The Ultimate Guide to Calculating Percentages, Increases & Discounts
Whether you are calculating discounts during a shopping sale, determining sales tax, evaluating stock portfolio gains, or calculating restaurant tips, percentages are a foundational mathematical concept. The Percentage Calculator evaluates arithmetic formulas instantly with 100% client-side precision, displaying full formula breakdowns with zero server delays.
Percentage Formulas & Mathematical Rules Quick Reference
Use this reference table to understand the underlying equations for all major percentage operations:
| Calculation Type | Formula | Example | Result |
|---|---|---|---|
| Percentage of a Value (P% of X) | Y = (P / 100) * X |
What is 15% of $80? | $12.00 |
| Percentage Ratio (X as % of Y) | P = (X / Y) * 100 |
45 scored out of 60 | 75% |
| Percentage Increase / Gain | Δ% = ((New - Old) / Old) * 100 |
Price increased from $50 to $65 | +30.0% increase |
| Percentage Decrease / Discount | Sale Price = Original * (1 - Discount/100) |
$120 jacket with 25% off | $90.00 (Save $30) |
| Relative Percentage Difference | Diff% = (|A - B| / ((A + B) / 2)) * 100 |
Difference between 100 and 120 | 18.18% difference |
How to Calculate a Percentage of a Percentage
When dealing with cumulative discounts, sales commissions, or tax markups, you often need to find a percentage of another percentage. The rule is simple: convert both percentages to decimal form, multiply them, and multiply by 100:
Example: What is 25% of 40%?
0.25 × 0.40 = 0.10 → 10%