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

( \text{Percentage} = (12 ÷ 30) × 100 = 40% )

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

( \text{Part} = (20 ÷ 100) × 80 = 0.2 × 80 = 16 )

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

( \text{Percentage} = (15 ÷ 60) × 100 = 0.25 × 100 = 25% )

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

( \text{Percentage Increase} = (400 ÷ 2000) × 100 = 0.2 × 100 = 20% )

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

( \text{Percentage Decrease} = (15 ÷ 50) × 100 = 0.3 × 100 = 30% )

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.

  1. Discount = 80 × (25 ÷ 100) = 80 × 0.25 = 20
  2. Sale Price = 80 − 20 = $60

Shortcut method:
Multiply by the remaining percentage.

If it’s 25% off, you pay 75%:

Sale Price = Original Price × 0.75

( 80 × 0.75 = 60 )

# 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?

( \text{Whole} = 16 ÷ (20 ÷ 100) = 16 ÷ 0.2 = 80 )

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:

  1. What is 15% of 200?
  2. 18 is what percentage of 90?
  3. A price increases from $40 to $50. What is the percentage increase?
  4. A $120 item has 35% off. What is the sale price?
  5. 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