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Percentage Calculator

Global tools

Five questions live behind the word "percentage", and this page answers all of them: a percentage of an amount, an amount as a percentage of another, a percentage increase or decrease, a change in percentage points, and a number converted between a fraction, a decimal, a percentage and scientific notation.

Percentage Calculator - Danfio

https://danfio.com/tools/percentage-calculator/ - printed from this page

Five different questions share this name; pick the one that matches the sum in front of you and the fields swap to suit it.

The share you are taking, which may go above 100; a negative value works as a markdown.

The amount the percentage is taken from.

Leave blank to name the files percentage-calculation.txt and .csv.

Results update as you type. Nothing leaves your device.

15% of 300

45

Multiply by 15 and divide by 100 - or multiply by 3/20, which is the same arithmetic with smaller numbers.

Answer
45
The percentage as a fraction
3/20
What is left
255 the rest of the whole
Check, answer back as a percentage
15%

The same answer, written out

FormValue
Percentage15%
Of the amount300
Answer45
Answer as a fraction of the amount3/20
Remainder255

Answers are shown to six significant digits and rounded to two for reading, because a percentage of a rounded number is itself rounded. The exact figures are in the download, written by the same function that drew this table.

Worth knowing about 15% of 300

  • A percentage of an amount is a multiplication: 15% of 300 is 300 × 0.15, which is 45. The percentage is a fraction of a hundred, so 15% is 15/100, and that reduces to 3/20 - multiplying by 3 and dividing by 20 is the same sum with smaller numbers.
  • A percentage above 100 is not an error: 150% of 40 is 60, which is exactly what a markup, a growth rate or an over-target figure looks like.
  • The check in the middle of the hero is the arithmetic run backwards: the answer as a percentage of the amount should be the percentage you typed, and if it is not, one of the two numbers was misread.

Two of those questions are the ones that cause arguments. Percentage change depends on the number you started from, so 100 to 125 is up 25% while 125 to 100 is down 20% - the same pair of values, two different percentages, both correct. And a change in something that is already a percentage - a rate, a share, a mark - moves in percentage points and in percent at the same time: 10% to 8% is down 2 points, which is down 20%.

The number converter keeps the digits: 0.125 is read as 125/1000 and reduced to exactly 1/8, and 1/3 is shown as 0.(3), the bracket meaning the digit repeats for ever. A page doing the arithmetic in ordinary browser numbers would print 0.3333333333333333 and 0.30000000000000004, which look like answers and are not.

About this percentage calculator

Percentages are rarely hard to compute and very easy to misread, and that gap is what this page is for: the same 100-and-125 pair is a 25% rise or a 20% fall depending only on which figure you started from, and a rate moving from 10% to 8% is two percentage points and twenty percent at once. The page names the base behind every answer, because an unstated base is where the argument starts.

It is written for whoever is checking somebody else’s number - a discount that sounds bigger than it is, a rate cut quoted as a percentage, a survey riding on a small share - and it refuses two things: reading a percentage written in words, and guessing which of the five questions you meant. Each mode says which number it treated as the whole, and the converter works on the digits, so a third comes back as 0.(3) rather than as a rounded decimal.

How this percentage calculator works

The three ordinary questions, and which number is the base

A percentage of an amount is a multiplication: 15% of 300 is 300 × 15 ÷ 100, which is 45. The percentage is a fraction of a hundred, so 15% is also 3/20 - the same sum with smaller numbers, which is why the exact fraction is printed beside the answer.

An amount as a percentage is a division: 15 out of 300 is 15 ÷ 300 = 0.05, which is 5%. Here the whole is the base, and that is the point of the mode: 300 as a percentage of 15 is 2000%, so the same two numbers give very different answers depending on which is treated as the whole.

When the whole is zero the page says the answer is undefined rather than printing 0%. Nothing is not a base for a percentage, and a page that printed 0% would be telling somebody that a zero in a report is a legitimate result rather than a mistake in a spreadsheet.

Percentage change is asymmetric, and that is not a bug

Percentage change is measured against the value you started from. 100 rising to 125 is +25%; the same pair the other way round, 125 falling to 100, is -20%. Both are right, because the base moved - and a business that reports "up 25%" and later, after a fall back to the original number, "down only 20%" is comparing two different denominators without saying so.

The symmetric alternative is percentage difference: the difference over the average of the two values, which is 22.22% for 100 and 125 in either order. It is the right measure when neither number is a base - two prices, two measurements of the same quantity - and the page prints it alongside the change so the two can be told apart.

Doubling and halving are the clearest case: a 100% increase takes 100 to 200, and a 50% decrease takes it back. The percentages differ because a percent is always a percent of something, and the something changed.

Percentage points against percent

A percentage point is a unit for a change in something already expressed as a percentage. An interest rate falling from 10% to 8% has fallen two percentage points. In relative terms it has fallen 20%, because the rate it started from was 10% - and both statements describe the same move.

This is the most misused pair of numbers in advertising and political reporting, in both directions: "a 20% cut in the rate" sounds twice as large as "a two point cut", and it is exactly the same fact. The page prints the points, the percent, and the sentence relating them, so whichever number a reader came for, the other is beside it.

The two measures coincide only at 100%: from 100% to 90% is ten percentage points and a 10% fall, because a percentage point and a percent of 100% are the same size.

Fractions, decimals and repeating cycles

Every decimal you type is read as digits - 0.125 is 125 over 1000 - and reduced to lowest terms, which gives exactly 1/8. Nothing is converted to a browser number and back, so the page cannot print 0.30000000000000004 for 0.1 plus 0.2, nor 870.0000000000001 for 8.7 × 100.

A fraction in lowest terms terminates if its denominator has no prime factors other than 2 and 5, and repeats otherwise. So 1/8 is 0.125 exactly, 1/5 is 0.2, and 1/3, 1/6 and 1/7 have no last digit. The repeating part is written in brackets: 0.(3) for a third, 0.1(6) for a sixth, 0.(142857) for a seventh - which also shows that a seventh has a six-digit cycle and a third has a one-digit cycle.

Scientific notation comes out of the digit string too, by moving the decimal point rather than by asking the browser’s number format for seventeen significant digits. A twenty-digit value keeps the digits it was typed with, and the page says when it has had to shorten one to fit.

What this page does not do

It does not read percentages written in words ("up by a half"), it does not chain percentages for you, and it does not apply a percentage series to a total. The arithmetic for the last of those is at least on the page: a 10% rise followed by a 10% fall is not back where you started, because 1.1 × 0.9 is 0.99 - a 1% loss, which is what "compound percentages" means in practice.

It also does not decide which percentage you meant. That is why there are five modes, and why each one states the base it used: a percentage question without a stated base has no answer, only an argument.

Worked examples

Each example below was run through the calculator on this page when the site was built, so the numbers match what you see when you enter the same inputs.

15% of 300

What do you want to work out?: A percentage of an amount (15% of 300) · Percentage: 15% · Of the amount: 300

15% of 300

45

Multiply by 15 and divide by 100 - or multiply by 3/20, which is the same arithmetic with smaller numbers.

Answer: 45 · The percentage as a fraction: 3/20 · What is left: 255 · Check, answer back as a percentage: 15%

45. Fifteen percent is 3/20, so the same answer is 300 × 3 ÷ 20: the fraction in the answer is not decoration, it is the same arithmetic with smaller numbers.

15 as a percentage of 300

What do you want to work out?: An amount as a percentage (15 is what % of 300) · This amount: 15 · As a percentage of: 300

15 as a percentage of 300

5%

Divide the part by the whole and multiply by 100: 15 ÷ 300 = 0.05, and that is 5%.

Percentage: 5% · As a decimal: 0.05 · The whole is: 300 · To reach 100%: 95%

5%. Reverse the two numbers and it becomes 2000%, which is why the page names the base it used rather than leaving the reader to work out which number is "the whole".

A price rising from 100 to 125

What do you want to work out?: A percentage increase or decrease (100 to 125) · Starting value: 100 · New value: 125

100 to 125

+25%

The base is 100 - the value you started from - which is why the same pair of numbers gives two different percentages depending on which end you start at.

Absolute change: 25 · Direction: up · The same move backwards: -20% · Percentage difference: 22.2222%

+25%. Coming back down from 125 to 100 is -20%, and the percentage difference is 22.22% either way: three numbers for one pair of prices, each answering a different question.

An interest rate falling from 10% to 8%

What do you want to work out?: Percentage points against percent (10% to 8%) · Starting percentage: 10% · New percentage: 8%

10% to 8%

-2 percentage points

That is 2 percentage points lower, which is 20% less than the starting figure of 10%.

Percentage points: -2 pp · Relative change: -20% · Starting percentage: 10% · New percentage: 8%

Down 2 percentage points, and down 20% in relative terms. Both are true, and a headline quoting the 20% is describing exactly the same move as one quoting 2 points.

A third, as a fraction and a decimal

What do you want to work out?: A number: fraction, decimal, percent, scientific · A number to convert: — · Or a fraction, numerator/denominator: 1/3

1/3 written another way

0.(3)

Read as digits rather than as a floating-point number, so nothing is rounded on the way through: 0.125 is exactly 1/8, and 1/3 is exactly 0.(3).

Fraction: 1/3 · Decimal: 0.(3) · Percentage: 33.333333% · Scientific: not shown exactly: the decimal does not terminate

0.(3): the bracket means the 3 repeats with no end. That is why a third cannot be written exactly as a decimal, and why a page printing 0.333 would be showing a rounded value as if it were the number.

Frequently asked questions

How do I work out a percentage of a number?

Multiply the number by the percentage and divide by 100: 15% of 300 is 300 × 15 ÷ 100 = 45. In your head, 10% is a decimal point moved one place and 5% is half of that, so 15% of 300 is 30 plus 15. The page also shows the percentage as a fraction in lowest terms, because 15% is 3/20 and that is often easier to multiply by.

What is the difference between percentage change and percentage difference?

Percentage change has a base: the value you started from. 100 to 125 is +25%, and 125 to 100 is -20%. Percentage difference has no base: it divides the gap by the average of the two values, so 100 and 125 differ by 22.22% whichever order they are given in. Use change when one value is the original, and difference when neither is.

What is a percentage point?

It is a unit for a change in something already measured as a percentage - a rate, a share, a tax band. 10% to 8% is a fall of two percentage points, which is also a fall of 20% relative to where it started. Both numbers describe the same change, which is why the page prints both.

Why is a 10% rise then a 10% fall not back to the start?

Because the second percentage is taken from a different number. 100 rising 10% is 110; 110 falling 10% is 99. Multiplying the multipliers gives the answer directly: 1.1 × 0.9 = 0.99, which is a 1% loss. Percentages only add up when they are taken from the same base.

Why does the page show 0.(3) instead of 0.333333?

Because a third has no exact decimal form: the digit 3 repeats for ever, and any finite string of threes is slightly less than a third. The bracket is standard notation for the repeating cycle, and it is more honest than printing six digits as though they were the whole number. A fraction whose denominator has prime factors other than 2 and 5 never terminates.

Why does the calculator refuse a percentage of zero?

It refuses one as a percentage *of* zero, because there is nothing to divide by and the answer is genuinely undefined rather than zero. Percentages of zero are fine: 15% of 0 is 0. The distinction matters on a report, where a zero in a denominator is usually a data problem rather than a result.

Can I use this for a discount or a tip?

For a rough figure, yes: 20% of a bill is a multiplication, which is the first mode. For a tip with a split, tax handling and rounding that keeps the cash total right, the tip calculator does that arithmetic - including the rounding decisions, which are the part that makes the bill add up.

Assumptions and sources

  • A percentage is a fraction over 100; a change is measured against the starting value, a difference against the mean of the two.
  • Browsers store decimals at a fixed binary precision of about fifteen digits, which is why 0.1 + 0.2 shows as 0.30000000000000004; this page works on the digits themselves, and the exact-arithmetic rules are fixed across the site.
  • Everything runs in your browser; nothing you type is uploaded.

Last reviewed 2026-09-15. Runs locally on your device; keep backups; no financial advice applies. Read the full disclaimer.

Where a figure on this page comes from an official agency — HUD, IRS, FICO or a state body — the site keeps a dated snapshot of the source page in its sources library, and a scheduled job re-checks that snapshot, so the number can be traced back to the document it came from.

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