A complete guide to all 5 percentage calculation methods with real-world examples you'll actually use.
Percentages are everywhere — sale prices, tax rates, tip calculations, grade scores, investment returns, and data analysis. Yet many people reach for a calculator (or Google) every time they need one. This guide covers every percentage formula you'll encounter, with worked examples for each.
This is the most fundamental percentage calculation: given a part and a whole, what percent is the part?
Formula
Percentage = (Part ÷ Whole) × 100
You scored 42 out of 56 on a test. What's your percentage?
(42 ÷ 56) × 100 = 0.75 × 100 = 75%
Answer: 75%
This is the calculation you use most often in daily life — finding a discount, calculating a tip, or determining tax.
Formula
Result = Number × (Percentage ÷ 100)
A $85 restaurant bill with an 18% tip:
$85 × 0.18 = $15.30
Total: $85 + $15.30 = $100.30
Tip amount: $15.30
Percentage change measures how much a value has grown or shrunk relative to its original value. This is directional — it matters whether it went up or down.
Formula
% Change = ((New Value - Old Value) ÷ Old Value) × 100
Positive = increase, Negative = decrease
Your rent went from $1,800 to $1,980. What's the percentage increase?
((1980 - 1800) ÷ 1800) × 100 = (180 ÷ 1800) × 100 = 10% increase
Rent increased by 10%
Percentage difference compares two values without assuming either is the "original." It's useful when comparing two similar things — like two prices, two salaries, or two test scores.
Formula
% Difference = |A - B| ÷ ((A + B) ÷ 2) × 100
Always positive — no direction
Comparing two job offers: $72,000 vs $85,000
|72000 - 85000| ÷ ((72000 + 85000) ÷ 2) × 100 = 13000 ÷ 78500 × 100 = 16.6% difference
The offers differ by 16.6%
| Use Percentage Change | Use Percentage Difference |
|---|---|
| Stock price went from $50 to $65 | Comparing two products' prices |
| Website traffic grew from 10K to 15K | Comparing two cities' populations |
| Your weight changed over time | Comparing two test scores |
| Revenue increased quarter over quarter | Comparing two salary offers |
Sometimes you know the final value after a percentage was applied and need to find the original. This trips up a lot of people — you can't just "add back" the percentage.
After an Increase
Original = Final Value ÷ (1 + percentage as decimal)
After a Decrease
Original = Final Value ÷ (1 - percentage as decimal)
A TV is priced at $420 after a 30% discount. What was the original price?
Original = $420 ÷ (1 - 0.30) = $420 ÷ 0.70 = $600
Original price: $600
A product costs $78 after a 30% markup. What was the wholesale price?
Wholesale = $78 ÷ (1 + 0.30) = $78 ÷ 1.30 = $60
Wholesale price: $60
Many people calculate $420 × 1.30 = $546 — that's wrong! You need to divide, not multiply. The 30% was taken from the original, not from $420. This is why understanding the formula matters.
| Calculation Type | Formula | Example |
|---|---|---|
| Find percentage | (Part ÷ Whole) × 100 | 42 of 56 = 75% |
| Percentage of number | Number × (Pct ÷ 100) | 15% of 80 = 12 |
| Percentage change | ((New - Old) ÷ Old) × 100 | 40→50 = +25% |
| Percentage difference | |A-B| ÷ avg(A,B) × 100 | 72K vs 85K = 16.6% |
| Reverse percentage | Final ÷ (1 ± pct) | $420 after 30% off → $600 |
Stop doing percentage math in your head.
Try Our Free Percentage Calculator →Divide the part by the whole and multiply by 100. Formula: Percentage = (Part ÷ Whole) × 100. Example: 25 out of 200 = (25 ÷ 200) × 100 = 12.5%.
Convert the percentage to a decimal and multiply. Formula: Result = Number × (Percentage ÷ 100). Example: 15% of 80 = 80 × 0.15 = 12.
Percentage change compares a new value to an old value (directional). Percentage difference compares two values without direction, using the average as the reference point.
Subtract the original value from the new value, divide by the original, and multiply by 100. Example: $40 to $50 = ((50-40)÷40)×100 = 25%.
Divide the final value by (1 - percentage) for discounts or (1 + percentage) for markups. Example: $75 after 25% off → $75 ÷ 0.75 = $100 original.
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