Quick answer: To find X% of a number, multiply the number by X and divide by 100. For example, 20% of 80 is 80 × 20 ÷ 100 = 16. The same idea, rearranged, gives you every other percentage calculation in this guide.
Percent means "out of one hundred", and that single idea is the key to every percentage question. A percentage is just a fraction with 100 on the bottom, written in a shorter way. Fifty percent is 50 out of 100, which is one half. Twenty-five percent is 25 out of 100, which is one quarter. Once you see a percentage as a fraction, the formulas stop looking like separate rules and start looking like the same calculation done in different directions.
The Five Percentage Formulas
There are five calculations people need most often. They look different, but they all come from the same relationship: part, whole, and percentage are linked by the equation percentage = (part ÷ whole) × 100. Rearrange that equation and you get the other four.
| What you want | Formula | Example |
|---|---|---|
| X% of Y | Y × X ÷ 100 | 20% of 80 = 16 |
| What % is X of Y? | X ÷ Y × 100 | 25 is 12.5% of 200 |
| Percentage increase | (New − Old) ÷ Old × 100 | 50 to 65 = 30% increase |
| Percentage decrease | (Old − New) ÷ Old × 100 | 80 to 60 = 25% decrease |
| Original value (reverse %) | Value ÷ (1 ± % ÷ 100) | $80 after 20% off = $100 originally |
Keep this table to hand while you read the examples below. Each section works through one row in detail, so you can see the formula in action before you try it yourself.
Formula 1: What Is X% of Y?
This is the most common percentage question. You know the percentage and the whole, and you want the part.
Formula: Part = Whole × Percentage ÷ 100
Worked example: What is 20% of 80?
Step 1: Write down the whole (80) and the percentage (20). Step 2: Multiply 80 by 20, which is 1,600. Step 3: Divide 1,600 by 100, which is 16.
So 20% of 80 is 16. A quicker way to see it is to turn 20% into a decimal first. Twenty percent is 0.20, and 80 × 0.20 = 16. The decimal method is the same calculation with the division by 100 done first.
Formula 2: What Percentage Is X of Y?
Here you know the part and the whole, and you want the percentage. This is the question behind exam marks, survey results, and progress towards a goal.
Formula: Percentage = Part ÷ Whole × 100
Worked example: 25 is what percent of 200?
Step 1: Divide the part by the whole: 25 ÷ 200 = 0.125. Step 2: Multiply by 100: 0.125 × 100 = 12.5.
So 25 is 12.5% of 200. The division gives you a decimal, and multiplying by 100 turns that decimal into a percentage. If the division gives a repeating decimal, round the percentage to one or two decimal places and say so: 1 out of 3 is 33.33%, not exactly 33%.
A practical example: you scored 36 out of 45 on a test. Divide 36 by 45 to get 0.8, multiply by 100, and you get 80%. If you scored 27 out of 40, the calculation is 27 ÷ 40 = 0.675, which is 67.5%. The same formula works for money: if you saved $30 out of a $150 budget, you saved 30 ÷ 150 × 100 = 20% of the budget.
Formula 3: Percentage Increase
A percentage increase tells you how much something has grown, relative to where it started. The starting value is always the denominator, because the increase is measured against the original amount.
Formula: Increase % = (New Value − Old Value) ÷ Old Value × 100
Worked example: a price rises from $50 to $65. What is the percentage increase?
Step 1: Find the increase: $65 − $50 = $15. Step 2: Divide the increase by the old value: $15 ÷ $50 = 0.3. Step 3: Multiply by 100: 0.3 × 100 = 30%.
So the price rose by 30%. A common mistake is to divide by the new value instead of the old one. Dividing $15 by $65 gives 23%, which is wrong, because the increase is measured from the starting price, not the final price.
Formula 4: Percentage Decrease
A percentage decrease works the same way, with the old value again as the denominator. The only difference is that the new value is smaller than the old one.
Formula: Decrease % = (Old Value − New Value) ÷ Old Value × 100
Worked example: a price falls from $80 to $60. What is the percentage decrease?
Step 1: Find the decrease: $80 − $60 = $20. Step 2: Divide the decrease by the old value: $20 ÷ $80 = 0.25. Step 3: Multiply by 100: 0.25 × 100 = 25%.
So the price fell by 25%. Notice that a 25% decrease does not undo a 25% increase. If a $80 item falls by 25% to $60, and then rises by 25%, it rises by 25% of $60, which is $15, to $75, not back to $80. Percentages are always relative to the value you start from, so the same percentage means a different amount when the starting value changes.
Formula 5: Reverse Percentage — Finding the Original Value
Reverse percentage is the trickiest of the five, because it is easy to add the percentage back on instead of dividing it out. It answers questions such as: "This shirt costs $80 after a 20% discount. What was the original price?" Adding 20% to $80 gives $96, which is wrong.
For a discount: Original = Sale Price ÷ (1 − Discount ÷ 100) For an increase: Original = Final Value ÷ (1 + Increase ÷ 100)
Worked example: after a 20% discount, a shirt costs $80. What was the original price?
Step 1: The sale price is 80% of the original, because 100% − 20% = 80%. Step 2: Write 80% as a decimal: 0.80. Step 3: Divide the sale price by that decimal: $80 ÷ 0.80 = $100.
So the original price was $100. Check it: 20% of $100 is $20, and $100 − $20 = $80, which matches the sale price.
Common Mistakes to Avoid
The most common mistake is using the wrong denominator. In an increase or decrease, always divide by the old value, not the new one. In a "what percentage is X of Y" question, always divide by Y, the whole, not by X, the part. Writing down which number is the part and which is the whole before you start will prevent most errors.
A second mistake is confusing percentage points with percent. If an interest rate rises from 5% to 7%, it has risen by 2 percentage points, but that is a 40% increase in the rate itself, because 2 ÷ 5 = 0.4. News reports usually mean percentage points when they say "rose by 2%", but the maths behind the two phrases is different.
If you want to check your work on any of these, the percentage calculator will work through the same formulas for you. It is useful for checking a homework answer, a shop discount, or a salary change before you rely on it. For a related calculation, the discount calculator applies the same percentage idea directly to prices.
Try it: Check any percentage in seconds with the Percentage Calculator — find a percentage of a number, work out what percentage one number is of another, or find the original value.
Frequently Asked Questions
How do you calculate 20% of a number? Multiply the number by 20 and divide by 100, or multiply by 0.20. For example, 20% of 80 is 80 × 0.20 = 16. To find 10%, move the decimal point one place left, then double it for 20%.
How do you work out what percentage one number is of another? Divide the part by the whole and multiply by 100. For example, 25 is 12.5% of 200, because 25 ÷ 200 = 0.125 and 0.125 × 100 = 12.5. Always divide by the whole, not by the part.
How do you calculate percentage increase? Subtract the old value from the new value, divide by the old value, and multiply by 100. A rise from $50 to $65 is ($65 − $50) ÷ $50 × 100 = 30%. The old value is always the denominator.
How do you find the original price after a discount? Divide the sale price by (1 − discount as a decimal). If a shirt costs $80 after a 20% discount, the original price is $80 ÷ 0.80 = $100. Adding 20% to $80 gives $96, which is wrong.
