Percentage Calculator
Easily calculate percentages, percentage increase/decrease and find percentage of a number.
The four percentage questions, and how they differ
Almost every percentage problem is one of four: finding a part, finding the whole, finding the rate, or finding the change. They share a formula but differ in which term you solve for, and mixing them up produces answers that are confidently wrong.
Formula
part = whole x (rate / 100) | rate = (part / whole) x 100 | whole = part / (rate / 100)
Percent means "per hundred", so 18% is simply the fraction 18/100 written in a different notation.
Identify which of the four you have
Write down which two of the three quantities - part, whole, rate - you already know. The one missing tells you which arrangement to use.
- Part unknown: "What is 18% of 250?" Multiply: 250 x 0.18 = 45.
- Rate unknown: "45 is what percent of 250?" Divide and scale: 45 / 250 x 100 = 18%.
- Whole unknown: "45 is 18% of what?" Divide by the decimal rate: 45 / 0.18 = 250.
- Change unknown: "From 250 to 295, what is the increase?" Difference over the original: 45 / 250 x 100 = 18% increase.
Increases and decreases do not cancel
A 20% rise followed by a 20% fall does not return you to where you started. From 100, you go to 120, then 20% of 120 is 24, leaving 96. You are 4% down.
The reason is that each percentage applies to a different base. To reverse a 20% increase you need a decrease of 16.67%, and to reverse a 20% decrease you need an increase of 25%.
The compact rule: an increase of x% is multiplication by (1 + x/100), and it is undone by multiplication by 1 / (1 + x/100), not by (1 - x/100).
Percentage points, and why journalists get corrected
When an interest rate moves from 4% to 5%, that is a rise of one percentage point and a rise of 25 percent. Both statements are accurate and they describe very different magnitudes.
The convention is settled: use percentage points when subtracting two percentages, and percent when expressing the relative change between them. Central banks and statistical agencies use "basis points" for hundredths of a percentage point, so 25 basis points is 0.25 percentage points.
Worked example
A team of 340 people grows to 391 over a year, and 22% of the new headcount is in engineering. Two different percentage questions are hiding here.
Growth rate: (391 - 340) / 340 x 100 = 15% increase. Engineering share of the growth: 22% of 51 new people is 11.22, so 11 people once rounded.
Note what you cannot conclude. Knowing engineering was 22% of the growth tells you nothing about engineering as a share of the whole team, because the two percentages have different bases.
Percentages as fractions and multipliers
| Percent | Fraction | Decimal | Multiplier for an increase |
|---|---|---|---|
| 5% | 1/20 | 0.05 | 1.05 |
| 10% | 1/10 | 0.10 | 1.10 |
| 12.5% | 1/8 | 0.125 | 1.125 |
| 20% | 1/5 | 0.20 | 1.20 |
| 25% | 1/4 | 0.25 | 1.25 |
| 33.3% | 1/3 | 0.333 | 1.333 |
| 50% | 1/2 | 0.50 | 1.50 |
| 100% | 1/1 | 1.00 | 2.00 |
Recognising 12.5% as one eighth and 33.3% as one third makes a great deal of mental arithmetic trivial.
Frequently Asked Questions
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References
- NIST Special Publication 811 - Guide for the Use of the SI
- OECD Glossary of Statistical Terms - percentage point
Last reviewed: 2026-08-07. This page is informational. For legal, medical, tax, or financial decisions, confirm the result with a qualified professional.