Percentage Calculator
Percent of a total, percentage change, discounts and tax, each with the formula shown
① A 是 B 的百分之几
② B 的 P% 是多少
③ 从 A 变到 B，变化了百分之几
④ 打折 / 立减 / 税率反算
原价与到手价只需填一个，工具会自动反算另一个；两项都填时以原价为准并校验是否吻合。
常见比例速查
点表格任意一行可把数值填入对应计算器，便于顺手核对。
在任意一张卡片里填入数字即可自动计算，无需点击按钮
About this tool
Everyday percentage questions come in four shapes. This tool splits them into four cards, gives the number immediately and writes out the formula so you can check it rather than trust it:
- Share of a total: what percent of B is A; 25 out of 200 is
12.5%, with the decimal and reduced fraction alongside - Part of a total: what is P percent of B; 13 percent of 2400 is 312, plus the value of each 1 percent and what remains
- Percentage change: how much did A change to reach B, including the often missed gain needed to return to the starting value
- Discounts and tax: supports a percentage discount, a fixed reduction and a tax rate, and back-calculates either list price or final price
- Clickable tables: fraction, decimal and percent equivalents, discount mappings and change pairs; click any row to load the value
When to use it
- Work out year-over-year and period-over-period changes in reports
- Compare promotions: is 15 percent off the same as paying 85 percent, and what does a second item at half price really save
- Quotes and invoicing: recover the pre-tax amount and the tax share from a tax-inclusive total
- Convert pass rates, attendance rates and scores into proportions
- Estimate the gain needed to recover an investment loss
Four core formulas
| Question | Formula | Example |
|---|---|---|
| A as a percent of B | A / B times 100 | 25 / 200 times 100 = 12.5 percent |
| P percent of B | B times P / 100 | 2400 times 13 / 100 = 312 |
| Change from A to B | (B - A) / A times 100 | (1000 - 800) / 800 = +25 percent |
| Final price from list price | List price times factor | 15 percent off gives a factor of 0.85 |
| List price from final price | Final price / factor | 170 / 0.85 = 200 |
| Pre-tax from tax-inclusive | Total / (1 + tax rate) | 100 / 1.13 is about 88.50 |
Common questions
- Does a 25 percent gain plus a 25 percent loss break even?No. 100 rises to 125, and falling back to 100 is a
20 percentdrop because the base grew. Gains and losses are never symmetric: a 50 percent loss needs a 100 percent gain to recover - With 100 including 13 percent tax, is the pre-tax amount 100 minus 13 percent?No. Use
100 / 1.13, about 88.50. Subtracting 13 percent gives 87 and understates by about 1.5. The tax is then about11.5 percentof the inclusive total, not 13 - What is the difference between points and percent?A pass rate moving from 5 to 7 percent rose
2 percentage points, but the relative increase is40 percent. Mixing the two exaggerates or hides the change - Is 20 percent off the same as a 20 percent reduction?The factor is 0.8 either way for a single item, but a spend-300-save-50 offer depends on the basket: 16.67 percent off at 300 and only 8.33 percent off at 600
- Why is there no result when the base is zero?Share and growth both divide by the base, and division by zero is undefined, so only absolute differences can be compared
- How do tenths and per-mille convert?One tenth is 10 percent, one discount tenth is 10 percent paid, and 1 per mille is 0.1 percent. Interest rates often use per-mille, so multiply the percentage by 10
To turn a result into a fraction or do fraction arithmetic, use the fraction calculator; for rates, monthly payments and total interest see the mortgage calculator; for salary and income tax see the income tax calculator; for units other than money use the unit converter. All calculations run locally and no numbers are uploaded.