Calculating percentages is one of the most useful everyday math skills. Whether you’re working out a discount, a grade, a tip, or a salary increase, the same few formulas keep showing up.
Below is a clear, step‑by‑step guide you can follow any time you need to work with percentages.
1. What Is a Percentage?
A percentage is a way of expressing a number as a fraction of 100.
- 50% means 50 out of 100 (i.e. 0.5)
- 25% means 25 out of 100 (i.e. 0.25)
- 100% means all of something
In math terms:
- 1% = 1/100 = 0.01
So to go from percent to decimal, divide by 100.
To go from decimal to percent, multiply by 100.
2. Basic Percentage Formula
The main formula you need:
Percentage = (Part ÷ Whole) × 100
Where:
- Part = the portion you are interested in
- Whole = the total amount
Example:
In a class of 30 students, 12 are left-handed. What percentage is that?
- Part = 12
- Whole = 30
So, 40% of the class is left-handed.
3. How to Find the Percentage of a Number
This is the classic “What is 20% of 80?” question.
Formula:
Part = (Percentage ÷ 100) × Whole
Example:
What is 20% of 80?
- Percentage = 20
- Whole = 80
So 20% of 80 is 16.
Quick shortcut:
To find 10% of a number, move the decimal one place left.
- 10% of 80 = 8
- 20% of 80 = 2 × 8 = 16
- 5% of 80 = half of 10% = 4
4. How to Find What Percentage One Number Is of Another
This is the “What percent is X of Y?” question.
Percentage = (Part ÷ Whole) × 100
Example:
What percentage is 15 of 60?
- Part = 15
- Whole = 60
So 15 is 25% of 60.
5. How to Calculate Percentage Increase and Decrease
Very useful for prices, salaries, and statistics.
5.1 Percentage Increase
Percentage Increase = (New − Old) ÷ Old × 100
Example:
Your salary goes from $2,000 to \$2,400. What is the percentage increase?
- Old = 2000
- New = 2400
- Change = 2400 − 2000 = 400
So your salary increased by 20%.
5.2 Percentage Decrease
Percentage Decrease = (Old − New) ÷ Old × 100
Example:
A product price goes from $50 down to \$35.
- Old = 50
- New = 35
- Change = 50 − 35 = 15
So the price decreased by 30%.
6. How to Calculate Discounts and Sale Prices
Shops often say “30% off” or “Save 15%”. You usually want to know the final price.
Step 1: Find the discount amount
Discount = Original Price × (Discount% ÷ 100)
Step 2: Subtract from original price
Sale Price = Original Price − Discount
Example:
A jacket costs $80 with 25% off.
- Discount = 80 × (25 ÷ 100) = 80 × 0.25 = 20
- Sale Price = 80 − 20 = $60
Shortcut method:
Multiply by the remaining percentage.
If it’s 25% off, you pay 75%:
\( 80 × 0.75 = 60 \)Sale Price = Original Price × 0.75
7. Common “Percentage of” Problems
7.1 Finding the Whole from the Part and Percentage
This is the “16 is 20% of what number?” question.
Whole = Part ÷ (Percentage ÷ 100)
Example:
16 is 20% of what?
So 16 is 20% of 80.
8. Everyday Examples of Percentages
Here are typical situations where you’ll apply the same formulas:
-
Tips at restaurants:
- 15% or 20% of the bill
-
Grades:
- Score ÷ Total × 100 = percentage grade
-
Interest rates:
- Interest = Principal × Rate × Time (where Rate is a percentage as a decimal)
-
Fitness and diet:
- “30% of calories from fat”, “60% of max heart rate”
Each one reduces to “part, whole, and a percentage.”
9. Quick Conversion Reminders
-
Percent → Decimal: divide by 100
- 7% → 0.07
- 125% → 1.25
-
Decimal → Percent: multiply by 100
- 0.3 → 30%
- 1.2 → 120%
10. Simple Practice Questions
Try these to check you understand:
- What is 15% of 200?
- 18 is what percentage of 90?
- A price increases from $40 to \$50. What is the percentage increase?
- A $120 item has 35% off. What is the sale price?
- 24 is 30% of what number?
(You can check your work using the formulas above.)
For more on basic math and everyday calculations, you may find these useful:
This is all you really need to calculate percentages confidently in daily life:
- Know the three variables: part, whole, percent
- Use the right formula for what you’re solving for
- Convert between percentages and decimals when needed