What is the difference between percentage change and percentage difference?

Change is directional and divides by the starting value: going from 80 to 100 is a 25% increase. Difference is symmetric and divides by the average of the two: the percentage difference between 80 and 100 is 22.22%. Change answers "how much did it grow", difference answers "how far apart are these two". Swapping the numbers changes the first and not the second.

How do I work out a percentage increase?

Subtract the old value from the new one, divide by the magnitude of the old value, then multiply by 100. From 80 to 100 that is (100 - 80) / 80 × 100 = 25%. For a negative starting value this calculator uses its absolute magnitude as the denominator. The tool shows that arithmetic for each calculation.

How do I reverse a percentage to get the price before a discount?

Divide the amount you have by the percentage it represents, then multiply by 100. If £60 is 75% of the original price, the original was 60 ÷ 75 × 100 = £80. Use the "X is P% of what" mode. Note that reversing a 25% discount is not the same as adding 25% back.

Why can't I calculate a percentage change from zero?

Because it is mathematically undefined: the formula divides by the starting value, and that value is zero. Spreadsheets show a divide-by-zero error for the same reason. Percentage difference uses the average magnitude instead and can compare zero with a nonzero value; percentage points can subtract a zero starting rate.

What is a percentage point?

The plain arithmetic gap between two percentages, as opposed to the relative change between them. If a rate rises from 4% to 5%, that is a rise of one percentage point, but a 25% increase. News reports mix these up often, and the difference matters a great deal in interest rates and polling.

How do the three basic percentage questions differ?

Use % of a number for 25% of 80 = 20; X is what % of Y for 20 out of 80 = 25%; and X is P% of what for 20 as 25% of an unknown total = 80. The known inputs decide which question to choose.

Can I multiply a number by a percentage, or find a percentage of a percentage?

Yes. % of a number multiplies the first input divided by 100 by the second. For 20% of 50%, enter 20 and 50 to get 10, interpreted as 10% of the original whole. A percent of a percent is multiplication, not the arithmetic gap between two rates.

Can I use a formula in Excel or Google Sheets?

For a part in A2 and a whole in B2, use =A2/B2 and format the cell as Percentage. For a percent stored as 25% in A2 and an amount in B2, use =A2*B2. A spreadsheet percentage cell stores 25% as 0.25, while the Percent box here takes 25. These are manual formula instructions; this page does not edit a workbook.

Can I convert percentages to fractions or ratios?

Use Fraction Calculator for exact fraction/decimal arithmetic and its percentage readout. To simplify 75% as a ratio to 100, enter 75:100 in Ratio Calculator to obtain 3:4. A part-to-whole ratio differs from a parts-to-parts split, so state which denominator you mean.

How are the results rounded?

Calculations use the browser’s finite double-precision numbers. Decimal results are rounded to twelve significant digits, while safe whole-number results retain their full value. The headline usually shows up to six decimal places; very small readings use scientific notation. Computed result and Copy retain the full computed display value, which is not a claim of exact decimal arithmetic.

How do I use an ordinary calculator to find a percentage?

Use the arithmetic directly: for 25% of 80, enter 25 ÷ 100 × 80 = 20; for 20 out of 80, enter 20 ÷ 80 × 100 = 25. Percentage-key behavior varies by calculator and the preceding operation, so these formulas avoid assuming a particular keypad or device.

How do I calculate a total from multiple percentages?

For an overall percentage from different groups, use the Weighted Average page under Average Calculator and supply each percentage with its group size. A group of 10 at 50% and a group of 90 at 100% gives 95%, rather than the equally weighted mean of 75%. Percentages with different denominators cannot simply be added. For a percentage of a percentage, % of a number performs multiplication: 20% of 50% is 10% of the original whole. Successive price changes instead use the latest amount each time in Add or subtract %, so +25% followed by -25% takes 80 to 100 to 75. That manual sequence is not a batch percentage table.

Which calculator should I use for growth over time?

Use % increase or decrease for a known earlier and later amount. Their dates describe the interval; the result is the total change across it. The CAGR page under ROI Calculator also accepts elapsed years or months and solves one equivalent annual rate. The Average Growth Rate page under Average Calculator compares an arithmetic mean with compound growth from supplied equal-period percentage observations. Compound Interest under APY Calculator applies a rate you already know to a starting amount over a duration. These inputs answer different questions; no missing observations or future rate is inferred.

Percentage Calculator

Nine percentage questions in one place, each showing its working so you can check the arithmetic rather than trust it. It includes the distinction most calculators blur: percentage change is measured against where you started, percentage difference against the average of the two. Add or subtract a supplied percentage when you want a new value, or choose Percentage points for the arithmetic gap between two rates.

What is 25% of 80?2025% × 80 = 25 ÷ 100 × 80

Question

Percent

Of what

The working
25% × 80 = 25 ÷ 100 × 80
Computed result
20

Change and difference are not the same thing. Going from 80 to 100 is a 25% increase, measured against where you started. But the percentage difference between 80 and 100 is 22.22%, because that one divides by the average of the two. Change has a direction; difference does not. Reports and spreadsheets mix these up constantly, which is why both are here as separate questions.

Margin and markup are the same profit over two different divisors. Something that costs 40 and sells for 100 earns 60 either way, but the margin divides that by the selling price and is 60%, while the markup divides it by the cost and is 150%. Margin can never pass 100%; markup has no ceiling. The profit margin question above reports both, each beside the number it divided by.

Common questions

What is the difference between percentage change and percentage difference?: Change is directional and divides by the starting value: going from 80 to 100 is a 25% increase. Difference is symmetric and divides by the average of the two: the percentage difference between 80 and 100 is 22.22%. Change answers "how much did it grow", difference answers "how far apart are these two". Swapping the numbers changes the first and not the second.
How do I work out a percentage increase?: Subtract the old value from the new one, divide by the magnitude of the old value, then multiply by 100. From 80 to 100 that is (100 - 80) / 80 × 100 = 25%. For a negative starting value this calculator uses its absolute magnitude as the denominator. The tool shows that arithmetic for each calculation.
How do I reverse a percentage to get the price before a discount?: Divide the amount you have by the percentage it represents, then multiply by 100. If £60 is 75% of the original price, the original was 60 ÷ 75 × 100 = £80. Use the "X is P% of what" mode. Note that reversing a 25% discount is not the same as adding 25% back.
Why can't I calculate a percentage change from zero?: Because it is mathematically undefined: the formula divides by the starting value, and that value is zero. Spreadsheets show a divide-by-zero error for the same reason. Percentage difference uses the average magnitude instead and can compare zero with a nonzero value; percentage points can subtract a zero starting rate.
What is a percentage point?: The plain arithmetic gap between two percentages, as opposed to the relative change between them. If a rate rises from 4% to 5%, that is a rise of one percentage point, but a 25% increase. News reports mix these up often, and the difference matters a great deal in interest rates and polling.
How do the three basic percentage questions differ?: Use % of a number for 25% of 80 = 20; X is what % of Y for 20 out of 80 = 25%; and X is P% of what for 20 as 25% of an unknown total = 80. The known inputs decide which question to choose.
Can I multiply a number by a percentage, or find a percentage of a percentage?: Yes. % of a number multiplies the first input divided by 100 by the second. For 20% of 50%, enter 20 and 50 to get 10, interpreted as 10% of the original whole. A percent of a percent is multiplication, not the arithmetic gap between two rates.
Can I use a formula in Excel or Google Sheets?: For a part in A2 and a whole in B2, use =A2/B2 and format the cell as Percentage. For a percent stored as 25% in A2 and an amount in B2, use =A2*B2. A spreadsheet percentage cell stores 25% as 0.25, while the Percent box here takes 25. These are manual formula instructions; this page does not edit a workbook.
Can I convert percentages to fractions or ratios?: Use Fraction Calculator for exact fraction/decimal arithmetic and its percentage readout. To simplify 75% as a ratio to 100, enter 75:100 in Ratio Calculator to obtain 3:4. A part-to-whole ratio differs from a parts-to-parts split, so state which denominator you mean.
How are the results rounded?: Calculations use the browser’s finite double-precision numbers. Decimal results are rounded to twelve significant digits, while safe whole-number results retain their full value. The headline usually shows up to six decimal places; very small readings use scientific notation. Computed result and Copy retain the full computed display value, which is not a claim of exact decimal arithmetic.
How do I use an ordinary calculator to find a percentage?: Use the arithmetic directly: for 25% of 80, enter 25 ÷ 100 × 80 = 20; for 20 out of 80, enter 20 ÷ 80 × 100 = 25. Percentage-key behavior varies by calculator and the preceding operation, so these formulas avoid assuming a particular keypad or device.
How do I calculate a total from multiple percentages?: For an overall percentage from different groups, use the Weighted Average page under Average Calculator and supply each percentage with its group size. A group of 10 at 50% and a group of 90 at 100% gives 95%, rather than the equally weighted mean of 75%. Percentages with different denominators cannot simply be added. For a percentage of a percentage, % of a number performs multiplication: 20% of 50% is 10% of the original whole. Successive price changes instead use the latest amount each time in Add or subtract %, so +25% followed by -25% takes 80 to 100 to 75. That manual sequence is not a batch percentage table.
Which calculator should I use for growth over time?: Use % increase or decrease for a known earlier and later amount. Their dates describe the interval; the result is the total change across it. The CAGR page under ROI Calculator also accepts elapsed years or months and solves one equivalent annual rate. The Average Growth Rate page under Average Calculator compares an arithmetic mean with compound growth from supplied equal-period percentage observations. Compound Interest under APY Calculator applies a rate you already know to a starting amount over a duration. These inputs answer different questions; no missing observations or future rate is inferred.

Browser double-precision arithmetic. Decimal results are rounded to twelve significant digits; safe integer results retain their full value. The formula shows the inputs used.