Percentage Calculator Guide | Formulas & Examples

A percentage is a rate per hundred: to find X% of a number, multiply the number by X and divide by 100. Percentage change is (new value - original value) / original value, times 100. That is not the same thing as a percentage-point gap between two rates. This guide works each formula with numbers you can check, including discounts, tax, grades, and raises, then shows how to run them in the free Percentage Calculator in your browser, with no sign-up.

Key facts: percentage calculator formulas

Use this block when you need a direct answer:

• Percent of a number: result = number × (percent / 100). Example from Statistics Canada: 12% of 250 = 30.
• What percent is X of Y: (X / Y) × 100. The whole (Y) cannot be zero.
• Percentage change: ((new - original) / original) × 100. Eurostat writes the same idea as ((later / earlier) - 1) × 100. The original cannot be zero.
• Percentage points: subtract two percentages. A rate that moves from 4% to 7% rises by 3 percentage points, which is a 75% relative increase because 3 / 4 = 0.75.
• Percentage difference in this calculator is symmetric: absolute difference divided by the average of the two values, times 100. Swapping the two inputs does not change the result.
• Successive discounts do not add. 20% off, then 10% off, leaves 0.80 × 0.90 = 0.72 of the price, which is a 28% discount, not 30%.
• Reverse a single discount by dividing the sale price by (1 - discount as a decimal). $85 after 15% off was $100, because 85 / 0.85 = 100.

What is a percentage, and when do you need a calculator?

"Percent" means per hundred. One percent is one hundredth of a whole, so 1% of 250 is 2.5 and 100% of any number is the number itself. You convert a percent to a decimal by dividing by 100 (15% = 0.15) and a decimal to a percent by multiplying by 100 (0.72 = 72%).

A percentage calculator is worth opening when the base shifts, when two rates are easy to mix up, or when money has to be rounded to cents. Typical jobs:

• Shopping: a discount, then sales tax on the reduced price.
• School: points earned divided by points possible, or the score you still need on a final.
• Pay: a raise, a bonus that is a percent of salary, or overtime as a percent of base hours.
• Reporting: growth from last period, or the gap between two rates such as conversion or unemployment.

Which percentage formula should you use?

Pick the row that matches the question you are actually asking. The first four rows return an amount. The last two return a rate. Percentage change has a direction (increase or decrease). Percentage difference does not: it compares two numbers against their average, so 100 versus 80 is the same result as 80 versus 100.

The 100 versus 80 row is the case people mis-state. Treated as a change from 100 to 80, the drop is 20%. Treated as a change from 80 to 100, the rise is 25%, because 20 is a quarter of 80. The symmetric difference uses the average, 90, so 20 / 90 × 100 = 22.22%. Use change when time or cause has a starting point. Use difference when you are only comparing two measurements and neither one is "before."

How do everyday percentage workflows work?

Match the job to a mode, then round money to the nearest cent after the multiplication. A tip of 18% on $47.80 is 47.80 × 0.18 = 8.604, which rounds to $8.60. A 4.5% raise on $62,400 is 62,400 × 1.045 = $65,208 exactly, because 62,400 × 0.045 = 2,808.

Grades that still have a final exam need one extra step. Suppose your current average is 88%, that work is 75% of the course, the final is the other 25%, and you want a 90% overall. First find what you already have locked in: 75% of 88 is 66 points toward the final course grade. You still need 90 - 66 = 24 points from a slice that is worth 25, so the final must be 24 / 0.25 = 96%. If that required score is above 100%, the target is no longer reachable from the remaining weight.

What is the difference between percentage change, percentage difference, and percentage points?

Percentage change compares a later number with an earlier number. Eurostat's worked case is employment rising from 4.8 million to 5.2 million: ((5.2 / 4.8) - 1) × 100 = 8.3% when rounded to one decimal. Always divide by the starting value. A 30% rise followed by a 30% fall does not cancel: 100 × 1.30 × 0.70 = 91.

Percentage points are the arithmetic gap between two percentages. Eurostat's education example subtracts 81.4% from 85.9% and reports 4.5 percentage points, not "4.5 percent." The same rule fixes headlines. A conversion rate that moves from 2% to 3% is up 1 percentage point. Relative to the old rate, that is a 50% increase, because (3 - 2) / 2 = 0.50. Saying the rate "rose 1%" is ambiguous: readers cannot tell whether you mean one point or one percent of the old rate.

Percentage difference, as this calculator implements it, is |first - second| / ((first + second) / 2) × 100. For 100 and 80 the average is 90 and the result is 22.22%. It is undefined when the average is zero, which happens if both values are zero or if they are equal in size and opposite in sign (10 and -10). Do not use it for a time series. Do not use percentage change when you only have two unordered measurements.

How do successive discounts and sales tax stack?

Each percent change becomes a multiplier. A decrease of r% multiplies by (1 - r/100). An increase multiplies by (1 + r/100). Apply the next percent to the new amount, not to the original. Two discounts of x% and y% have a single equivalent discount of x + y - (x × y / 100). For 20% then 10%, that is 20 + 10 - 2 = 28%.

Tax usually hits the price after the discount. A $120 item at 25% off is $90. Sales tax of 8% is then 90 × 0.08 = $7.20, so you pay $97.20. Netting the percents first (25% off plus 8% tax = 17% off) gives 120 × 0.83 = $99.60, which is $2.40 too high. To recover the list price from a final amount, divide by each multiplier in reverse: 97.20 / 1.08 / 0.75 = 120.

Markup and margin use different bases, so they are not interchangeable. If an item costs $40 and sells for $50, markup on cost is (50 - 40) / 40 = 25%. Margin on price is (50 - 40) / 50 = 20%. Quoting a 25% margin when you mean a 25% markup prices the item at $50 instead of $53.33 (40 / 0.75).

How do you find the original number before a percentage was applied?

Divide by what remains, not by the percent that was removed or added.

• After a discount: original = sale price / (1 - discount). $85 after 15% off is 85 / 0.85 = $100. Subtracting 15 from 85, or adding 15% of 85, both miss $100.
• After an increase: original = final / (1 + increase). A value that grew 25% to $150 started at 150 / 1.25 = $120. Check forward: 120 × 1.25 = 150.
• After two changes: divide by the product of the multipliers. A price of $126 after 20% off and then another 10% off started at 126 / (0.80 × 0.90) = 126 / 0.72 = $175. Dividing by 0.70 (a fake 30% off) gives $180, and 180 × 0.80 × 0.90 = 129.60, which is not 126.

Method 1: Use the free Percentage Calculator

The Percentage Calculator runs the six formulas above in the browser and shows the steps. There is no separate Calculate button: the result updates as soon as both fields contain numbers.

1. Open the tool and set Calculation Type. The options are "What is X% of Y?", "X is what % of Y?", "X% more than Y", "X% less than Y", "Percentage Change", and "Percentage Difference".
2. Read the field labels. They change with the mode: Percentage and Number, Part and Whole, Percentage and Base Number, Original Value and New Value, or First Value and Second Value.
3. Type both numbers. The Result panel fills in, and the step-by-step breakdown shows the decimal conversion or the division.
4. Optional: use an example button such as "15% of 200" or "From 100 to 120" to load a known sample and confirm you picked the right mode.
5. Use Reset to clear the fields. The address bar stores the current inputs, so a refresh keeps the same problem. Copy that URL only if you are comfortable sharing the numbers.

Rate results ("what percent", change, and difference) are shown to two decimal places. Amount results use normal grouping, so 65208 displays with a thousands separator in locales that use one. If the whole or the original value is zero, the field shows an error instead of a divide-by-zero result. Empty fields clear the result. Non-numeric input shows "Please enter valid numbers".

Method 2: Calculate percentages in Excel or Google Sheets

Spreadsheet formulas match the table above. Format the cell as Percentage when the formula returns a decimal, or multiply by 100 if you want a plain number. Microsoft's percentage guide uses earnings of $2,342 in November and $2,500 in December: =(2500-2342)/2342 equals about 0.06746, which displays as 6.75% at two decimal places. From $2,500 to $2,425 the same pattern is =(2425-2500)/2500, or -3.00%.

• X% of Y: =Y*X/100 or =Y*15% when X is 15.
• X is what percent of Y: =X/Y with Percentage format.
• X% more or less: =Y*(1+X/100) or =Y*(1-X/100).
• Percentage change: =(New-Old)/Old with Percentage format. A zero in Old returns a divide-by-zero error.
• Percentage difference: =ABS(B2-A2)/((A2+B2)/2) with Percentage format.
• Reverse a discount: =Sale/(1-Discount) where Discount is a decimal such as 0.15.

Tips and common mistakes

• Mistake: dividing by the new number. Change from 35 hours to 45.5 hours is (45.5 - 35) / 35 = 30%, not 10.5 / 45.5.
• Mistake: calling a point gap a percent change. 20% to 25% is 5 percentage points and also a 25% relative increase. Write which one you mean.
• Mistake: adding stacked discounts or mixing tax with the discount. Multiply the keep-rate and the tax rate. 20% then 10% is 28% off, not 30%.
• Mistake: reversing a discount by adding the percent back onto the sale price. 15% of $85 is not the amount that was removed. Divide by 0.85.
• Mistake: percent change from zero. There is no original amount to divide by. Report the absolute change instead.
• Mistake: treating markup as margin. 25% markup on a $40 cost is a $50 price. A 25% margin on that cost is a $53.33 price.
• Tip: check a result forward. Apply the percent to your answer and confirm you land on the number you started from.
• Tip: round money last. Keep extra decimals through stacked steps, then round the final currency amount to cents.

Related free tools

• Percentage Change Calculator - increase or decrease between two values, with the original as the base
• Percentage Point Calculator - subtract two rates without turning the gap into a relative percent
• Discount Calculator - sale price, amount saved, and stacked discounts
• Grade Percentage Calculator - points earned over points possible, as a percent

Percent of a number, percent change, and a gap between two rates answer different questions. Write the formula that matches the question, check it forward on a round number, and use the Percentage Calculator when the steps or the rounding need to be visible.