How to solve the 7 most common percentage problems
Learn the exact math formulas to calculate tips, discounts, salary raises, and percent changes. This guide breaks down the seven most common percentage problems with easy real-world examples.
Jun 25, 2026 5 min read
A percentage is just a number out of 100. Saying 25% means 25 parts out of a total of 100. The basic concept is simple, but real-world math gets confusing because the formulas change depending on what you are trying to solve. Figuring out a tip takes different math than calculating a sale discount or tracking a stock portfolio. Here are the exact formulas for the seven most common percentage problems.
1. How do I calculate a percentage of a number?
This is the math you use to figure out a restaurant tip or set aside a portion of your freelance income for taxes. To find a percentage of a specific number, multiply that number by the percentage divided by 100.
Formula: Y × (X ÷ 100)
If you have a restaurant bill of $54.50 and want to leave an 18% tip, first convert 18% into a decimal by dividing it by 100. That gives you 0.18. Then multiply your bill by that decimal.
$54.50 × 0.18 = $9.81. Your tip is $9.81.
2. How do I find what percent one number is of another?
Use this when you have a part and a whole, and you need to know what percentage the part represents. Divide the first number by the second number. Then multiply the result by 100 to turn it back into a percentage.
Formula: (X ÷ Y) × 100
Say an item originally cost $80 and is now on sale for $60. You want to know what percent $60 is of $80.
60 ÷ 80 = 0.75. Multiply by 100, and you get 75%. Since the new price is 75% of the original price, you are getting a 25% discount.
A quick caveat: If your second number (your “whole”) is zero, this math is impossible. You cannot divide by zero.
3. How is percent change calculated?
Percent change measures how much a value has grown or shrunk relative to its starting point. Subtract the original number from the new number. Divide that difference by the absolute value of the original number (its distance from zero, ignoring any negative signs), and multiply by 100.
Formula: ((New − Original) ÷ abs(Original)) × 100
A positive result means an increase. A negative result means a decrease.
If a stock you own falls from $120 a share to $90 a share, plug those numbers in: 90 − 120 = −30. −30 ÷ 120 = −0.25. −0.25 × 100 = −25%.
The stock experienced a 25% decrease. Conversely, if a metric grows from 80 to 100, the math is (100 − 80) ÷ 80 = 0.25, which translates to a 25% increase.
4. How do I increase a number by a percentage?
Adding a percentage to an existing number is how you calculate a salary raise or add sales tax to a purchase. Multiply the original number by 1 plus the percentage expressed as a decimal.
Formula: Y × (1 + (X ÷ 100))
Imagine you currently earn $65,000 a year and receive a 4.5% raise. First, divide 4.5 by 100 to get 0.045. Add 1 to get 1.045. Multiply your current salary by this number:
$65,000 × 1.045 = $67,925. Your new salary will be $67,925.
5. How do I decrease a number by a percentage?
To decrease a number by a certain percentage, multiply the original number by 1 minus the decimal percentage.
Formula: Y × (1 − (X ÷ 100))
If you need to decrease 200 by 15%, convert 15% to 0.15. Subtract that from 1, leaving you with 0.85.
200 × 0.85 = 170.
Summary of core formulas
Here is a quick reference table for the five primary operations to keep them distinct.
| Goal | Math Formula | Example |
|---|---|---|
| What is X% of Y? | Y × (X ÷ 100) | 15% of 200 = 30 |
| X is what % of Y? | (X ÷ Y) × 100 | 30 of 200 = 15% |
| % change X to Y | ((Y − X) ÷ abs(X)) × 100 | 80 → 100 = +25% |
| Increase Y by X% | Y × (1 + (X ÷ 100)) | 200 + 15% = 230 |
| Decrease Y by X% | Y × (1 − (X ÷ 100)) | 200 − 15% = 170 |
6. If a value drops 20% and then gains 20%, am I back to where I started?
No. This is a common mathematical error known as the symmetry trap. Percentages are relative to their starting point, which means the base number changes after the first calculation.
If you start with $100 and lose 20%, you subtract $20. You are left with $80. If you then gain 20% on that $80, you do not get $20 back. You gain 20% of $80, which is only $16. $80 + $16 = $96.
A 20% drop followed by a 20% gain actually results in a 4% net loss. To recover fully from a 20% loss (getting from $80 back up to $100), you need a 25% gain.
7. What is the difference between a percentage and a percentage point?
Headlines routinely confuse these two terms, but they measure completely different things. A percentage measures a relative change. A percentage point measures an absolute difference between two rates.
If a bank’s interest rate moves from 4% to 5%, that is an increase of exactly 1 percentage point (5 − 4 = 1).
However, it is a 25% relative increase. Because 1 is 25% of 4, the rate itself has grown by a quarter of its original size. If a loan officer tells you your rate is going up by “one percent,” always clarify whether they mean it is moving to 4.04% (a 1% relative increase) or to 5% (a 1 percentage point increase).
If you want to skip doing the algebra by hand, you can run all five of these core operations instantly using our Percentage Calculator.