A percentage is simply a fraction out of 100. "47%" means 47 out of every 100. This makes it easy to compare proportions regardless of the total — 47% of 1,000 is the same proportion as 47% of 2.
The word "percent" comes from the Latin per centum, meaning "by the hundred."
The most common operation: you want to know what X% of Y is.
Step 1: 15 ÷ 100 = 0.15
Step 2: 0.15 × 240 = 36
Answer: $36
To quickly estimate in your head: move the decimal two places left, then multiply. 15% of 240 → 0.15 × 240 = 15 × 24 = 360, then divide by 10 → 36.
How do you measure the change between an old value and a new value?
Step 1: 65 − 50 = 15
Step 2: 15 ÷ 50 = 0.30
Step 3: 0.30 × 100 = 30%
Answer: 30% gain
Step 1: 1,380 − 1,200 = 180
Step 2: 180 ÷ 1,200 = 0.15
Step 3: 0.15 × 100 = 15%
Answer: 15% increase
Sometimes you know the final number and the percentage, and you need to find the original. This is common in tax situations, markups, and discounts.
Step 1: 25% = 0.25. So 1 + 0.25 = 1.25
Step 2: 124.99 ÷ 1.25 = 99.99
Pre-tax price: $99.99
30% off → you pay 70% of original. So:
Original = 70 ÷ 0.70 = 100
Original price: $100
To increase a number by a percentage:
1 + 0.08 = 1.08
55,000 × 1.08 = 59,400
New salary: $59,400
To decrease by a percentage (multiply by less than 1):
1 − 0.05 = 0.95
4,200 × 0.95 = 3,990
Final rent: $3,990
Interest, inflation, and investment returns compound over time. The formula:
Where r = rate per period, t = number of periods.
| Initial | Rate | Time | Formula | Result |
|---|---|---|---|---|
| $10,000 | 7% / year | 10 years | 10,000 × (1.07)^10 | $19,672 |
| $10,000 | 7% / year | 20 years | 10,000 × (1.07)^20 | $38,696 |
| $10,000 | 10% / year | 10 years | 10,000 × (1.10)^10 | $25,937 |
💡 Rule of 72: To estimate how long it takes to double your money at a given rate, divide 72 by the rate. At 7% → 72 ÷ 7 = ~10.3 years to double. At 6% → 12 years. Simple and accurate for rates under 15%.
Use our percentage calculator for: % of a number, % change, increase/decrease, and more.
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