Percent Formulas Guide

Comprehensive reference of percentage calculation formulas with examples and explanations. Learn how to calculate any percentage problem manually.

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All Major Formulas

Complete collection of percentage calculation methods in one place

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Step-by-Step Examples

Practical examples showing manual calculation process

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Calculator Links

Direct access to relevant percentage calculators

ℹ️ Why Learn Manual Calculation?
Understanding the underlying formulas helps you verify calculator results, solve problems without tools, and build strong mathematical foundations for financial and business decisions.

Percentage Calculation Formulas

Calculation Type	Formula	Example
Percentage of a Number	`result = (number × percentage) / 100`	What is 15% of 200? result = (200 × 15) / 100 = 30
Percentage as Proportion	`percentage = (part / whole) × 100`	What percent is 45 of 300? percentage = (45 / 300) × 100 = 15%
Percentage Increase	`increase = ((new - original) / original) × 100`	From 80 to 100: increase = ((100 - 80) / 80) × 100 = 25%
Percentage Decrease	`decrease = ((original - new) / original) × 100`	From 150 to 120: decrease = ((150 - 120) / 150) × 100 = 20%
Reverse Percentage	`original = (part × 100) / percentage`	75 is 25% of what number? original = (75 × 100) / 25 = 300
Compound Interest	`A = P(1 + r/n)^(nt)`	$1,000 at 5% annual interest, compounded yearly for 3 years: A = 1000(1 + 0.05/1)^(1×3) = $1,157.63
VAT/NDС Calculation	`VAT = amount × (rate / 100)`	VAT at 20% on $500: VAT = 500 × (20 / 100) = $100

Step-by-Step Calculation Examples

Calculating a Discount

Problem: A $120 item has a 25% discount. What is the final price?

Calculate discount amount:

discount = (120 × 25) / 100 = 30

Subtract from original price:

final price = 120 - 30 = 90

Alternative method:

final price = 120 × (100 - 25)/100 = 120 × 0.75 = 90

Final price after 25% discount: $90

Finding Original Value

Problem: After a 15% increase, the price is $115. What was the original price?

Understand the relationship:

new price = original + 15% of original = 115% of original

Set up the equation:

115 = original × 1.15

Solve for original:

original = 115 / 1.15 = 100

Original price before 15% increase: $100

Percentage Calculation FAQ

How do I calculate percentage without a calculator?

To calculate percentages manually:

1. For 10%: Move decimal point one place left
2. For 5%: Take half of 10%
3. For 1%: Move decimal point two places left
4. Combine these to calculate any percentage

Example: 17% of 200
- 10% = 20
- 5% = 10
- 1% = 2
- 17% = 10% + 5% + 2×1% = 20 + 10 + 4 = 34

What is the difference between percentage and percentage points?

Percentage points measure absolute change, while percentage measures relative change.

Example: If interest rate rises from 5% to 6%:
- Change in percentage points: 1 pp (6% - 5%)
- Percentage increase: (6-5)/5 × 100 = 20%

Confusing these can lead to significant errors in financial and statistical analysis.

How do I calculate percentage change between two numbers?

Use this formula:

Percentage Change = ((New Value - Original Value) / Original Value) × 100

If the result is positive, it's an increase. If negative, it's a decrease.

Example: From 80 to 100
((100 - 80) / 80) × 100 = 25% increase

Example: From 150 to 120
((120 - 150) / 150) × 100 = -20% (20% decrease)

When should I use simple vs compound interest formulas?

Use simple interest when:
- Interest is not reinvested
- Short-term calculations (less than 1 year)
- Formula: A = P(1 + rt)

Use compound interest when:
- Interest is added to principal periodically
- Long-term investments or loans
- Formula: A = P(1 + r/n)^(nt)

Most financial products (savings accounts, mortgages) use compound interest, while some short-term loans use simple interest.

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