A part as a percentage of the whole
Divide the part by the whole and multiply by 100. A percentage is undefined when the whole is zero.
If 12 of 30 respondents choose an option, the result is 40%.
- Percentage = part ÷ whole × 100
- Part = whole × percentage ÷ 100
Change rate uses the earlier value
A rise from 80 to 100 is a difference of 20 but a 25% increase because 80 is the base. A fall from 100 to 80 is 20%.
The same absolute difference can produce asymmetric rise and fall rates when the bases differ.
Example: 20% off, then another 10%
A 100,000-won price becomes 80,000 won after 20% off, then 72,000 won after another 10%. The effective discount is 28%, not 30%.
The result also depends on whether a coupon is fixed or percentage-based and when it is applied.
- First price = original × (1 - first rate)
- Final = first price × (1 - second rate)
- Effective rate = savings ÷ original × 100
Confirm checkout conditions
Shipping, tax, minimum purchase, and discount caps may sit outside the basic calculation. Confirm the final checkout amount.
When reporting a change rate, include both the comparison period and the base value.
Define the base before calculating a percentage
A percentage needs an explicit quantity treated as 100%. Advertising cost of 400,000 won is 8% of five million won in revenue, but that does not mean the advertising return is 8%. Share, growth, margin, and completion rate use different denominators. Write the question in one sentence before entering values.
A change rate from zero is undefined under the usual formula. Moving from zero to 100,000 won is a 100,000-won new amount, not a conventional finite percentage increase. Negative profit values and temperatures also require contextual interpretation rather than ordinary retail-discount language.
- Share uses the whole as denominator
- Growth uses the earlier value
- Explain zero or negative bases separately
Calculate stacked discounts in their actual order
Do not add successive rates. A 120,000-won item discounted 25% becomes 90,000 won; another 10% reduces it to 81,000 won. The effective discount is 32.5%, not 35%, a 3,000-won difference.
A fixed coupon and percentage coupon may give different totals depending on order. From 100,000 won, subtracting 10,000 then taking 10% gives 81,000; taking 10% then subtracting 10,000 gives 80,000. Follow the merchant's checkout order and account for minimum purchase and maximum discount caps.
- Apply each rate to the remaining price
- Confirm the order of fixed and percentage coupons
- Treat thresholds and caps as separate rules
Use growth, reverse pricing, and target calculations
Required growth from a current value to a target is (target-current) ÷ current × 100. Moving from 800 visitors to 1,000 requires 25%. After a 20% drop, a 25% increase—not 20%—is needed to return to the original value because the second percentage uses the smaller base.
To recover an original price, divide the discounted price by one minus the discount rate. If 80,000 won is the result after 20% off, the original is 100,000, not 96,000. Include the formula, comparison period, decimal precision, and rounding rule in reports so another reader can reproduce the result.
- Required growth = (target-current) ÷ current
- Original = discounted price ÷ (1-discount rate)
- Label the base value and comparison period
Validation checklist and common questions
Check whether the metric can legitimately exceed 100%, whether a decline below negative 100% makes sense for the quantity, and where rounding occurred. Rounding after every step can differ from rounding only the final amount. Keep taxes, shipping, points, and statement credits separate when they sit outside the item price.
A 20% discount followed by a 20% increase does not restore the original: 100,000 becomes 80,000 and then 96,000. Percentages from groups of unequal size should not be averaged directly either. Recalculate the combined percentage from the combined underlying counts.
When publishing a percentage, show the original and final values. A rate alone hides scale, and a large percentage from a very small sample can overstate practical importance.
- Distinguish intermediate from final rounding
- Separate checkout additions and credits
- Weight group percentages by the underlying counts