The percentage calculator runs the four everyday formulas for you: a percent of a number, what percent one number is of another, the change between two numbers, and adding or taking off a percentage.
Open the percentage calculatorEvery percentage formula on one page
Almost every percentage question is one of these. “Old” is the starting value, “new” is the value after the change, and p is the percentage as a plain number (15 for 15%).
| To find | Formula | Example |
|---|---|---|
| Percentage | part ÷ whole × 100 | 18 ÷ 24 × 100 = 75% |
| Part (p% of a number) | p ÷ 100 × whole | 15 ÷ 100 × 80 = 12 |
| Whole, from a part and its % | part ÷ p × 100 | 12 ÷ 15 × 100 = 80 |
| Percentage increase | (new − old) ÷ old × 100 | (65 − 50) ÷ 50 × 100 = 30% |
| Percentage decrease | (old − new) ÷ old × 100 | (50 − 40) ÷ 50 × 100 = 20% |
| Increase by p% | number × (1 + p ÷ 100) | 200 × 1.15 = 230 |
| Decrease by p% | number × (1 − p ÷ 100) | 200 × 0.85 = 170 |
| Original before an increase | new ÷ (1 + p ÷ 100) | 230 ÷ 1.15 = 200 |
| Original before a decrease | new ÷ (1 − p ÷ 100) | 170 ÷ 0.85 = 200 |
| Percentage difference | |a − b| ÷ ((a + b) ÷ 2) × 100 | |40 − 60| ÷ 50 × 100 = 40% |
The first three are the same relationship rearranged. Learn that one and the rest follow from it.
Part, whole and percent
A percentage is a fraction out of 100. Every basic question has three numbers in it, the part, the whole and the percentage, and gives you two of them:
part = percentage ÷ 100 × whole
- You want the percentage. 18 out of 24 people said yes: 18 ÷ 24 = 0.75, and 0.75 × 100 = 75%.
- You want the part. 15% of 80 is 0.15 × 80 = 12.
- You want the whole. 12 is 15% of what? 12 ÷ 0.15 = 80.
The whole is always the thing you are comparing against: the full class, the total bill, the original price. It goes on the bottom of the fraction. If an answer looks wrong, check which number you put underneath. The percentage of a number guide has more worked examples and mental shortcuts for this part.
Percent, fraction and decimal
A percentage, a fraction and a decimal are three ways of writing the same amount. To convert, divide or multiply by 100:
| Percent | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.3% | 0.333… | 1/3 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 150% | 1.5 | 3/2 |
A fraction becomes a percentage by dividing the top by the bottom and multiplying by 100: 3/8 = 0.375 = 37.5%. Knowing the common ones by heart is a fast check on any answer.
Percentage increase and decrease formula
Percentage change = (new − old) ÷ old × 100
A positive answer is an increase and a negative one is a decrease. Some people prefer to keep the answer positive and write the decrease formula the other way round, (old − new) ÷ old × 100. Both give the same size of change.
| Change | Working | Result |
|---|---|---|
| Rent goes from $1,200 to $1,290 | 90 ÷ 1,200 × 100 | 7.5% increase |
| A share falls from ₹840 to ₹756 | −84 ÷ 840 × 100 | 10% decrease |
| Visitors go from 3,500 to 4,200 | 700 ÷ 3,500 × 100 | 20% increase |
| Weight goes from 92 kg to 85 kg | −7 ÷ 92 × 100 | 7.6% decrease |
Always divide by the old value. Dividing by the new one is the most common slip and gives a different answer: 90 ÷ 1,290 is 7.0%, not 7.5%. The percentage increase guide covers the traps that come with it, such as a rise followed by a fall of the same percentage.
Adding or taking off a percentage in one step
To add a percentage, multiply by 1 plus the percentage as a decimal. To take one off, multiply by 1 minus it. This saves working out the amount and then adding or subtracting.
| Question | Multiplier | Answer |
|---|---|---|
| $64 plus 8.25% sales tax | × 1.0825 | $69.28 |
| ₹2,500 plus 18% GST | × 1.18 | ₹2,950 |
| $120 with 30% off | × 0.70 | $84 |
| A $48,000 salary with a 4% rise | × 1.04 | $49,920 |
| A 2 GB file made 35% smaller | × 0.65 | 1.3 GB |
Multipliers also handle changes in a row. A 10% rise followed by another 10% rise is × 1.10 × 1.10 = × 1.21, a 21% rise in total, not 20%. For shop prices, the discount calculator shows the sale price and the saving.
Finding the original amount (reverse percentage)
When you only know the number after a percentage was added or removed, divide by the same multiplier. Taking the percentage off the new number gives the wrong answer.
Original = new amount ÷ (1 + p ÷ 100) after an increase
Original = new amount ÷ (1 − p ÷ 100) after a decrease
- A receipt says ₹1,770 including 18% GST: 1,770 ÷ 1.18 = ₹1,500 before tax, so the GST was ₹270. Taking 18% off ₹1,770 gives ₹1,451.40, which is wrong.
- A coat costs $91 after 35% off: 91 ÷ 0.65 = $140 before the sale.
- A town has 46,000 people after growing 15%: 46,000 ÷ 1.15 = 40,000 before.
Percentage of marks formula
Percentage of marks = marks obtained ÷ total marks × 100
For a single paper, 68 out of 80 is 68 ÷ 80 × 100 = 85%. For several subjects, add up all the marks obtained and all the maximum marks first, then divide once.
| Subject | Marks | Out of |
|---|---|---|
| English | 72 | 100 |
| Maths | 88 | 100 |
| Science | 65 | 80 |
| History | 41 | 50 |
| Total | 266 | 330 |
266 ÷ 330 × 100 = 80.6%
Averaging the four subject percentages instead (72%, 88%, 81.25% and 82%) gives 80.8%, which is slightly off because the papers have different maximum marks. If your school or board says how to work out the overall percentage, follow its rule. Grades given as a CGPA use a conversion formula instead, which the CGPA to percentage converter handles.
Percent and percentage points
When the two numbers you are comparing are already percentages, there are two ways to describe the change, and they are easy to mix up:
- Percentage points are the plain difference. An interest rate going from 4% to 5% rose by 1 percentage point.
- Percent uses the change formula. The same move is (5 − 4) ÷ 4 × 100 = a 25% increase in the rate.
Both statements are true. News reports and loan offers usually mean points; if a rate is said to have “gone up 25%”, check which one is meant.
The same formulas in Excel or Google Sheets
With the old or whole value in A2 and the new value or part in B2:
| To find | Formula | Format the cell as |
|---|---|---|
| What percent B2 is of A2 | =B2/A2 | Percentage |
| Percentage change | =(B2-A2)/A2 | Percentage |
| 15% of A2 | =A2*15% | Number |
| A2 plus 15% | =A2*(1+15%) | Number |
| A2 minus 15% | =A2*(1-15%) | Number |
| Original before 15% was added | =A2/(1+15%) | Number |
The spreadsheet does the × 100 when you format the cell as a percentage. Multiplying by 100 as well gives answers like 7500%.
Common mistakes with percentage formulas
- Dividing by the wrong number. Change is measured against the old value; a share is measured against the whole.
- Adding percentages of different totals. 20% of one class and 30% of another isn’t 50% of anything.
- Reversing a change with the same percentage. A 20% fall needs a 25% rise to get back, because the second percentage is taken from a smaller number.
- Rounding halfway through. Keep every decimal until the final answer, then round once.
- Forgetting the 100. 18 ÷ 24 is 0.75. It only becomes 75 once you multiply by 100.