Percentage Calculator

Five percentages, done five ways

The fastest way to understand percentages is to see them. Five everyday cases, with the math written out:

1. The tip: 18% of $42

Convert 18% to 0.18, multiply: 42 × 0.18 = $7.56. Mental shortcut: 10% of $42 is $4.20; 8% is another $3.36; total $7.56. Adding the bill: $49.56.

2. The sale: $80 jacket marked 30% off

30% of 80 = 24; $80 − $24 = $56. Mental shortcut: a "30% off" is the same as paying 70%, so 80 × 0.7 = 56 directly. Use this for any "X% off" — pay (100 − X)%.

3. The exam: 47 correct out of 60

47 ÷ 60 = 0.7833; × 100 = 78.3%. The pattern: when you have the part and the whole, divide and multiply by 100.

4. The portfolio: $14,200 grew to $16,560

Change = 16,560 − 14,200 = 2,360. Percent change = (2,360 / 14,200) × 100 = +16.6%. The denominator is always the old value, never the new one. This is the single most-confused step in percentage math.

5. The reverse: a $69 price tag includes 15% sales tax. What was the pre-tax price?

The $69 represents 115% of the pre-tax price. Pre-tax = 69 / 1.15 = $60. Pattern: when a percentage has already been added, divide by (1 + rate) to unwind it. The calculator above's "X is what % of Y" mode handles this directly.

The one mistake people make with percentage changes

A 50% drop followed by a 50% gain does not bring you back to where you started. Take $100, lose 50%: you have $50. Gain 50% on $50: you have $75 — not $100. The reason: the second percentage is taken against the smaller post-drop base, not the original.

To undo a 50% drop you need a 100% gain. To undo a 20% drop you need a 25% gain. To undo a 90% drop you need a 900% gain. This asymmetry is why investment losses are mathematically heavier than gains of the same nominal size, and why "percent change" reports always have to specify the reference point.

The three formulas, in one place

• Percent of a number: result = (percent / 100) × number. e.g. 18% of 42 = 0.18 × 42 = 7.56
• One number as a percent of another: percent = (part / whole) × 100. e.g. 47/60 = 78.3%
• Percent change: ((new − old) / old) × 100. e.g. (16,560 − 14,200)/14,200 = 16.6%

Where you will see these in real life

• Shopping: discount calculator, percentage off, sales tax.
• Money: compound interest, tax brackets, profit margins.
• School: grade calculator, GPA calculator.
• Tracking changes over time: percent increase, percent decrease.

A note on percent vs. percentile

A percentage is a fraction of a whole, expressed out of 100. "I scored 78%" means I got 78 out of every 100 points possible. A percentile is a rank, not a fraction. "I scored in the 78th percentile" means I scored higher than 78% of the people who took the test. The two get confused constantly because they share the word "percent." They are not the same number — a 78% raw score can be in the 92nd percentile, the 50th, or the 5th, depending on how others performed.