Free percentage calculator
Calculate percentages three ways — find P% of X, find what % X is of Y, or find the whole when you know a part and the %, updated live, as you type.
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Result = (percent ÷ 100) × value. Standard arithmetic percentage.
Results are estimates. Consult a professional.
How the percentage calculator works
Percentage problems come in three standard forms. This calculator handles all three: finding a percentage of a number, finding what percentage one number is of another, and finding the whole when you know the part and the percentage.
Worked example: three percentage types
Three classic question types solved step by step using the core formula Part = Whole × (Percent / 100).
Common percentage calculations reference
Memorising a few benchmark percentages speeds up mental math. Each row shows a fraction, its decimal equivalent, and how it applies to a base of 200.
| Percentage | Fraction | Decimal | Of 200 |
|---|---|---|---|
| 1% | 1/100 | 0.01 | 2 |
| 5% | 1/20 | 0.05 | 10 |
| 10% | 1/10 | 0.10 | 20 |
| 20% | 1/5 | 0.20 | 40 |
| 25% | 1/4 | 0.25 | 50 |
| 33.3% | 1/3 | 0.333… | 66.67 |
| 50% | 1/2 | 0.50 | 100 |
| 75% | 3/4 | 0.75 | 150 |
| 100% | 1/1 | 1.00 | 200 |
Source: standard fraction–percent equivalences
Tips for working with percentages
A clear mental model prevents the most common percentage mistakes. These tips apply in school, shopping, and everyday data analysis.
- Convert % to decimal first — dividing by 100 before multiplying reduces errors; 15% becomes 0.15, then multiply as normal.
- "Of" means multiply — whenever you see "X% of Y", translate it directly to X/100 × Y.
- Percentage of a percentage — 10% of 20% is not 30%; it is 0.10 × 0.20 = 0.02 = 2%.
- Order matters for Type 2 — "45 is what % of 180" differs from "180 is what % of 45"; always put the base (the 100% reference) in the denominator.
- Reverse-check your answer — after solving Type 3, verify by computing P% of your result and confirming you get back the original part.
Accuracy and limitations
This calculator uses IEEE 754 double-precision arithmetic (approximately 15–16 significant decimal digits). For most everyday percentage problems — tax, discounts, grades, statistics — the result is exact to all displayed digits. Division-by-zero occurs when the base (Y in Type 2 or P in Type 3) is zero; the calculator will warn you if this happens. Very large numbers (> 10¹⁵) or inputs with more than 15 significant digits may accumulate floating-point rounding error in the last one or two digits.
Key terms
About this calculator
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