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CalcMax

Decimal to Percent Calculator

Result

37.5000%

As a percentage (%)

Per thousand (‰)
375.000

A decimal to percent calculator moves the decimal point two places to the right and puts a percent sign on the end: 0.375 becomes 37.5 percent. That is the whole conversion, and it is worth being blunt about how little there is to it, because the arithmetic is not where the value of this page sits — the value is in seeing the same number written three ways at once. Every value on this page comes back as a percentage and as a per thousand figure, and the per thousand figure is the same shift by three places rather than two: 0.375 is 375 per thousand. The reason to print both is that people read past the first one. A percentage is a fraction over a hundred, so 0.375 is 37.5 hundredths; a per thousand figure is a fraction over a thousand, so the same number is 375 thousandths, written 375‰. Neither is more precise than the other — they are two ways of writing one quantity — and the one that matches the sentence in front of you is the one to use. Rates in the news are often quoted per thousand for the same reason they are sometimes quoted as a fraction: a change of 0.001 per unit is awkward as a percentage, where it reads 0.1 percent, and plain as a per thousand figure, where it reads 1. The underlying rule comes from the meaning of the percent sign itself: it stands for the number 0.01, which is why multiplying by a hundred is what performs the conversion, and why going the other way — a percentage conversion back into a decimal — divides by a hundred and shifts the point left. One consequence of that definition is worth stating early, because it catches people who are comparing this page with others: a percentage point and a per thousand point are both absolute steps, but a basis point is neither — it is one ten-thousandth, so a single basis point is 0.01 percent and 0.1 per thousand, and a rate quoted in basis points is a smaller unit than anything named on this page. Three things about the outputs are worth knowing before you trust them. The percentage carries four decimal places while the per thousand figure carries three, and the difference is deliberate rather than a slip: the per thousand value is the percentage value times ten, so giving both the same number of decimals would print two lines that contradict each other — a panel showing 12.3457 percent beside 123.4568 per thousand is showing you a factor of ten that does not hold, where the correct pairing is 12.3457 and 123.457. Both readings are computed from the decimal you typed rather than one from the other, so the rounding never compounds. And the fourth decimal place of the percentage is a floor on what this page can show: a value smaller than 0.00005 reads as zero percent and zero per thousand, not because the number was treated as zero but because there is no room for it in four places — 0.0001 is 0.01 percent and survives, while a value ten million times smaller than that does not.

One quantity, three ways of writing it

Percent (%)DecimalPer thousand (‰)
0.10.0011
0.50.0055
10.0110
20.0220
40.0440
50.0550
100.1100
200.2200
250.25250
500.5500

Each row is a single number written three ways, and the three columns are in the order the page works them: fill in the middle column and the two outer ones are what the panel prints. The ten rows are the percentages a person meets most often, starting at a tenth of a percent — which is the row that matters most here, because it is where this page and the finance calculator that quotes basis points meet: 0.1 percent is 1 per thousand, and it is also 10 basis points. Read any row across and the relations hold: 0.05 is 5 percent and 50 per thousand, so the first column times ten gives the third. Four of these rows are worth knowing without a tool — a quarter, a fifth, a tenth and a half — and the rest are here so that a rate you already have in mind can be looked up rather than converted.

Formula

Percent = decimal × 100 Per thousand = decimal × 1000

Decimal
The number to convert, as a plain decimal: 0.375, 0.07, 2.5. There is no lower or upper limit, because the conversion is a multiplication and every finite number has an answer — a decimal above one simply gives a percentage above a hundred
Percent
The decimal multiplied by a hundred, shown with four decimal places. It is a fraction over a hundred: 0.375 is 37.5 hundredths, and the percent sign is what says so
Per thousand
The same decimal multiplied by a thousand, shown with three decimals and marked with the per mille sign ‰. One place further along than the percentage — 0.375 is 375 per thousand — and the form used for rates where a percentage would be an awkwardly small number
The shift
Two places to the right for a percentage, three for a per thousand figure. Nothing is rounded and nothing is added: the digits you typed are the digits you get back, in a different position

Three uses are worth separating. Reading a probability or a share as a percentage is the commonest: a decimal that came out of a division — 0.375 from three eighths, or 0.07 from a test score — is easier to compare with other rates once it is a percentage, because percentages are the units people think in. Quoting a rate per thousand is the second, and it is the reason the second output exists: rates of births, deaths, accidents and defaults are conventionally quoted per thousand in official statistics, and a decimal like 0.012 reads as 1.2 percent but as 12 per thousand, which is the figure those tables print. The third use is checking a conversion you did by hand, and the per thousand line is what makes that possible — if 0.375 is 37.5 percent then it must be 375 per thousand, and a pair of numbers that are not in a ten-to-one relation is a shifted decimal point rather than a rounding difference. Two cases are outside what this page does. Going from a percentage back to a decimal is the reverse direction, which is a division by a hundred and a separate tool; and a rate expressed in basis points is a unit four times smaller than a per thousand point, so a figure in basis points has to be converted twice before it can be compared with the outputs here. If a number you are working with is smaller than one hundredth of a percent, check whether the source meant per thousand or basis points before reading it as a percentage — the two differ by a factor of ten and the mistake is easy to make in the other direction.

Worked examples

  1. 0.375 as a percentage

    1. Shift the decimal point two places to the right: 0.375 becomes 37.5
    2. Attach the percent sign: 37.5 percent
    3. Shift three places instead for the per thousand figure: 0.375 becomes 375, written 375 per thousand
    4. Check the pair: 37.5 × 10 = 375, so the two readings agree

    The default case, and the one worth reading twice: 37.5 percent and 375 per thousand are the same number, and the ten-to-one relation between them is the arithmetic that confirms the conversion went the right way. Three eighths is a convenient value to keep in mind because it appears on every ruler and in every recipe, and both of its readings are whole numbers.

  2. 0.001 — one thousandth, and the basis-point boundary

    1. Shift two places: 0.001 becomes 0.1, so the percentage is 0.1 percent
    2. Shift three places: 0.001 becomes 1, so the per thousand figure is 1
    3. Read the pair as a statement of the same thing: a tenth of a percent is one part in a thousand

    The row this page exists for, and the one that keeps it clear of the finance calculator that quotes basis points. One thousandth is 0.1 percent and 1 per thousand — the same quantity, and the point where the two scales cross. A basis point is a different unit: it is one ten-thousandth, so it is 0.01 percent and 0.1 per thousand, ten times smaller than the number in this example. A rate quoted as 10 basis points is therefore 0.1 percent, which is exactly the percentage output above.

  3. 2.5 as a percentage — no upper limit

    1. Shift two places: 2.5 becomes 250, so the percentage is 250 percent
    2. Shift three places: 2.5 becomes 2500, so the per thousand figure is 2500
    3. Nothing is refused — the conversion is a multiplication and applies to any finite decimal

    A decimal above one, which is not a mistake: growth of two and a half times is 250 percent, and a markup that multiplies a price by 2.5 is quoted that way. The page sets no ceiling, because a value above one is a legitimate number and not a sign that the wrong field was filled in — the number typed here is unambiguous and there is only one way to read it.

  4. 0.0001 — the last place the percentage can show

    1. Shift two places: 0.0001 becomes 0.01, which is the fourth decimal place of the percentage
    2. Shift three places: 0.0001 becomes 0.1, the per thousand figure
    3. Note the asymmetry: one ten-thousandth is 0.01 percent but 0.1 per thousand, so the per thousand reading stays readable a place longer

    A ten-thousandth, which lands exactly on the fourth decimal place of the percentage — the smallest position the page displays. One step further down and the percentage reading fails: 0.0000001, a ten-millionth, prints as 0 percent because the fourth place cannot hold it, while its per thousand reading still shows 0.0001. That gap is the subject of the limitation below, and it is worth seeing the edge of the display before running into it.

Limitations

The percentage is displayed to four decimal places, so a value below a ten-millionth reads as zero percent and zero per thousand. That is a limit of the display and not a decision about the input — the number was not treated as zero, it simply has nowhere to sit in four places — and the consequence is that very small decimals come back as a flat zero rather than as a small non-zero percentage. Compare the two readings when that happens, since the per thousand figure carries one more significant position and will still show a value after the percentage has given up. The two outputs are rounded independently, from the decimal you typed rather than one from the other, so no rounding error is multiplied on the way through; the price is that a pair of readings can look inconsistent in the last place if you compare them by shifting a digit rather than by multiplying. Nothing on this page goes the other way: converting a percentage back into a decimal is a division by a hundred, and it is not offered here. The per thousand figure is not a basis point, and the difference is a factor of ten — one basis point is 0.01 percent, one per thousand point is 0.1 percent — so a rate quoted in basis points cannot be read off either output directly and has to be converted first, which is the mistake most likely to be made by someone comparing this page with a finance calculator. The page does no rounding to a sensible number of significant figures, no formatting as a fraction, and no interpretation of what the number means: it reports a share as a percentage and a per thousand figure and stops, with an answer above 100 percent treated as an ordinary result rather than as an error worth flagging.

Frequently asked questions

How do I turn a decimal into a percentage?
Move the decimal point two places to the right and attach the percent sign: 0.375 becomes 37.5 percent, and 0.07 becomes 7 percent. The reason two places is the right number of places is the meaning of the sign — a percent is one hundredth, so expressing a number in hundredths is multiplying it by a hundred. Converting back is the same move to the left, dividing by a hundred.
What is the per thousand figure for?
It is the same number in a smaller unit, and it is what official statistics quote for rates: births, deaths, accidents and defaults are conventionally published per thousand rather than as percentages. The shift is three places instead of two, and the sign is the per mille mark ‰. A decimal of 0.001 is 0.1 percent and 1 per thousand, so the per thousand reading stays a readable small number where the percentage has already dropped below a tenth.
Is a per thousand figure the same as a basis point?
No, and they are exactly ten times apart. One per thousand is a tenth of a percent — 0.1 percent — while one basis point is a hundredth of a percent, or 0.01 percent, which makes a basis point a tenth of a per thousand point. Rates quoted in basis points are therefore smaller than they look: 50 basis points is 0.5 percent, which is 5 per thousand. Finance pages use basis points because the unit is small enough to express rate changes without decimals.
Why do the two outputs have a different number of decimal places?
Because they are a factor of ten apart, and showing the same number of places in both would print two lines that do not agree. The per thousand value is the percentage value times ten, so it gets one fewer decimal place: 12.3457 percent belongs beside 123.457 per thousand, and pairing it with 123.4568 would be showing a ten-to-one relation that is not there. Each is rounded from the decimal you entered, so neither inherits a rounding error from the other.
What happens with a really small decimal?
Below a ten-millionth it prints as zero percent. The percentage is displayed to four decimal places, so 0.0000001 has no place to sit and comes back as 0, while the per thousand reading still shows 0.0001. That is a display limit rather than a judgement about the number — it was not treated as zero, it just could not be written in four places. If you are working with values that small, the per thousand figure is the one to read.
Can the answer be more than 100 percent?
Yes, and it is an ordinary answer rather than an error. A decimal of 2.5 is 250 percent, which is what growth of two and a half times looks like written as a rate. The page sets no upper limit because there is only one way to read the input: the number you type is a decimal, and every finite decimal has a percentage. A figure above a hundred becomes worth a second look only when you know the quantity is supposed to be a share of something whole.

References

Related calculators

Decimal to Fraction CalculatorTurn any decimal into a fraction in lowest terms.Fraction to Decimal CalculatorConvert a fraction to its decimal value, exact or rounded.Percentage CalculatorA percentage of a number, or what percent one is of another.Percent to Decimal CalculatorConvert a percentage to a decimal, with the working.