How to use it
- Pick the card that matches your question – percent of a number, what percent, change, increase, decrease, reverse or percentage points.
- Type the two numbers. The card shows its answer immediately and the big result box repeats the last card you edited as a sentence.
- Set the number of decimals (0–4) once; it applies to every card. Results are rounded for display only.
- Copy the result (plain number, no thousands separators) or copy the link – the link restores every card you filled in.
Example
A jacket costs 120 after a 20% discount. “Value before a % change” with 120 and −20 gives 150(120 ÷ 0.8). If the shop instead raised a 100 price to 120, “Percentage change” reports +20%, and lowering it back from 120 to 100 is −16.67%, because the second change is measured against 120. A tax rate moving from 20% to 25% is +5 percentage points and a 25% relative increase.
Formulas used by each card
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 20% of 150 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 30 ÷ 150 × 100 = 20% |
| Change from A to B | (B − A) ÷ |A| × 100 | (120 − 100) ÷ 100 × 100 = +20% |
| Increase Y by X% | Y × (1 + X ÷ 100) | 100 × 1.2 = 120 |
| Decrease Y by X% | Y × (1 − X ÷ 100) | 100 × 0.8 = 80 |
| Value before a change | after ÷ (1 + X ÷ 100) | 120 ÷ 1.2 = 100 |
| Percentage points | B − A | 25% − 20% = 5 points |
The change formula divides by the absolute value of the start, so a move from −100 to −50 is reported as +50% (the value increased) rather than −50%. When the start is 0 there is no percentage change; the card says so instead of showing infinity.
relative change of two rates = (B − A) ÷ A × 100 e.g. (25 − 20) ÷ 20 × 100 = 25%Internally every answer is rounded to 10 decimal places to remove binary floating-point artefacts, then shown with the number of decimals you chose. Inputs accept thousands separators and spaces (“1,250.5”).
Sources: Wikipedia – Percentage, Wikipedia – Percentage point.
Why a 20% drop does not cancel a 20% rise
Percentages always refer to the number they are applied to. Raising 100 by 20% gives 120; cutting 120 by 20% takes away 24, not 20, and leaves 96. To get back to the original you need the reverse card, which divides by 1.2 instead of multiplying by 0.8. The same asymmetry explains why a stock that falls 50% must then rise 100% to recover.
Questions
- How do I calculate a percentage of a number?
- Multiply the number by the percentage and divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12. The first card does exactly this.
- What is the difference between percent and percentage points?
- Percentage points are the arithmetic difference between two percentages; percent change is the relative difference. From 4% to 6% is 2 percentage points, but a 50% increase (2 ÷ 4).
- How do I find the original price before a discount?
- Use “Value before a % change” with the sale price and the discount as a negative number: 60 after −25% gives 60 ÷ 0.75 = 80.
- Can I enter negative numbers?
- Yes. Negative percentages turn an increase into a decrease and vice versa, and the change card handles negative starting values by measuring against their absolute value.