How to Calculate Percentages: Simple Methods for Everyday Use

A percentage is simply a way of expressing a number as a fraction of 100. The word itself comes from the Latin 'per centum' — per hundred. When you see 25%, it means 25 out of every 100, or the fraction 25/100, which simplifies to 0.25 as a decimal. This single conversion — percentage to decimal — unlocks most percentage calculations.

The Three Core Percentage Problems

Almost every percentage question falls into one of three types:

• What is X% of Y? (finding the part)
• X is what percentage of Y? (finding the percentage)
• X is Y% of what? (finding the whole)

Type 1: What Is X% of Y?

Convert the percentage to a decimal and multiply. What is 30% of 250? Convert 30% to 0.30, then multiply: 0.30 × 250 = 75. So 30% of 250 is 75.

Real-world example: A jacket costs $80 and is on sale for 35% off. The discount is 0.35 × 80 = $28. You pay $80 − $28 = $52.

Type 2: X Is What Percentage of Y?

Divide the part by the whole, then multiply by 100. You scored 42 out of 60 on a test. What percentage is that? (42 ÷ 60) × 100 = 70%.

Real-world example: Your monthly grocery bill was $340 last month and $290 this month. What percentage decrease is that? Change = 340 − 290 = 50. Percentage decrease = (50 ÷ 340) × 100 = 14.7%.

Type 3: X Is Y% of What?

Divide the part by the percentage (as a decimal). After a 20% discount, a phone costs $480. What was the original price? 480 ÷ 0.80 = $600.

Note: a common mistake is to add 20% back to $480 ($480 × 1.20 = $576). This is wrong because 20% of $600 ≠ 20% of $480. Always divide by the decimal complement.

Percentage Increase and Decrease

Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. If the result is positive, it is an increase; if negative, it is a decrease.

Example: A house was worth $250,000 five years ago and is worth $310,000 today. Percentage increase = ((310,000 − 250,000) ÷ 250,000) × 100 = (60,000 ÷ 250,000) × 100 = 24%.

Mental Math Shortcuts

• 10% of any number: move the decimal point one place to the left (10% of 350 = 35)
• 5% = half of 10% (5% of 350 = 17.5)
• 25% = divide by 4 (25% of 360 = 90)
• 50% = divide by 2
• 1% = move decimal two places left (1% of 4,500 = 45)
• Combine: 15% = 10% + 5%; 17.5% = 10% + 5% + 2.5%

VAT and Sales Tax

To add a percentage tax to a price, multiply by (1 + tax rate). A $200 item with 15% VAT: 200 × 1.15 = $230. To find the pre-tax price from a tax-inclusive price, divide by (1 + tax rate): $230 ÷ 1.15 = $200. This is different from simply subtracting 15% of $230 ($230 × 0.85 = $195.50), which would be wrong.

Use Our Percentage Calculator

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