fox tools
1. Every percentage needs a baseline
A percentage only makes sense when you know what it is a percentage of. If a price falls from 50 to 40, divide the saving of 10 by the original 50 to get a 20% discount. The same pair of numbers can produce a different percentage when you change the baseline.
Use the discount calculator for a sale price, and percentage change for visits or output measured at two different times. Percentage difference compares values without a direction and divides by their average, so it answers a different question from percentage change.
2. An extra 10% after 20% off is not 30% off
Taking 20% off a price of 50 leaves 40. A further 10% off applies to 40, not 50, and saves another 4. You pay 36 and save 14 against the original price: a combined discount of 28%.
You can calculate the fraction of the price remaining: (1 − 0.20) × (1 − 0.10) = 0.72. You pay 72% of the original. A seller may apply both coupons to the original price or combine a percentage with a fixed amount instead. Check the actual coupon rules before using the sequential calculation.
- In the discount calculator, enter an original price of 50 and a discount of 20. The final price is 40.
- Change the original price to 40 and the discount to 10. The final price is 36.
- In the percentage calculator, compare an original value of 50 with a new value of 36. Percentage change is −28%.
| Situation | Calculation | Result |
|---|---|---|
| 20% off 50, then another 10% off | 50 × 0.8 × 0.9 | 36 · 28% total discount |
| Recover from 80 to 100 | (100 − 80) ÷ 80 × 100 | +25% |
| Rate rises from 10% to 15% | 15 − 10; (15 − 10) ÷ 10 × 100 | 5 percentage points; +50% relative |
| Percentage difference of 100 and 120 | 20 ÷ 110 × 100 | About 18.18% |
3. Recovering from a 20% drop takes a 25% rise
Output falling from 100 to 80 is a 20% decrease. Getting back to 100 needs an increase of 20, but the new baseline is 80. That is 20 ÷ 80 × 100 = 25%. Adding just 20% to 80 reaches 96.
Do not add successive percentage changes to find the overall change. The sequence 100 → 80 → 96 ends 4% below the start. A percentage change from zero is undefined because it would divide by zero. Describe the actual numbers instead, such as “increased from 0 visits to 20”.
4. Separate percentages from percentage points
A response rate rising from 10% to 15% increases by 5 percentage points. Relative to the original rate of 10%, it increases by (15 − 10) ÷ 10 × 100 = 50%. Saying only “up 5%” leaves the meaning unclear.
Report the starting and ending rates: “Response rate rose from 10% to 15%, an increase of 5 percentage points.” Even correct arithmetic can mislead if the groups or periods differ. When comparing visits, check that both figures cover the same length of time and the same metric.
5. Check rounding and the final amount
Rounding every intermediate figure can accumulate differences. Keep the original values during calculation and round for display at the end. Choosing a currency changes formatting only; it does not convert using an exchange rate.
The discount calculator does not include shipping, taxes, reward points or minimum spending rules. Compare the simple calculated price with the actual checkout amount. The values and table in this guide illustrate the arithmetic, not an offer from any particular retailer.
Before you finish
- Identify the original value and the comparison value
- Apply each successive discount to the reduced price
- Label percentage points, percentage change and difference accurately