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
- 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
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.
百分比无处不在——折扣、税收、小费、考试成绩和统计数据中都能看到它的身影。然而，它们几乎在某些时候会让所有人感到困惑。本指南涵盖了你实际会用到的五种 percentage 计算方式，每种都提供了公式和计算示例。
核心公式
- Part — 你要测量的部分
- Whole — 总量或参考值
每一次 percentage 计算都是这一关系的变体。
五种 percentage 计算模式
我们的计算器在一个页面上展示了所有五种模式。下面是每种模式的计算方式：
- X% of Y — 乘法运算：
result = (X ÷ 100) × Y。例如：80 的 15% = 12。 - X is what % of Y — 除法运算后缩放：
(X ÷ Y) × 100。例如：12 是 80 的 15%。 - % change (old → new) —
((new − old) ÷ old) × 100。例如：80 → 100 为 +25%。 - % increase — 与正向 % change 相同：将原数值加上原数值的百分比。
- % decrease — 负向情况：从原数值中减去原数值的百分比。
常见 percentage 计算错误
加法 vs. 乘法。先增加 50% 再减少 50% 并不会回到原点。100 → 150（+50%）→ 75（−50%）。百分比是基于新基数计算的，而不是原始值。
- 混淆「percentage of」与「percentage points」。从 10% 到 15% 是 5 个 percentage point 的绝对增长，但却是 50% 的 relative 增长。
- 忘记换算。在百分比与小数之间转换时，务必除以 100。
- 使用错误的基数。在 percent change 计算中，始终要除以原始值，而非新值。
付诸实践
计算器将所有五种模式并列展示——只需在任意卡片中输入数字，即可即时看到结果。
Try the Percentage Calculator
All five modes on one page, no tab switching.
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