How to Calculate Percentages
How to calculate percentage problems: X% of Y, what percent one number is of another, the percentage increase formula, reverse percentages and common mistakes.
By Udit Agarwal · Updated October 17, 2026
To calculate a percentage, divide the part by the whole and multiply by 100: 30 out of 150 is 30 ÷ 150 × 100 = 20%. Every everyday percentage question, from a discount to a pay rise, is a rearrangement of one relationship: part = percent ÷ 100 × whole. Once you know which number is the whole, the rest is a single multiplication or division.
Per cent means "per hundred", so 20% is 20 hundredths: 20/100, or 0.20 as a decimal. To turn a percentage into a decimal, divide it by 100. To turn a decimal or a fraction into a percentage, multiply by 100: 3/4 is 0.75, or 75%, and 1/3 is 0.333…, or 33.33% to two decimal places.
Part, whole and percent are linked, so knowing any two gives the third:
| You know | You want | Formula | Example |
|---|---|---|---|
| Percent and whole | Part | whole × percent ÷ 100 | 20% of 150 = 30 |
| Part and whole | Percent | part ÷ whole × 100 | 30 of 150 = 20% |
| Part and percent | Whole | part ÷ percent × 100 | 30 is 20% of 150 |
| Old and new value | Percent change | (new − old) ÷ old × 100 | 100 to 150 = +50% |
Turn the percent into a decimal and multiply. 20% of 150 is 0.20 × 150 = 30. A 15% tip on a $64 bill is 0.15 × 64 = $9.60, and 17.5% of 80 is 0.175 × 80 = 14.
For mental arithmetic, start from 10%, which just moves the decimal point one place left: 10% of $64 is $6.40. Half of that is 5% ($3.20), and the two together make 15% ($9.60). Percentages can also be swapped around: 8% of 50 is the same as 50% of 8, which is 4. The Tip Calculator does the tip version for a whole bill and splits it between people.
Divide the part by the whole and multiply by 100. 42 correct answers out of 48 is 42 ÷ 48 × 100 = 87.5%. In "X is what percent of Y", X always goes on top: 30 is 20% of 150, but 150 is 500% of 30. A result above 100% simply means the part is bigger than the whole you are comparing it with.
The same division gives the share of a loan payment that goes to interest: $1,000 of a $1,199.10 mortgage payment is 83%, as the amortization guide shows.
Percentage change = (new value − old value) ÷ old value × 100. A positive answer is an increase and a negative one is a decrease.
The base is always the starting value, which is why the same move of 50 is a different percentage up than down. A related measure, percent error, compares a measured value with a true one: |measured − true| ÷ |true| × 100. A reading of 9.8 against a true 9.81 is about 0.10% off, and the Percent Error Calculator works it out.
When the quantity is itself a percentage, such as an interest rate, "up 1%" is ambiguous. A rate that goes from 4% to 5% has risen by one percentage point, but by 25% in relative terms, because 1 is 25% of 4. A mortgage rate moving from 6% to 7% is up one point, or 16.67%. Using "percentage points" for the plain difference and "percent" for the relative change keeps the two apart. The mortgage guide shows what that one-point move does to a monthly payment.
When a number already has a percentage added or taken off, divide to undo it. Applying the same percentage in the other direction gives the wrong answer.
After a 25% discount, a jacket costs $60. The sale price is 75% of the original, so the original was 60 ÷ 0.75 = $80. Adding 25% to $60 gives $75, which is wrong because the 25% was taken off $80, not $60.
A receipt shows $108 including 8% sales tax. The total is 108% of the pre-tax price, so the price was 108 ÷ 1.08 = $100 and the tax was $8. Taking 8% off $108 gives $99.36, wrong for the same reason. In general:
With 20% VAT, the tax inside a gross price is one-sixth of it (20 ÷ 120), so £240 including VAT is £200 plus £40 of VAT. The Sales Tax Calculator and the VAT Calculator both have a remove mode that does this division. For money questions like these, treat the results as estimates rather than financial or tax advice, because the rate and rounding rules that apply depend on where you buy.
A fall and an equal rise do not cancel out. A $100 price cut by 50% is $50, and raising $50 by 50% gives $75, not $100. After a fall of L%, getting back to the start takes a rise of L ÷ (100 − L) × 100%:
| Fall | Rise needed to get back |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 25% | 33.33% |
| 50% | 100% |
| 75% | 300% |
The same happens with small changes: up 10% and then down 10% takes 100 to 99, a 1% loss.
Stacked discounts do not add. 20% off followed by an extra 10% off is 28% off, not 30%: $100 becomes $80, then $72. Multiply what remains instead, 0.80 × 0.90 = 0.72. The Discount Calculator takes a stacked second discount and reports the effective total.
Growth over several periods compounds. Three years of 10% growth is 1.1 × 1.1 × 1.1 = 1.331, a rise of 33.1%, not 30%. The compound interest guide covers that effect in detail.
Percentages with different bases cannot be averaged directly. A student who scores 18 out of 20 (90%) on one test and 30 out of 50 (60%) on another has not averaged 75%. Combined, it is 48 out of 70, or 68.57%.
Margin is not markup. An item that costs $40 and sells for $100 makes $60 profit: a 150% markup on the cost but a 60% margin on the price. The Profit Margin Calculator shows both.
The Percentage Calculator has three modes: X% of Y (a percent and a value), X is what % of Y (a part and a whole) and Percent change (a from value and a to value). Each answer comes with a worked line, such as "20% of 150 = 30", and the result or the line can be copied. Results are rounded to two decimal places. Negative numbers and percentages over 100 work, and commas, % signs and the $, €, £ and ₹ symbols typed into the fields are ignored. A whole of 0, or a starting value of 0, gives an error, because the formula would divide by zero.
There is no mode for reverse percentages or percentage points, so use the formulas above, or the sales tax, VAT and discount calculators for prices. Percent change is meant for positive starting values: from a negative start, such as −50 rising to −25, the formula returns −50% even though the number went up. The calculation runs in your browser and nothing you type is uploaded.
How do I calculate a percentage of a number? Multiply the number by the percentage and divide by 100. 20% of 150 is 0.20 × 150 = 30, and 15% of $64 is $9.60.
What is the formula for percentage increase? Percentage increase = (new value − old value) ÷ old value × 100. From $80 to $92 is (92 − 80) ÷ 80 × 100 = 15%. A negative result means the value fell.
How do I calculate a percentage decrease? Use (old value − new value) ÷ old value × 100 to get a positive figure. From $150 to $120 is 30 ÷ 150 × 100, a 20% decrease.
How do I find the original price before a discount? Divide the sale price by the share that remains after the discount. After 25% off, $60 ÷ 0.75 = $80. Adding 25% back to $60 gives the wrong answer, $75.
What is the difference between percent and percentage points? Percentage points are the plain difference between two percentages, and percent is the change relative to the starting value. A rate moving from 4% to 5% is up one percentage point, which is a 25% increase.
Why doesn't a 50% drop followed by a 50% rise get back to the start? The rise is calculated on the smaller number. 100 falls to 50, and 50% of 50 is only 25, so it ends at 75. After a 50% fall, it takes a 100% rise to recover.
How do I calculate a percentage in Excel or Google Sheets? Divide the part by the whole, for example =A2/B2, and format the cell as a percentage. For percentage change, use =(B2-A2)/A2 with the old value in A2 and the new one in B2.