%
So a $15 discount on a $60 item is a:
25% discount
To find the sale price:
Original Price - Discount Amount = Sale Price
60 - 15 = 45
The sale price is $45.
How to Calculate Price After a Percentage Discount
To apply a discount, convert the discount percentage to a decimal and subtract it from 1.
Use:
Sale Price = Original Price × (1 - Discount Rate)
Example: 30% Off $120
Convert 30% to a decimal:
30 ÷ 100 = 0.30
Subtract from 1:
1 - 0.30 = 0.70
Multiply:
120 × 0.70 = 84
So the sale price is:
$84
You can also calculate the discount amount first:
120 × 0.30 = 36
Then subtract:
120 - 36 = 84
Both methods give the same answer.
How to Calculate Tip Percentage
To calculate a tip, multiply the bill amount by the tip percentage as a decimal.
Use:
Tip Amount = Bill × (Tip Percentage ÷ 100)
Example: 18% Tip on $45
Convert:
18 ÷ 100 = 0.18
Multiply:
45 × 0.18 = 8.10
So the tip is:
$8.10
The total bill is:
45 + 8.10 = 53.10
So the final total is $53.10.
How to Calculate Tax Percentage
Sales tax works much like a tip or markup.
Use:
Tax Amount = Price × (Tax Rate ÷ 100)
Example: 7.5% Tax on $80
Convert:
7.5 ÷ 100 = 0.075
Multiply:
80 × 0.075 = 6
So the tax is:
$6
The total price is:
80 + 6 = 86
So the total after tax is $86.
How to Calculate Reverse Percentage
Reverse percentage is useful when you know the final value and want to find the original value.
Use:
Original Value = Final Value ÷ (1 + Percentage Increase)
for an increase, and:
Original Value = Final Value ÷ (1 - Percentage Decrease)
for a decrease.
Convert the percentage to a decimal before using the formula.
Example: Final Price After 20% Tax Is $120
The final value is 120.
The increase rate is:
20% = 0.20
Use:
Original Value = 120 ÷ (1 + 0.20)
120 ÷ 1.20 = 100
So the original value was:
$100
Example: Sale Price After 25% Off Is $90
The final value is 90.
The discount rate is:
25% = 0.25
Use:
Original Value = 90 ÷ (1 - 0.25)
90 ÷ 0.75 = 120
So the original price was:
$120
Percentage Points vs Percentage
Percentage points and percent change are not the same thing.
Suppose a rate increases from 40% to 50%.
The percentage point change is:
50% - 40% = 10 percentage points
But the percent increase is:
((50 - 40) ÷ 40) × 100 = 25%
So the rate increased by 10 percentage points, which is a 25% increase relative to the starting rate.
This distinction matters in statistics, finance, polling, grades, and interest rates.
Quick Percentage Reference
| Task | Formula |
|---|---|
| Find percentage | (Part ÷ Whole) × 100 |
| Find percentage of a number | Number × (Percentage ÷ 100) |
| Percentage increase | ((New - Old) ÷ Old) × 100 |
| Percentage decrease | ((Old - New) ÷ Old) × 100 |
| Percentage change | ((New - Old) ÷ Old) × 100 |
| Discount percentage | (Discount Amount ÷ Original Price) × 100 |
| Sale price after discount | Original Price × (1 - Discount Rate) |
| Original before an increase | Final Value ÷ (1 + Increase Rate) |
| Original before a decrease | Final Value ÷ (1 - Decrease Rate) |
Remember to convert percentages to decimals when multiplying or dividing by a rate.
Common Percentage Mistakes
Dividing by the Wrong Number
For percentage change, always divide by the original value.
If a price goes from 50 to 75:
((75 - 50) ÷ 50) × 100 = 50%
Do not divide by the new value unless the question specifically asks for a different comparison.
Confusing 50% With 0.50
When multiplying, use the decimal form.
50% = 0.50
So 50% of 80 is:
80 × 0.50 = 40
Treating Percentage Increase and Decrease as Reversible
An increase of 20% followed by a decrease of 20% does not return to the original value.
For example:
100 increased by 20% = 120
120 decreased by 20% = 96
The decrease is applied to the new larger number.
Mixing Percentage Points and Percent Change
Going from 4% to 5% is an increase of 1 percentage point.
But relative to 4%, it is:
((5 - 4) ÷ 4) × 100 = 25%
The wording matters.
Rounding Too Early
Keep a few extra decimal places during the calculation and round the final answer.
This is especially useful for tax, interest, statistics, grades, and financial calculations.
Frequently Asked Questions
How do you calculate a percentage?
Use:
Percentage = (Part ÷ Whole) × 100
For example, 18 out of 30 is:
(18 ÷ 30) × 100 = 60%
How do you find 10% of a number?
Move the decimal one place to the left.
For example:
10% of 80 = 8
10% of 250 = 25
10% of 43 = 4.3
This works because 10% is the same as 0.10.
How do you find 20% of a number?
Convert 20% to 0.20 and multiply.
For example:
150 × 0.20 = 30
So 20% of 150 is 30.
What is 15% of 200?
Convert:
15% = 0.15
Multiply:
200 × 0.15 = 30
So:
15% of 200 is 30.
How do you calculate percentage increase?
Use:
((New Value - Old Value) ÷ Old Value) × 100
For example, increasing from 40 to 50 is:
((50 - 40) ÷ 40) × 100 = 25%
How do you calculate percentage decrease?
Use:
((Old Value - New Value) ÷ Old Value) × 100
For example, decreasing from 80 to 60 is:
((80 - 60) ÷ 80) × 100 = 25%
What is the difference between percent and percentage points?
Percentage points describe the direct difference between two percentages.
Percent change describes the relative change compared with the starting value.
For example, going from 40% to 50% is a 10 percentage point increase, but a 25% relative increase.
How do you calculate a discount percentage?
Use:
Discount Percentage = (Discount Amount ÷ Original Price) × 100
For example, $15 off a $60 item is:
(15 ÷ 60) × 100 = 25%
How do you reverse a percentage?
If a value increased by a percentage, divide the final value by 1 + rate.
If a value decreased by a percentage, divide the final value by 1 - rate.
For example, if $90 is the price after a 25% discount:
90 ÷ 0.75 = 120
So the original price was $120.
Related Tool and Source
If you need to combine several percentage values, use the Average Percentage Calculator. For more practice with percent problems and equivalent forms, Khan Academy’s percentages unit is a useful outside reference.
Final Thoughts
Most percentage calculations come back to one idea:
Percentage = (Part ÷ Whole) × 100
Once you understand that, the other formulas become easier to recognize.
To find a percentage of a number, convert the percentage to a decimal and multiply. To calculate increase or decrease, compare the change with the original value. To reverse a percentage, divide by the remaining or increased rate.
The main habit is to identify the part, the whole, and the starting value before calculating. That prevents most percentage mistakes.