Percentage Formula: Every Formula You Need (With Examples)
By CalcMulti Editorial Team··8 min read
Percentages are among the most universally useful calculations — appearing in tax rates, discounts, stock prices, test scores, interest rates, and dosage calculations. Yet many people confuse the different formula variations.
This guide covers every percentage formula you will encounter, with worked examples for each. Whether you need to find X% of a number, calculate a stock price change, or reverse a percentage to find the original value, the right formula is here.
Formula
P% of X = X × (P ÷ 100)
Formula 1: Basic Percentage — "What is X% of Y?"
Formula: Result = Y × (X ÷ 100)
Example: What is 20% of 150?
Result = 150 × (20 ÷ 100) = 150 × 0.20 = 30
Reverse (find the percentage): If 30 is what percentage of 150? → (30 ÷ 150) × 100 = 20%
Reverse (find the base): 30 is 20% of what number? → 30 ÷ 0.20 = 150
| Question type | Formula | Example (20% of 150 = 30) |
|---|---|---|
| Find the part | Part = Base × Rate | 150 × 0.20 = 30 |
| Find the rate | Rate = Part ÷ Base × 100 | (30 ÷ 150) × 100 = 20% |
| Find the base | Base = Part ÷ Rate | 30 ÷ 0.20 = 150 |
Formula 2: Percentage Change — Increase or Decrease
Formula: % Change = ((New − Old) ÷ Old) × 100
A positive result means increase; negative means decrease.
Example (stock price): A stock was $120 and rose to $138.
% Change = ((138 − 120) ÷ 120) × 100 = (18 ÷ 120) × 100 = +15%
Example (salary cut): Salary dropped from $5,000 to $4,250.
% Change = ((4250 − 5000) ÷ 5000) × 100 = (−750 ÷ 5000) × 100 = −15%
Important asymmetry: A 15% increase followed by a 15% decrease does NOT return to the original. Example: 100 × 1.15 = 115 → 115 × 0.85 = 97.75. You end up 2.25% below the start. Always apply changes sequentially, not additively.
Formula 3: Stock Price Change Percentage
Stock percentage change follows the same formula as percentage change, but traders use it constantly:
Formula: % Change = ((Current Price − Previous Close) ÷ Previous Close) × 100
Example: Apple closed at $182.50 yesterday. Today it is $191.63.
% Change = ((191.63 − 182.50) ÷ 182.50) × 100 = (9.13 ÷ 182.50) × 100 = +5.00%
For total return over a period: % Return = ((Ending Value − Starting Value + Dividends) ÷ Starting Value) × 100
For annualized return (CAGR): CAGR = ((Ending ÷ Beginning)^(1/Years) − 1) × 100
| Scenario | Start | End | % Change |
|---|---|---|---|
| Stock gain | $50.00 | $57.50 | +15.0% |
| Stock loss | $100.00 | $87.00 | −13.0% |
| Volatile round trip | $200.00 | $200.00 after +20% then −16.7% | 0.0% |
| Year-over-year | $1,200 | $1,350 | +12.5% |
Formula 4: Reverse Percentage — Find the Original
Use this when you know the value after a percentage change and want the original.
Formula: Original = Current Value ÷ (1 ± Percentage/100)
Use + for increase (current is higher than original), − for decrease.
Example (sale price): A jacket costs $85 after a 15% discount. What was the original price?
Original = 85 ÷ (1 − 0.15) = 85 ÷ 0.85 = $100
Common mistake: Calculating 15% of $85 = $12.75 and adding it back → $97.75. This is WRONG. The 15% was of the original price ($100), not the sale price ($85).
Example (tax-inclusive): A bill is $112 including 12% VAT. Pre-tax amount = 112 ÷ 1.12 = $100.
Formula 5: Markup vs Margin
Two formulas that are often confused in business:
Markup is based on cost: Markup% = (Selling Price − Cost) ÷ Cost × 100
Gross Margin is based on selling price: Margin% = (Selling Price − Cost) ÷ Selling Price × 100
Example: A product costs $40 and sells for $60.
Markup = (60 − 40) ÷ 40 × 100 = 50% markup
Margin = (60 − 40) ÷ 60 × 100 = 33.3% gross margin
A 50% markup ≠ 50% margin. Retailers quote margins; manufacturers often quote markups. Always ask which is being used.
Common Percentage Mistakes
1. Adding percentages from different bases: A 10% tax on top of a 5% fee on a $100 item is NOT 15% of $100. If the fee applies first: $100 × 1.05 = $105 → $105 × 1.10 = $115.50 (15.5% total, not 15%).
2. Confusing percentage points vs percent change: If interest rates rise from 2% to 3%, that is a 1 percentage point increase but a 50% relative increase.
3. Applying percentage decrease symmetrically: A 25% increase followed by a 25% decrease gives: 1.25 × 0.75 = 0.9375 — a 6.25% net loss, not zero.
4. Forgetting to convert: To use a percentage in multiplication, divide by 100 first (35% = 0.35). Multiplying by 35 instead of 0.35 gives a result 100× too large.
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Frequently Asked Questions
Educational use only. Content is based on publicly documented mathematical formulas and reviewed for accuracy by the CalcMulti Editorial Team. Last updated: March 2026.