Percentage Calculator

What this percentage calculator is for

Percent problems show up everywhere—shopping discounts, exam scores, tip math, budget shares, and year-over-year growth. This percentage calculator bundles the three formulas people search most often into one page so you do not have to remember whether to multiply or divide.

Mode A: What is X% of Y?

Classic "take a percent of a number"—15% of 200, 8.25% tax on a subtotal, or 70% of your maximum points. Formula: Result = (X ÷ 100) × Y. Example: 15% of 200 = 0.15 × 200 = 30. Use this when you know the rate and the base and need the portion.

Mode B: X is what percent of Y?

Finds the share or ratio expressed as a percent—"30 out of 150 questions correct" or "my score vs the class maximum." Formula: Percent = (X ÷ Y) × 100. Example: 30 ÷ 150 × 100 = 20%. The whole (Y) must not be zero. This mode is common in grading and survey response rates.

Mode C: Percent change from X to Y

Measures relative growth or decline between two values—price hikes, salary changes, or population shifts. Formula: Change = ((Y − X) ÷ X) × 100. A move from 120 to 150 is a 25% increase; from 150 to 120 is a 20% decrease (note: decrease percentages use the original value as the denominator, so up and down moves are not symmetric).

Percent vs percentage points

Do not confuse a percent change with percentage points. If an interest rate rises from 4% to 5%, that is a 1 percentage-point increase but a 25% relative increase in the rate itself. This calculator reports relative percent change (Mode C); for simple point differences, subtract the two percentages directly.

Academic and financial connections

Students often chain percent tools with grade planners. After finding what fraction you scored on a quiz (Mode B), use the final grade calculator to see what you need on the final, or the GPA calculator for semester-wide averages. For sales-tax back-outs from a receipt total, the reverse sales tax calculator handles jurisdiction-specific tax math. Long-horizon growth belongs in the compound interest calculator, which applies repeated compounding rather than a single-step percent change.

Tips for accurate results

• Use the same units in X and Y (dollars with dollars, points with points).
• For discounts, decide whether "20% off" applies to pre-tax or post-tax totals per store policy.
• Round only at the end if your context requires fixed decimal places (currency, grades).
• Negative bases in percent-change mode still compute mathematically but may lack real-world meaning.

Everyday examples

Tip math (Mode A): 18% tip on a $64.50 check → 18% of 64.50 = $11.61. Quiz score (Mode B): 42 correct out of 50 → 42 is 84% of 50. Price hike (Mode C): rent rises from $1,200 to $1,350 → ((1350 − 1200) ÷ 1200) × 100 = 12.5% increase. Keeping all three modes on one page avoids opening a spreadsheet for quick sanity checks during homework or household budgeting.

Reverse problems and mental shortcuts

Mode A also answers reverse questions when you already know the result: if 15% of a number is 30, divide 30 by 0.15 to recover the base (200). For Mode B, doubling a part while the whole stays fixed doubles the percent—useful when a exam adds extra credit points. For Mode C, remember that equal absolute changes up and down are not symmetric in percent terms: +50% then −50% does not return to the start because each step uses a different base.

Disclaimer

Educational math only. Tax, finance, and scientific applications may require additional rules, rounding conventions, or regulatory formulas not modeled here.