April 2, 2026•7 min read•By Marcus Chen

How to Calculate Percentages: Every Formula You Actually Need

Percentage math formulas, pie charts, and calculation examples

Six percentage formulas cover 99% of real-world math problems. Here's when to use each one, with worked examples and mental math shortcuts.

The 6 Core Percentage Formulas

1. Basic percentage

Percentage = (Part ÷ Whole) × 100

Use when: What percent is X of Y?

Example: 30 is what percent of 150?

Part = 30, Whole = 150
(30 ÷ 150) × 100
0.2 × 100 = 20%

Common uses: Grading, statistics, proportionsUse Percentage of Number Calculator →

2. Percentage of a number

Result = (Percentage ÷ 100) × Whole

Use when: What is X% of Y?

Example: What is 15% of $60?

Percentage = 15, Whole = 60
(15 ÷ 100) × 60
0.15 × 60 = $9

Common uses: Tips, discounts, taxesUse Percentage of Number Calculator →

3. Percentage change

Change (%) = ((New − Old) ÷ Old) × 100

Use when: How much did X change from Y to Z?

Example: Price went from $80 to $100. What % increase?

New = 100, Old = 80
((100 − 80) ÷ 80) × 100
(20 ÷ 80) × 100 = 25%

Common uses: Price changes, growth rates, statisticsUse Percentage Change Calculator →

4. Percentage increase

New Value = Old Value × (1 + Percentage ÷ 100)

Use when: What is Y after an X% increase?

Example: What is $50 after a 30% increase?

Old = 50, Percentage = 30
50 × (1 + 30 ÷ 100)
50 × 1.30 = $65

Common uses: Salary raises, price hikes, growth projectionsUse Percentage Increase Calculator →

5. Percentage decrease (discount)

New Value = Old Value × (1 − Percentage ÷ 100)

Use when: What is Y after an X% discount?

Example: 30% off a $120 item?

Old = 120, Percentage = 30
120 × (1 − 30 ÷ 100)
120 × 0.70 = $84

Common uses: Sale prices, tax reductions, depreciationUse Discount Calculator →

6. Reverse percentage (find the original)

Original = New Value ÷ (1 ± Percentage ÷ 100)

Use when: What was Y before an X% change?

Example: Price is $120 after a 20% increase. What was the original?

New = 120, Percentage increase = 20%
120 ÷ (1 + 20 ÷ 100)
120 ÷ 1.20 = $100

Common uses: Pre-tax prices, original values before markupUse Percentage Change Calculator →

Mental Math Shortcuts

For quick percentage estimates without a calculator:

10%: Move the decimal one place left. 10% of 340 = 34.
5%: Halve the 10% result. 5% of 340 = 17.
20%: Double the 10% result. 20% of 340 = 68.
25%: Divide by 4. 25% of 340 = 85.
15% tip: 10% + half of 10%. On $45: $4.50 + $2.25 = $6.75.
Quick discount check: “30% off $70” → 70 × 0.7 = $49. Think of it as: you pay (100 − discount)%.

QuickPercent Calculators

Skip the formula and get instant answers:

Percentage Of Percentage Change Tip Calculator Discount Markup

Frequently Asked Questions

What is the basic percentage formula?+

The basic percentage formula is: Percentage = (Part ÷ Whole) × 100. To find what percent 30 is of 150: (30 ÷ 150) × 100 = 20%. This formula handles the most common percentage question — 'X is what percent of Y?'

How do you calculate percentage change?+

Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. If a price went from $80 to $100: ((100 − 80) ÷ 80) × 100 = 25% increase. If it went from $100 to $80: ((80 − 100) ÷ 100) × 100 = −20% decrease. The sign tells you increase (+) or decrease (−).

How do you calculate a percentage of a number?+

To find X% of Y: multiply Y by (X ÷ 100). So 15% of 200 = 200 × (15 ÷ 100) = 200 × 0.15 = 30. Mental math shortcut: 10% is always one decimal place left (10% of 240 = 24), then scale up or down from there.

How do you calculate a tip?+

Multiply your bill by the tip percentage as a decimal. For 20% on a $65 bill: $65 × 0.20 = $13. Mental math: find 10% ($6.50), then double it for 20% ($13). For 15%: find 10% ($6.50) and add half ($3.25) = $9.75.

What's the difference between percentage increase and markup?+

Percentage increase uses the original value as the base. Markup uses cost as the base to set a selling price. If you buy something for $50 and sell it for $75, the markup is 50% (($75 − $50) ÷ $50 × 100). But the percentage increase from cost to price is also 50%. The formulas are the same — the difference is context.

How do you reverse a percentage (find the original before a percent change)?+

Divide by (1 + the percentage as a decimal) for increases, or (1 − the percentage as a decimal) for decreases. If a price is $120 after a 20% increase, the original was $120 ÷ 1.20 = $100. If $80 after a 20% decrease: $80 ÷ 0.80 = $100.