Percentages express proportional relationships on a standardized scale of one hundred, simplifying comparisons across financial budgets, sales markdowns, and scientific measurements. This multi-mode calculator solves the three primary percentage relationships: computing direct percentage portions, finding the relative percentage share between two values, and determining percentage change over time.

### Governing Percentage Equations The calculator features three dedicated computational modes:

- **Mode 1: Direct Percentage Portion (What is A% of B?):** $$\text{Portion} = \left(\frac{A}{100}\right) \times B$$ - **Mode 2: Relative Percentage Share (A is what % of B?): $$\text{Percentage Share} = \left(\frac{A}{B}\right) \times 100\%$$ - **Mode 3: Percentage Increase or Decrease (Change from A to B):** $$\Delta \% = \left(\frac{B - A}{|A|}\right) \times 100\%$$

### Worked Numeric Examples Applying the default workspace inputs across all three operational modes: - **Mode 1 Calculation (15% of 250):** $$\text{Step 1: Convert percentage to decimal:} \quad 15 / 100 = 0.15$$ $$\text{Step 2: Multiply by base:} \quad 0.15 \times 250 = \mathbf{37.50}$$ - **Mode 2 Calculation (45 is what % of 180):** $$\text{Step 1: Divide part by whole:} \quad 45 / 180 = 0.25$$ $$\text{Step 2: Scale to percentage:} \quad 0.25 \times 100 = \mathbf{25.00\%}$$ - **Mode 3 Calculation (Change from 80 to 100):** $$\text{Step 1: Absolute difference:} \quad 100 - 80 = +20$$ $$\text{Step 2: Relative to initial value:} \quad (+20 / 80) \times 100 = \mathbf{+25.00\%\text{ increase}}$$

### Commercial Markup vs Margin Principles A common commercial error is confusing percentage markup on cost with gross profit margin. Adding a 25% markup to an $80 wholesale cost yields a $100 retail price. However, the resulting $20 gross profit divided by the $100 selling price represents a 20% profit margin, not 25%. All calculations process entirely client-side in local browser memory with zero network data transmission.