How to Calculate Percentages: 5 Formulas for Everyday Math

To calculate a percentage, turn the percent into a decimal by dividing it by 100. Then multiply it by the number you're taking the percentage of. For example, 15% of 80 is 0.15 × 80 = 12. To find what percent one number is of another, divide the part by the whole and multiply by 100: 12 ÷ 80 × 100 = 15%.

Almost every everyday percentage question fits one of five formulas: X% of Y, what percent X is of Y, percent change, adding or removing a percentage, and working backward to an original value. The arithmetic stays simple. Where people go wrong is picking the base, meaning the number the percentage is measured against.

Below, each formula comes with a worked example and a shortcut you can do in your head. After that, you'll find the mistakes that cause most wrong answers.

The one idea behind every percentage formula

"Percent" means "per hundred," so 35% is 35/100, or 0.35. Every formula in this article is a rearrangement of one relationship:

part = rate × base

Here, the rate is the percentage written as a decimal. If you know two of the three values, you can find the third. The five formulas just cover the common ways that question shows up.

In the last two rows, p is the percentage as a plain number, so for 30% you use p = 30 and p/100 = 0.30.

Formula 1: How to find X% of Y

Multiply Y by the percentage as a decimal.

Worked example: an 18% tip on a $65 bill

1. Convert the percent: 18 ÷ 100 = 0.18.
2. Multiply: 0.18 × 65 = 11.70.
3. The tip is $11.70, and the total is $65 + $11.70 = $76.70.

Mental-math shortcut: build from 10% and 1%

To get 10% of a number, move the decimal point one place left. To get 1%, move it two places. Then combine the pieces:

• 10% of 65 = 6.50
• 1% of 65 = 0.65
• 20% = 2 × 6.50 = 13.00
• 18% = 20% − 2% = 13.00 − 1.30 = 11.70

A second trick is that X% of Y always equals Y% of X, because both are X × Y ÷ 100. So 8% of 50 is the same as 50% of 8, which is 4. Swap the numbers whenever the swapped version is easier.

Formula 2: How to calculate what percent X is of Y

Divide the part by the whole, then multiply by 100.

Worked example: a test score of 42 out of 56

1. Divide: 42 ÷ 56 = 0.75.
2. Multiply by 100: 0.75 × 100 = 75%.

Mental-math shortcut: simplify the fraction or count in 1% steps

If the fraction reduces to something familiar, you're done. 42/56 reduces to 3/4 (divide both by 14), and 3/4 is 75%.

When it doesn't reduce neatly, work out 1% of the whole and count how many of those fit into the part. What percent is 27 of 120? 1% of 120 is 1.2. Then 27 ÷ 1.2 = 22.5, so the answer is 22.5%. You can also build it up: 20% of 120 is 24, and the remaining 3 is 2.5% (because 3 ÷ 1.2 = 2.5). That gives 22.5% again.

Formula 3: How to calculate percent increase and decrease

Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive result is an increase. A negative result is a decrease.

Worked example: rent rising from $1,200 to $1,260

1. Change: 1,260 − 1,200 = 60.
2. Divide by the old value: 60 ÷ 1,200 = 0.05.
3. Multiply by 100: a 5% increase.

Worked example: a price dropping from $80 to $68

1. Change: 68 − 80 = −12.
2. Divide by the old value: −12 ÷ 80 = −0.15.
3. Multiply by 100: a 15% decrease.

Mental-math shortcut: find 1% or 10% of the starting value

1% of $1,200 is $12, and the $60 change is 5 of those, so it's 5%. For the price drop, 10% of $80 is $8 and 5% is $4. Since $12 = $8 + $4, the drop is 15%.

Percent vs. percentage points

When the thing that changes is itself a percentage, keep two kinds of change apart. If an interest rate goes from 4% to 5%, it rose by 1 percentage point, which is simple subtraction. In relative terms, it rose by 25%, because 1 ÷ 4 = 0.25. Both statements are correct, but they mean different things. Saying "the rate went up 1%" is ambiguous.

Formula 4: How to add or subtract a percentage

To add a percentage, multiply by (1 + p/100). To subtract one, multiply by (1 − p/100). This one-step multiplier saves you from calculating the percentage and then adding or subtracting it separately.

Worked example: 7.5% sales tax on a $40 item

1. Multiplier: 1 + 7.5/100 = 1 + 0.075 = 1.075.
2. Multiply: 40 × 1.075 = 43.00.
3. You pay $43.00, and $3.00 of that is tax.

Worked example: 30% off an $85 jacket

1. Multiplier: 1 − 30/100 = 1 − 0.30 = 0.70.
2. Multiply: 85 × 0.70 = 59.50.
3. The sale price is $59.50, a saving of $25.50.

Stacked percentages multiply, they don't add

Multipliers also show why "20% off, then an extra 10% off at checkout" doesn't mean 30% off. The second discount applies to the already-reduced price:

• 0.80 × 0.90 = 0.72
• On a $100 item: $100 → $80 → $72

You pay 72% of the original price, so the total discount is 28%, not 30%. The same rule covers a raise followed by a cost-of-living adjustment, or growth over several years. Multiply the multipliers. Don't add the percentages.

Mental-math shortcut

For a discount, think in terms of what you keep. "30% off" means you pay 70%. Then 10% of 85 is 8.50, and 7 × 8.50 = 59.50.

Formula 5: How to find the original price before a discount or tax

This is the reverse percentage. You know the final amount and the percentage that was applied, and you want the starting value. Divide by the same multiplier you would have multiplied by.

• After an increase (tax, markup): original = final ÷ (1 + p/100)
• After a decrease (discount): original = final ÷ (1 − p/100)

Worked example: you paid $54 after a 25% discount

1. You paid 75% of the original price, so the multiplier is 1 − 0.25 = 0.75.
2. Divide: 54 ÷ 0.75 = 72.
3. Check: 72 × 0.75 = 54. The original price was $72.

Worked example: a $86.40 total that includes 8% tax

1. Multiplier: 1 + 0.08 = 1.08.
2. Divide: 86.40 ÷ 1.08 = 80.
3. The pre-tax price was $80.00, and the tax was $6.40.

Mental-math shortcut: know the "inside share"

When a percentage has been added on, the added part makes up a smaller share of the new total than the rate suggests. If 20% was added, the total is 120% of the original, and the added part is 20/120 = 1/6 of the total. For a $150 price that includes 20% VAT (value-added tax), the tax is 150 ÷ 6 = $25 and the net price is $125. Check: 125 × 1.20 = 150.

The general rule is p ÷ (100 + p), with p as a plain number. For 25%: 25 ÷ 125 = 0.20, or 20%.

Common percentage mistakes and how to avoid them

Using the wrong base

"More than" and "less than" use different bases, so they give different percentages. Suppose A = 125 and B = 100:

• A is 25% more than B, because 25 ÷ 100 = 0.25.
• B is 20% less than A, because 25 ÷ 125 = 0.20.

The difference is 25 either way, but the base changes. Before you divide, ask: "percent of what?" The word after "than" or "of" is usually the base.

Undoing a 20% increase by subtracting 20%

If a price goes from $100 up 20% to $120, and then drops 20%, it doesn't come back to $100:

• 120 × 0.80 = 96

The 20% decrease is measured from the larger number, so it takes off $24, not $20. To truly undo a 20% increase, divide by 1.20, which is a decrease of 1/6, or about 16.67%. It works the other way too. An investment that falls 50% needs a 100% gain to get back to where it started ($200 → $100 → $200).

Removing tax by subtracting the tax rate from the total

Taking 8% off the $86.40 total from earlier gives 86.40 × 0.92 = 79.488, or about $79.49. That's wrong, because the 8% was calculated on $80, not on $86.40. Divide by 1.08 instead.

Averaging percentages with different bases

If you scored 9 out of 10 (90%) on one quiz and 30 out of 50 (60%) on another, your overall score is not 75%. Add the parts and the wholes: 39 ÷ 60 = 0.65, or 65%. A plain average of percentages only works when the bases are equal.

Rounding too early

Keep full precision until the last step. For example, if you round 1/3 to 33%, then 33% of $90 = 0.33 × 90 = $29.70 instead of the correct $30, so a 30-cent error appears before any later steps. Errors like this grow in reverse percentages and chained changes, because each step builds on the rounded result.

How to calculate percentages on a calculator or spreadsheet

On a calculator, the safest method is to type the decimal yourself. Enter 65 × 0.18 rather than relying on the % key. What the % key does varies between calculators and phone apps, especially when it's combined with + or −. If you do use it, check it against a calculation you already know.

In spreadsheet apps such as Microsoft Excel and Google Sheets, the % sign works inside formulas, so =A2*18% returns 18% of the value in A2. Useful patterns:

• Percent of a total: =B2/C2, then format the cell as a percentage
• Percent change: =(C2-B2)/B2
• Add tax: =A2*(1+B2), where B2 holds the rate entered as 7.5% or 0.075
• Original before a discount: =A2/(1-B2)

Formatting a cell as a percentage only changes how it looks. The underlying value 0.05 shows up as 5%, so don't multiply by 100 a second time.

Quick reference: percentage checklist

Before you calculate:

1. Name the base. Ask "percent of what?" For a change, the base is the old value.
2. Convert the percent to a decimal by dividing by 100.
3. Choose the formula: find a part, find a rate, measure a change, apply a change, or reverse one.
4. For several changes in a row, multiply the multipliers.
5. To undo a percentage change, divide by the multiplier. Never subtract the same percentage.
6. Round only at the end.
7. Sanity-check the result. A discount should lower the price, and a reversed tax total should be smaller than the receipt total.

Useful fraction equivalents for mental math:

Frequently Asked Questions

How do I calculate the percentage difference between two numbers when neither one is the starting value?

Use the average of the two numbers as the base: divide the absolute difference by their average and multiply by 100. For 40 and 60, the difference is 20 and the average is 50, so the percentage difference is 20 ÷ 50 × 100 = 40%. Use percent change instead when one value clearly came first.

How do I find a percentage of a percentage?

Convert both to decimals and multiply them. For example, 40% of 25% is 0.40 × 0.25 = 0.10, or 10%. This often comes up with shares of a group, such as 40% of the 25% of customers who signed up for a newsletter.

Can a percentage be more than 100%?

Yes. A value can be more than 100% of another value, and an increase can be more than 100%. Going from 50 to 150 is a 200% increase. A decrease can't be more than 100% for something that can't go below zero, such as a price.

How do I convert a fraction or decimal into a percentage?

For a fraction, divide the top number by the bottom number, then multiply by 100. So 3/8 = 0.375 = 37.5%. For a decimal, just multiply by 100, which means moving the decimal point two places to the right: 0.062 becomes 6.2%.

Is a 50% increase followed by a 50% decrease a net zero change?

No. The multipliers are 1.5 and 0.5, and 1.5 × 0.5 = 0.75, so you end up 25% below where you started. For example, 100 rises to 150 and then falls to 75. The order doesn't change the result, because multiplication gives the same answer either way.