Percentage Calculator — Four Modes in One
A percentage expresses a number as a fraction of 100. Percentages are used everywhere — from shopping discounts and tax calculations to test scores, investment returns, and statistical analysis.
This calculator covers the four most common percentage operations. Select a mode, enter your values, and the result appears instantly alongside the formula that was used and a concrete worked example.
Percentage Formulas
Mode 1
What is X% of Y?
Result = Y × (X ÷ 100)
e.g. 20% of 150 = 150 × 0.20 = 30
Mode 2
X is what % of Y?
% = (X ÷ Y) × 100
e.g. 30 is what % of 200? = (30 ÷ 200) × 100 = 15%
Mode 3
Increase / Decrease Y by X%
Result = Y × (1 ± X ÷ 100)
e.g. Increase 200 by 15% = 200 × 1.15 = 230
Mode 4
Percent change from X to Y
% = ((Y − X) ÷ X) × 100
e.g. 50 to 75 = ((75−50)÷50) × 100 = +50%
Percentage Reference Table
Common fractions and their percentage equivalents — useful for quick mental math:
| Fraction | Decimal | Percentage | Example (of 200) |
|---|---|---|---|
| 1/100 | 0.01 | 1% | 2 |
| 1/20 | 0.05 | 5% | 10 |
| 1/10 | 0.10 | 10% | 20 |
| 1/8 | 0.125 | 12.5% | 25 |
| 1/5 | 0.20 | 20% | 40 |
| 1/4 | 0.25 | 25% | 50 |
| 1/3 | 0.333… | 33.3% | 66.7 |
| 1/2 | 0.50 | 50% | 100 |
| 3/4 | 0.75 | 75% | 150 |
| 1/1 | 1.00 | 100% | 200 |
Real-World Percentage Uses
Shopping discounts
"30% off $80" — use Mode 1: what is 30% of 80? = $24 saved; pay $56.
Investment returns
Stock went from $42 to $57 — use Mode 4: percent change = +35.7%.
Test scores
Got 78 out of 95 — use Mode 2: 78 is what % of 95? = 82.1%.
Tax & tip calculation
Add 18% tip to $65 bill — use Mode 3: increase 65 by 18% = $76.70.
Frequently Asked Questions
Multiply the number by the percentage divided by 100. For example, 25% of 80 = 80 × (25 ÷ 100) = 80 × 0.25 = 20. This is the most common percentage operation — used for discounts, tax amounts, tips, and commissions.
Divide the part by the whole and multiply by 100. For example, 45 is what percent of 180? = (45 ÷ 180) × 100 = 25%. This is useful for grading, market share calculations, and measuring proportions.
New value = Original × (1 + percentage ÷ 100). For a 20% increase on 500: 500 × 1.20 = 600. Alternatively, calculate the increase amount first (500 × 0.20 = 100) and add it to the original (500 + 100 = 600).
New value = Original × (1 − percentage ÷ 100). For a 15% decrease on 400: 400 × 0.85 = 340. This is the same formula used for discount calculations — a 30% discount on an item means multiplying the price by 0.70.
Percent change = ((new value − old value) ÷ old value) × 100. A positive result is an increase; a negative result is a decrease. For example, from 80 to 60: ((60 − 80) ÷ 80) × 100 = −25%. Note that percent change is always relative to the starting value.
Percent change measures how much a value changed relative to its starting point — it has a defined direction (from X to Y). Percent difference compares two values without a defined starting point, using the average as the denominator: |A − B| ÷ ((A + B) ÷ 2) × 100. Use percent change for before/after comparisons and percent difference for comparing two unordered values.
Because percent change is always calculated relative to the starting value. Going from 50 to 100 is a +100% increase, but going from 100 to 50 is a −50% decrease. The magnitudes differ because the denominators (50 vs 100) differ. Always identify which value is the original before calculating.
People Also Search For
Related Math tools on CalcPocket: