A percentage calculator answers the three percent questions people ask most: what is X% of a number, what percentage one number is of another, and the percentage change between two values. Percentages express a part of a whole in terms of 100, which makes quantities of very different sizes easy to compare.
Pick the question you want answered, enter your two numbers, and the calculator applies the correct formula instantly. Each result also shows the formula with your numbers plugged in, so you can see exactly how the answer was reached — useful for checking homework, tips, discounts, taxes, and statistics.
The Three Percentage Formulas
Each mode of this calculator uses one core formula:
- What is X% of Y? — Answer = (X ÷ 100) × Y. Example: 25% of 200 = 0.25 × 200 = 50.
- X is what % of Y? — Answer = (X ÷ Y) × 100. Example: 50 is what % of 200? 50 ÷ 200 = 0.25, so 25%.
- % change from X to Y — Answer = ((Y − X) ÷ |X|) × 100. Example: from 200 to 250 is (50 ÷ 200) × 100 = a 25% increase.
All three come from the same idea: a percent is simply a fraction with 100 as the denominator, so 25% means 25/100 or 0.25. Converting between the percent form and the decimal form is what makes each calculation work.
Where Each Formula Shows Up in Real Life
Knowing which formula to reach for is half the battle:
- Percent of a number: sales tax (8% of a $60 purchase), tips (20% of a restaurant bill), commissions, and interest for one period.
- What percent X is of Y: test scores (42 correct out of 50 = 84%), completion rates, market share, and budget breakdowns.
- Percentage change: price increases, salary raises, stock returns, and population growth.
A quick mental shortcut: 10% of any number is that number with the decimal point moved one place left, so 10% of 84 is 8.4. From there, 5% is half of that (4.2) and 20% is double (16.8) — enough to sanity-check most everyday calculations.
Worked Example: A Price Increase
Suppose a gym membership rises from $48 to $60 per month. Which formula applies? You are comparing an old value to a new value, so use percentage change.
Step 1: Find the difference: 60 − 48 = 12. Step 2: Divide by the original value: 12 ÷ 48 = 0.25. Step 3: Multiply by 100: 0.25 × 100 = 25%.
The membership increased by 25%. Now reverse-check it with the percent-of formula: 25% of 48 is (25 ÷ 100) × 48 = 12, and 48 + 12 = 60. Both formulas agree, which is a reliable way to verify any percentage answer.
X Out of Y as a Percentage
Turning a score into a percentage is one division and one multiplication:
Percentage = (Score ÷ Total) × 100
So 16 out of 20 is (16 ÷ 20) × 100 = 80%. The same arithmetic answers 16/20 percentage queries — the slash simply means divide. Likewise 17 out of 20 as a percentage is 85%, 15 as a percentage of 20 is 75%, and 14/20 percentage works out at 70%.
Tests marked out of 20 are the most-searched case because each mark is worth exactly 5%, which makes the whole scale easy to hold in your head: every point up or down moves you 5 percentage points.
Other denominators worth knowing:
- Out of 25, each mark is 4%
- Out of 50, each mark is 2%
- Out of 8, each mark is 12.5%
Fractions above 1 give percentages above 100, which is correct rather than an error: 5/4 in percentage terms is 125%. Going the other way, what percentage is 1/8th? 12.5%, and 4/5 to a percentage is 80%. That comes up whenever something exceeds a target.
| Score | Fraction | Percentage | Typical letter grade |
|---|---|---|---|
| 20 out of 20 | 20/20 | 100% | A |
| 19 out of 20 | 19/20 | 95% | A |
| 18 out of 20 | 18/20 | 90% | A- |
| 17 out of 20 | 17/20 | 85% | B |
| 16 out of 20 | 16/20 | 80% | B- |
| 15 out of 20 | 15/20 | 75% | C |
| 14 out of 20 | 14/20 | 70% | C- |
| 13 out of 20 | 13/20 | 65% | D |
| 12 out of 20 | 12/20 | 60% | D- |
Letter grades follow the most common US scale. Individual schools set their own cutoffs, so check your syllabus.
Percentage Change vs. Percentage Difference
These two are routinely confused, and they answer different questions.
Percentage change measures movement from a starting value, so it has a direction:
Percentage change = ((New − Old) ÷ Old) × 100
Going from 40 to 50 is ((50 − 40) ÷ 40) × 100 = +25%. Going back from 50 to 40 is ((40 − 50) ÷ 50) × 100 = −20%.
That asymmetry surprises people but is correct: the same absolute move of 10 is a different share of 40 than of 50. It is also why a 50% loss needs a 100% gain to recover.
Percentage difference compares two values with no starting point, dividing by their average instead:
Percentage difference = (|A − B| ÷ ((A + B) ÷ 2)) × 100
For 40 and 50 that is (10 ÷ 45) × 100 = 22.2%. Because it uses the mean, the answer is the same whichever value you list first — which is exactly when you want it, for instance comparing two measurements where neither is the "before".
Percentages in Excel and Google Sheets
The formulas, assuming your numbers are in cells A2 and B2:
- Percent of a number: =A2*B2 with B2 formatted as a percentage, or =A2*(B2/100) if B2 holds a plain number like 15
- What percent A is of B: =A2/B2, then format the cell as a percentage
- Percentage change: =(B2-A2)/A2
- Excel formulas: increase by percentage with =A2*(1+B2) — so £200 up 15% is =200*(1+0.15) = 230
- Decrease by a percentage: =A2*(1-B2)
The formatting catch that causes most errors: Excel treats a cell formatted as a percentage as the underlying decimal. Typing 15 into a percentage-formatted cell may become 1500%, while 0.15 displays as 15%. Decide whether your column stores 15 or 0.15 and keep it consistent.
To add a percentage across a whole column at once, put the rate in one cell and lock it with a dollar sign: =A2*(1+$D$1) copies down without the reference drifting.
Frequently Asked Questions
What is 16 out of 20 as a percentage?
80%. Divide 16 by 20 to get 0.8, then multiply by 100. On a test marked out of 20 each mark is worth 5%, so 17/20 is 85% and 15/20 is 75%.
What is 15 out of 20 as a percentage?
75%. That is 15 ÷ 20 = 0.75, times 100. It usually corresponds to a C on the common US grading scale.
What percentage is 1/8?
12.5%. Divide 1 by 8 to get 0.125 and multiply by 100. The eighths run 1/8 = 12.5%, 1/4 = 25%, 3/8 = 37.5%, 1/2 = 50%, 5/8 = 62.5%, 3/4 = 75%, 7/8 = 87.5%.
What is the percentage difference formula?
Percentage difference = (|A − B| ÷ ((A + B) ÷ 2)) × 100 — the gap divided by the average of the two values. For 40 and 50 that is 10 ÷ 45 = 22.2%. Use it when neither value is the starting point; use percentage change when one is.
How do I increase a number by a percentage in Excel?
Multiply by 1 plus the rate: =A2*(1+B2) where B2 is formatted as a percentage, or =A2*1.15 to add 15% directly. Watch the formatting — typing 15 into a percentage-formatted cell can become 1500%.
Can a percentage be more than 100?
Yes. Any fraction greater than 1 exceeds 100%: 5/4 is 125%, and a value that triples has increased by 200%. Percentages above 100 are only impossible when the total is a fixed maximum, like a test score.
How do I calculate a percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. For example, 15% of 80 is 0.15 × 80 = 12. Equivalently, multiply the two numbers and divide by 100: (15 × 80) ÷ 100 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If you scored 42 out of 50 on a test, compute 42 ÷ 50 = 0.84, then 0.84 × 100 = 84%. The order matters: the number after "of" always goes in the denominator.
How is percentage change calculated?
Percentage change = (new value − old value) ÷ |old value| × 100. Going from 200 to 250 gives (250 − 200) ÷ 200 × 100 = 25% increase. A negative result means a decrease. The original (older) value is always the divisor.
What is the difference between percentage and percentage points?
Percentage points measure the arithmetic difference between two percentages, while percent change measures relative change. If an interest rate rises from 4% to 5%, that is 1 percentage point, but a 25% relative increase — because 1 is 25% of the original 4.
Can a percentage be greater than 100?
Yes. A value more than double the original represents a change above 100%. For example, growing from 50 to 150 is a 200% increase, and 150 is 300% of 50. Percentages over 100 simply mean the part exceeds the whole you are comparing against.