Percentage Calculator Solve any percentage problem instantly — with visualizations, real-world examples, and step-by-step...
Percentage Calculator
Solve any percentage problem instantly — with visualizations, real-world examples, and step-by-step explanations.
Basic Formula**:
$$\text{Part} = \text{Whole} \times \frac{\%\ \text{Value}}{100}$$
Example: 15% of $200 = $200 × 0.15 = **$30**
Common Confusions**:
- “20% of 100”** = 20 “20% off 100”** = 80 (i.e., 100 − 20)
- Sequential %**: 10% ↑ then 10% ↓ ≠ 0% net $100 → $110 → $99 = **−1%
✅ Pro Tip**: Convert % → decimal (÷100) before calculating.
⚠️ % Increase/Decrease is directional**:
From $80 → $100 = +25% From $100 → $80 = −20%
✅ % Difference is symmetric** (used in science, stats):
$$\text{% Difference} = \frac{|V_1 - V_2|}{\frac{V_1 + V_2}{2}} \times 100\%$$
$120 vs. $80: = |120−80| / ((120+80)/2) × 100% = 40 / 100 × 100% = **40%**
📉 When to use which**:
- Finance, sales: % change (direction matters)
- Lab reports, surveys: % difference (no direction)
| Context | Average % | Example |
|---|---|---|
| Restaurant Tip | 19.3% | $45 bill → $8.69 tip |
| Sales Tax (U.S.) | 7.12% | $100 → $107.12 |
| Annual Raise | 4.1% | $60K → $62,460 |
| Inflation (2024) | 3.4% | $100 in 2023 = $96.71 in 2024 |
💡 Tip Math Hack**:
- 10% = move decimal left 1 (e.g., $45 → $4.50)
- 15% = 10% + half of 10% = $4.50 + $2.25 = $6.75
- 20% = double 10% = $9.00
➡️ What is X% of Y?
Tips, tax, discounts: “What’s 18% of $62?”
➡️ X is what % of Y?
Score: “45/60 = ?%”, savings: “$250 off $1,250 = ?%”
➡️ X is Y% of what?
Sales: “$99 is 30% off — what’s original price?”
➡️ Increase/Decrease
Salary, stock, weight: “$55K → $60K = ?% raise”
➡️ % Difference
Compare products: “$120 vs. $95 — how different?”
➡️ Compound %
Investments: “+8% this year, −3% next = net +4.76%”
All results include exact formulas and visual explanations.