How do you calculate a percentage of a number?

Multiply the number by the percentage, then divide by 100. For example, 25% of 80 = 80 × 25 ÷ 100 = 20. Shortcut: move the decimal in the percentage two places left and multiply. 25% becomes 0.25, so 0.25 × 80 = 20.

How do you calculate percentage increase?

Percentage increase = ((New Value - Old Value) ÷ Old Value) × 100. For example, if a price goes from $80 to $100: ((100-80) ÷ 80) × 100 = 25% increase.

What is the easiest way to calculate percentages mentally?

Use these shortcuts: 10% = move decimal one place left. 20% = double the 10%. 25% = divide by 4. 50% = divide by 2. 1% = move decimal two places left. For 15%, calculate 10% + 5% (half of 10%).

📐 Math Guide

How to Calculate Percentage: Formulas, Shortcuts & Real Examples

Updated April 2026 · 5 min read

To find a percentage of a number: multiply the number by the percentage and divide by 100. Example: 25% of 80 = 80 × 25 ÷ 100 = 20. For percentage change: ((New − Old) ÷ Old) × 100.

The Three Fundamental Percentage Formulas

Every percentage question falls into one of three categories. Master these three formulas and you can solve any percentage problem:

What is X% of Y? → Y × X ÷ 100

Example: 15% of 200 = 200 × 15 ÷ 100 = 30

X is what % of Y? → (X ÷ Y) × 100

Example: 45 is what % of 180? = (45 ÷ 180) × 100 = 25%

% Change = ((New − Old) ÷ Old) × 100

Example: Price from $80 to $100 = ((100−80) ÷ 80) × 100 = +25%

Mental Math Shortcuts for Common Percentages

You don't always need a calculator. These mental math tricks let you estimate percentages instantly:

Percentage	Mental Shortcut	Example (of $160)
1%	Move decimal 2 places left	$1.60
10%	Move decimal 1 place left	$16.00
15%	10% + half of 10%	$24.00
20%	10% × 2	$32.00
25%	Divide by 4	$40.00
33%	Divide by 3	$53.33
50%	Divide by 2	$80.00
75%	Subtract 25% from whole	$120.00

Real-World Percentage Applications

Tipping: 20% of an $85 dinner bill — 10% is $8.50, double it = $17.00 tip. Discounts: 30% off a $79.99 item — 10% is $8, × 3 = $24 off, final price ≈ $56. Tax: 8.5% sales tax on $200 — 10% is $20, minus 1.5% ($3) = $17 tax. Grades: Scored 42 out of 50 — (42 ÷ 50) × 100 = 84%.

Common Percentage Mistakes to Avoid

Percentage increase ≠ percentage decrease. If a $100 item increases by 50% it becomes $150. But a 50% decrease from $150 is $75, not back to $100. This is because the base number changes. A 50% increase followed by a 50% decrease always results in a 25% net loss.

Double discounts are not additive. "20% off + extra 10% off" is NOT 30% off. It is 20% off first ($100 → $80), then 10% off that ($80 → $72). Effective discount: 28%, not 30%.

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The Three Basic Percentage Formulas Everyone Should Know

Every percentage problem falls into one of three patterns: finding the percentage, finding the part, or finding the whole.

1. What is X% of Y? Formula: (X/100) × Y. Example: What is 15% of 200? → (15/100) × 200 = 30. Use for: tips, discounts, tax calculations.

2. X is what % of Y? Formula: (X/Y) × 100. Example: 45 is what % of 180? → (45/180) × 100 = 25%. Use for: grades, completion rates, market share.

3. X is Y% of what? Formula: X / (Y/100). Example: 30 is 20% of what? → 30 / 0.20 = 150. Use for: finding original prices from sale prices, reverse tax calculations.

These three formulas handle 95% of real-world percentage problems. The trick is identifying which pattern your question matches. Use our Percentage Calculator for instant answers to any percentage question.

Percentage Increase and Decrease: The Formula That Trips Everyone Up

Percentage change = ((New Value − Old Value) / Old Value) × 100. A common mistake: a 50% increase followed by a 50% decrease does NOT return to the original number.

Example: $100 increases by 50% → $150. Then $150 decreases by 50% → $75. You lost $25! This asymmetry is why stock market losses hurt more than gains help. A 50% loss requires a 100% gain just to break even. A 33% loss requires a 50% gain. This is mathematically proven and explains why protecting against losses (diversification, stop-losses) is more important than chasing gains. Real-world applications: if your rent goes from $1,500 to $1,800, the increase is ($1,800−$1,500)/$1,500 × 100 = 20%. If your salary goes from $60,000 to $65,000, that is an 8.3% raise. Always divide by the OLD value, not the new one — this is the most common error in percentage calculations.

The Three Essential Percentage Formulas

Every percentage problem falls into one of three categories. Master these three formulas and you can solve any percentage question instantly.

1. Find X% of Y: Multiply Y by X/100. Example: What is 15% of 200? → 200 × 0.15 = 30. Real-world use: calculating tips (15% of $48 bill = $7.20), sale discounts (30% off $80 = $24 off), and tax amounts.

2. X is what percent of Y? Divide X by Y, then multiply by 100. Example: 45 is what % of 180? → (45 ÷ 180) × 100 = 25%. Real-world use: calculating test scores (got 42 out of 50 = 84%), completion rates, and market share.

3. Percentage change: (New − Old) ÷ Old × 100. Example: Price went from $80 to $100 → (100-80) ÷ 80 × 100 = 25% increase. Real-world use: salary raises, stock returns, inflation, and weight change.

A common mistake: percentage increase and decrease are NOT symmetric. A 50% increase followed by a 50% decrease does NOT return to the original value. $100 + 50% = $150. $150 - 50% = $75. You lost $25! This is why investment losses hurt more than gains help — a 50% drop requires a 100% gain to recover. Use our Percentage Calculator to solve any percentage problem instantly.

Percentages in Everyday Life: Tips, Taxes, and Discounts

Quick mental math tricks for common percentage calculations can save time every day.

Tipping: For 20%, move the decimal one place left (that gives 10%) and double it. $47.50 bill → 10% = $4.75 → 20% = $9.50. For 15%, calculate 10% and add half of that: $4.75 + $2.38 = $7.13.

Discounts: For 25% off, divide by 4 and subtract. $80 item at 25% off: $80 ÷ 4 = $20 off → pay $60. For 33% off, divide by 3: $90 ÷ 3 = $30 off → pay $60.

Sales tax: Multiply by the tax rate. In an 8% tax state: $50 purchase × 1.08 = $54. Quick shortcut: calculate 10% ($5) and subtract 20% of that ($1) = $4 tax → $54 total.

Grade to percentage: Divide score by total and multiply by 100. Got 87 out of 100 on a test = 87%. Got 42 out of 50 = 84%. Got 28 out of 35 = 80%.

Salary increase: Offered a 4% raise on $65,000? $65,000 × 0.04 = $2,600/year increase → new salary $67,600 → extra $217/month before taxes.