1. Percent of a Number
This is the one you use for tips, discounts, taxes, and commissions. The formula: Result = number x (percentage / 100). Move the decimal two places left on the percentage to turn it into a multiplier, then multiply.
Examples: 20% of 80 is 80 x 0.20 = 16. A 30% discount on $149 is 149 x 0.30 = $44.70 off, so you pay $104.30. 8.5% sales tax on $60 is 60 x 0.085 = $5.10.
For mental math, remember easy anchors: 10% is just moving the decimal one place left, 50% is half, 25% is a quarter. For 15%, take 10% and add half of that: on $200, 10% is $20, half is $10, so 15% is $30.
2. What Percent Is One Number of Another?
This answers "45 out of 180 is what percent?" and "I got 23 of 30 right, what is my score?" The formula: (part / whole) x 100.
So 45 / 180 = 0.25, times 100 = 25%. A test score of 23 out of 30 is 23 / 30 x 100 = 76.7%. This formula also powers every "X% of your daily goal" stat you have ever seen: if you walked 7,000 of a 10,000-step goal, you hit 70%.
The order matters and trips people up: the part you are measuring goes on top, the total goes on the bottom. Ask "what fraction of the whole is this?" first, then convert to a percent.
3. Percent Change (Increase and Decrease)
This one covers price changes, raises, growth stats, and weight loss. The formula: (new - old) / old x 100. Subtract the old value from the new value, divide by the old value, multiply by 100. Positive means an increase, negative means a decrease.
Gas going from $3.50 to $4.20: (4.20 - 3.50) / 3.50 x 100 = 20% increase. A salary moving from $60,000 to $66,000 is a 10% raise. A stock dropping from $120 to $90: (90 - 120) / 120 x 100 = -25%, a 25% drop.
The classic trap: a 50% increase followed by a 50% decrease does not return to the original. 100 becomes 150 after a 50% increase, but 50% off of 150 is 75, leaving you at 75, not 100. Each percentage applies to the current base, never the original.
One related distinction worth knowing: percentage points vs. percent. If an interest rate rises from 4% to 6%, that is a 2-percentage-point increase, but a 50% increase in the rate itself (2 / 4 x 100). Headlines often blur the two, so when a number sounds dramatic, check which one they mean.
Frequently Asked Questions
How do I find 15% of a number?
Multiply the number by 0.15. For example, 15% of 200 is 200 x 0.15 = 30. The trick: move the decimal two places left on the percentage (15% becomes 0.15), then multiply.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 45 out of 180 is (45 / 180) x 100 = 25%.
What is the percent change formula?
Percent change = (new value - old value) / old value x 100. A positive result is an increase, a negative result is a decrease. For example, going from 50 to 65 is a 30% increase.
Why is a 50% increase then a 50% decrease not back to the original?
Because the base changes. A 50% increase on 100 gives 150, but a 50% decrease on 150 takes off 75, leaving 75. Percentages always apply to the current base, not the original one.