Keep this percentage formulas cheat sheet handy for quick reference. Whether you're a student, professional, or just need to calculate percentages occasionally, this comprehensive guide has all the formulas you need in one place.
Quick Reference Table
| Calculation Type | Formula | Example |
|---|---|---|
| Find X% of Y | Y × (X/100) | 20% of 150 = 150 × 0.20 = 30 |
| What % is X of Y | (X/Y) × 100 | 30 is what % of 150? (30/150) × 100 = 20% |
| % Increase | ((New - Old) / Old) × 100 | 100 to 150: ((150-100)/100) × 100 = 50% |
| % Decrease | ((Old - New) / Old) × 100 | 150 to 100: ((150-100)/150) × 100 = 33.33% |
| Original after X% increase | New / (1 + X/100) | After 25% increase = 125: 125/1.25 = 100 |
| Original after X% decrease | New / (1 - X/100) | After 20% decrease = 80: 80/0.80 = 100 |
Basic Percentage Formulas
1. Finding a Percentage of a Number
Result = Number × (Percentage / 100)
Example: What is 25% of 80?
Result = 80 × (25/100) = 80 × 0.25 = 20
Result = 80 × (25/100) = 80 × 0.25 = 20
2. Finding What Percentage One Number is of Another
Percentage = (Part / Whole) × 100
Example: What percentage is 15 of 60?
Percentage = (15/60) × 100 = 0.25 × 100 = 25%
Percentage = (15/60) × 100 = 0.25 × 100 = 25%
3. Finding the Whole from a Percentage
Whole = Part / (Percentage / 100)
Example: If 30 is 20% of a number, what is the number?
Whole = 30 / (20/100) = 30 / 0.20 = 150
Whole = 30 / (20/100) = 30 / 0.20 = 150
Percentage Change Formulas
4. Percentage Increase
% Increase = ((New Value - Original Value) / Original Value) × 100
Example: Price increased from $50 to $65
% Increase = ((65 - 50) / 50) × 100 = (15/50) × 100 = 30%
% Increase = ((65 - 50) / 50) × 100 = (15/50) × 100 = 30%
5. Percentage Decrease
% Decrease = ((Original Value - New Value) / Original Value) × 100
Example: Stock price fell from $100 to $75
% Decrease = ((100 - 75) / 100) × 100 = (25/100) × 100 = 25%
% Decrease = ((100 - 75) / 100) × 100 = (25/100) × 100 = 25%
6. Value After Percentage Change
New Value = Original × (1 ± Percentage/100)
Increase: $100 + 15% = 100 × 1.15 = $115
Decrease: $100 - 15% = 100 × 0.85 = $85
Decrease: $100 - 15% = 100 × 0.85 = $85
Business & Finance Percentage Formulas
7. Profit Margin
Profit Margin % = (Profit / Revenue) × 100
Example: Profit = $20,000, Revenue = $100,000
Profit Margin = (20,000 / 100,000) × 100 = 20%
Profit Margin = (20,000 / 100,000) × 100 = 20%
8. Markup Percentage
Markup % = ((Selling Price - Cost) / Cost) × 100
Example: Cost = $50, Selling Price = $75
Markup = ((75 - 50) / 50) × 100 = 50%
Markup = ((75 - 50) / 50) × 100 = 50%
9. Return on Investment (ROI)
ROI % = ((Gain - Cost) / Cost) × 100
Example: Invested $1,000, Returned $1,300
ROI = ((1,300 - 1,000) / 1,000) × 100 = 30%
ROI = ((1,300 - 1,000) / 1,000) × 100 = 30%
10. Commission Calculation
Commission = Sales × (Commission Rate / 100)
Example: $50,000 sales at 5% commission
Commission = 50,000 × 0.05 = $2,500
Commission = 50,000 × 0.05 = $2,500
Advanced Percentage Formulas
11. Compound Percentage Growth
Final = Initial × (1 + Rate/100)^Periods
Example: $1,000 at 5% for 3 years
Final = 1,000 × (1.05)³ = $1,157.63
Final = 1,000 × (1.05)³ = $1,157.63
12. Percentage Error
% Error = |Actual - Expected| / |Expected| × 100
Example: Expected 100, Actual 95
% Error = |95 - 100| / |100| × 100 = 5%
% Error = |95 - 100| / |100| × 100 = 5%
13. Weighted Average Percentage
Weighted Avg = Σ(Value × Weight) / Σ(Weight)
Example: Test 1: 80% (weight 30%), Test 2: 90% (weight 70%)
Average = (80×0.3 + 90×0.7) / 1 = 87%
Average = (80×0.3 + 90×0.7) / 1 = 87%
14. Percentage Point Difference
PP Difference = New Percentage - Old Percentage
Example: Interest rate: 3% → 5%
Difference = 5% - 3% = 2 percentage points
Difference = 5% - 3% = 2 percentage points
Special Cases & Tips
⚡ Quick Mental Math Tricks
- 10%: Move decimal one place left (e.g., 10% of 54 = 5.4)
- 5%: Half of 10% (e.g., 5% of 54 = 2.7)
- 25%: Divide by 4 (e.g., 25% of 80 = 20)
- 50%: Divide by 2 (e.g., 50% of 80 = 40)
- 1%: Move decimal two places left (e.g., 1% of 300 = 3)
Converting Between Forms
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.10 | 1/10 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.3333 | 1/3 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
Common Formula Mistakes to Avoid
- Wrong base for percentage change: Always use the original value as the denominator
- Forgetting to multiply by 100: Remember to convert decimal to percentage
- Confusing percentage with percentage points: 5% to 7% is a 2 percentage point increase, but a 40% relative increase
- Adding percentages incorrectly: 20% off then 10% off ≠ 30% off total
- Reversing increase/decrease formulas: Check your formula matches the direction of change
Keep This Handy!
This percentage formulas cheat sheet covers all the essential calculations you'll need. Bookmark this page or print it out for quick reference whenever you need to calculate percentages.
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