how to calculate percentage
Calculating a percentage means applying a base-100 fraction to a value. The formula barely changes with the question, how much is P% of a number, what percent one number is of another, or how much a value changed, but the usual mix-up is not the arithmetic: it is confusing percent change with a percentage point.
The calculator divides 15 by 100, getting 0.15, and multiplies by 200: 0.15 × 200 = 30. It is the same arithmetic used for discounts, simple interest and any P% of V.
The formula (final − initial) ÷ initial × 100 gives (6 − 4) ÷ 4 × 100 = 50%. In percentage points the difference is only 2, showing how the two readings diverge for the same pair of numbers.
120 × 0.80 = 96, four short of the original 100 before the 20% increase. The following discount applies to the already larger base, which is why the value never returns to its starting point.
Start with 10%, which is the value divided by 10, and build the rest from it: 1% is dividing by 100, 5% is half of 10%, 20% is double 10%, 25% is dividing by 4 and 50% is dividing by 2. For 15% of 80, take 10% (8) plus 5% (4), which is 12. For 35% of 200, add 30% (60) and 5% (10), which is 70. If the numbers are awkward, swap the order: 8% of 50 equals 50% of 8, which is 4.
Because the second percentage is taken from a different base: 100 rises to 120 with the increase, and the following 20% discount is calculated on 120, not on 100, giving 96 instead of the original 100.
A percentage point is the plain subtraction between two percentages, 6% − 4% = 2 points; percent change is that same difference divided by the starting base and multiplied by 100, which gives 50% for a rate rising from 4% to 6%.
Divide the number by the reference and multiply by 100: 30 divided by 150 gives 0.20, which times 100 is 20%. The same formula works to find a test score as a percentage or a budget line's share of the total.
Find how much a percentage of a value is.
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