Percentage Calculator Guide: How Percentages Work
Percentages show up everywhere — discounts, taxes, tips, test scores, and statistics. Yet they trip up almost everyone at some point. This guide covers the five percentage calculations you'll actually use, with the formula and a worked example for each.
The Core Formula
Percentage = (Part ÷ Whole) × 100
- Part — the portion you're measuring
- Whole — the total or reference amount
Every percentage calculation is a variation of this single relationship.
The Five Percentage Modes
Our calculator shows all five modes on one page. Here's how each one works:
- X% of Y — Multiply:
result = (X ÷ 100) × Y. Example: 15% of 80 = 12. - X is what % of Y — Divide and scale:
(X ÷ Y) × 100. Example: 12 is 15% of 80. - % change (old → new) —
((new − old) ÷ old) × 100. Example: 80 → 100 is +25%. - % increase — Same as positive % change: add the percentage of the original.
- % decrease — The negative case: subtract the percentage of the original.
Common Percentage Mistakes
⚠️ Watch out
Additive vs. multiplicative. A 50% increase followed by a 50% decrease does NOT return you to the start. 100 → 150 (+50%) → 75 (−50%). Percentages compound on the new base, not the original.
- Confusing "percentage of" with "percentage points." Going from 10% to 15% is a 5 percentage point increase, but a 50% relative increase.
- Forgetting to convert. Always divide by 100 when moving between percent and decimal.
- Dividing by the wrong base. In % change, always divide by the original value, not the new one.
Put It Into Practice
The calculator lays out all five modes side by side — just type into any card and see the result instantly.
Try the Percentage Calculator
All five modes on one page, no tab switching.
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