Percentage Calculations Explained: Percent Change, Percentage Points, Stacked Discounts and VAT

Four basic formulas

A percentage is a ratio expressed per hundred. Every percentage calculation comes down to choosing the right base (the denominator), and most everyday cases fit one of these four.

① What is B% of A?        A × B ÷ 100          (15% of 80,000 = 12,000)
② A is what % of B?       A ÷ B × 100          (12 ÷ 48 × 100 = 25%)
③ Change from A to B      (B − A) ÷ A × 100    (200 → 250 = +25%)
④ A increased/decreased   A × (1 ± B ÷ 100)    (50,000 + 20% = 60,000)

Change the base, change the result

100 plus 50% is 150. But 150 minus 50% is 75, not 100, because the base for the decrease is 150. Likewise, a share that falls 50% must rise 100%, not 50%, to recover.

When reporting growth, always divide by the earlier value: year-on-year growth is (this year − last year) ÷ last year. Dividing by this year's figure understates growth.

Percent versus percentage points

If an interest rate moves from 2% to 3%, it rose by one percentage point (1 pp). In percent terms the rise is (3 − 2) ÷ 2 × 100 = 50%.

The distinction matters for any metric already expressed in percent—approval ratings, unemployment, interest rates, conversion rates. Describing a conversion rate going from 4% to 5% as a '1% improvement' understates what is really a 25% improvement.

Stacked discounts: 20% + 10% is not 30%

A 20% discount on a 100,000 item gives 80,000. An extra 10% coupon applies to the discounted 80,000, not the original price, giving 72,000. The total discount is 28%, not 30%.

In general, the final price is list × (1 − a) × (1 − b) and the total discount is 1 − (1 − a)(1 − b). The order does not matter, but claims like 'up to 30% off' should match the real calculation.

Working backwards: original prices and VAT

If 72,000 is the price after a 20% discount, the original was 72,000 ÷ 0.8 = 90,000. Adding 20% to 72,000 (86,400) is a common mistake: the discount's base was the original price, so you must divide.

Korean VAT is 10%. To split a VAT-inclusive 110,000 into net and tax, divide by 1.1: 100,000 net plus 10,000 VAT. Subtracting 10% of 110,000 (11,000) to get 99,000 is wrong. The same logic applies to any tax rate.

Percentages in everyday business

The AIBIZAP percent calculator handles the basic cases instantly, and for multi-step calculations you can type the whole formula into the step-by-step expression calculator to see every intermediate result.

• Margin versus markup: cost 7,000 and price 10,000 give a margin of profit ÷ price = 30% and a markup of profit ÷ cost ≈ 42.9%. Confusing them breaks pricing.
• Achievement rate: actual ÷ target × 100. 96 against a target of 120 is 80%.
• Share: part ÷ total × 100. Rounded shares may add up to 100.1% or 99.9%.
• Compound annual growth rate: do not average yearly growth rates; use (final ÷ initial)^(1 ÷ years) − 1.