Percent to Decimal Calculator
Result
As a decimal
- Per thousand (‰)
- 375.000
A percent to decimal calculator divides by a hundred and hands back the plain number: 37.5 percent is 0.375. The conversion is one division, and the reason it is worth a page anyway is that this is the direction people get wrong. The percent sign invites multiplication, so a percentage is routinely left as 37.5 in a place that wanted 0.375, and the answer that comes out is a hundred times too large while looking entirely reasonable on the page. Dividing by a hundred is also just a shift of the decimal point two places to the left, which is worth seeing once because it explains the sign itself: a percentage is a count of hundredths, so 37.5 percent is 37.5 hundredths, and 37.5 hundredths written as a plain number is 0.375. The panel prints a second reading beside the first, the same number per thousand, and that one moves the point a single place to the right instead: 37.5 percent is 375 per thousand. The pair is there because the two readings catch different mistakes. A per thousand figure is ten times the percentage, so if the two lines do not stand in a ratio of ten to one, something upstream is wrong. The decimal is what a spreadsheet, a script or any formula actually wants: a rate entered as 7 rather than 0.07 will multiply a quantity by seven instead of by seven hundredths, and nothing in the output will look unusual. Both readings come from the percentage you typed rather than one from the other, so the rounding of the first line never compounds into the second. Three boundaries are worth stating early. Negative percentages are accepted and keep their sign, because a rate of change and a temperature both run below zero. Values above a hundred are accepted too and give a decimal above one, which is not a mistake but what it means for a quantity to more than double. And the decimal is printed to six places while the percentage is printed to four, because dividing by a hundred shifts the point two places and those two places have to land somewhere; the per thousand figure is printed to three places for the same reason in reverse, since it is ten times the percentage rather than a hundredth of it.
Common percentages written as decimals
| Percent (%) | Decimal | Per thousand (‰) |
|---|---|---|
| 1 | 0.01 | 10 |
| 2.5 | 0.025 | 25 |
| 5 | 0.05 | 50 |
| 7.5 | 0.075 | 75 |
| 10 | 0.1 | 100 |
| 12.5 | 0.125 | 125 |
| 20 | 0.2 | 200 |
| 25 | 0.25 | 250 |
| 40 | 0.4 | 400 |
| 50 | 0.5 | 500 |
| 75 | 0.75 | 750 |
| 100 | 1 | 1000 |
Every row is one number in the three spellings this page moves between, and the columns are in the order the page works them: fill in the first and the other two are what the panel prints. The rows are the percentages that come up most often in ordinary use, and the two that carry a half are the ones worth knowing by heart, because 2.5 and 7.5 percent are where a decimal that looks like a typo turns out to be right. Read any row across and the relations hold: 12.5 percent is 0.125 and 125 per thousand, so the first column divided by a hundred gives the second and multiplied by ten gives the third. The last row is the one that matters for catching errors, because it is the only row where the decimal is not smaller than the percentage: 100 percent is 1, and anything above that row is a decimal above one.
Formula
Decimal = percent ÷ 100 Per thousand = percent × 10
- Percent
- The number to convert, without the percent sign: 37.5, 7, 0.0001, -25. Any finite value is accepted, and there is no lower or upper bound on it.
- Decimal
- The percentage divided by one hundred, which is the number to put into a formula. For any percentage above one this is smaller than the percentage it came from, and that is the quickest way to catch a missed division.
- Per thousand
- The percentage multiplied by ten, marked with the per thousand sign. It is the same quantity as the first line and the second line, so it must always be ten times the percentage and a thousand times the decimal.
- The shift
- Two places left for the decimal, one place right for the per thousand figure. Nothing is rounded on the way in: the percentage you type is used exactly, and only the printed readings are rounded.
Three uses are worth separating. The first is a formula that takes a rate, where the input has to be a plain number: interest written as 0.05, a growth factor written as 1.03, a discount written as 0.15. The second is reading a figure that was quoted as a percentage back into the scale of the thing it describes, which is where the per thousand reading helps, because a rate in the news is often given per thousand or in basis points rather than in percent. The third is checking a number you already have: if a percentage and a decimal are supposed to describe the same rate and the decimal is not the percentage over a hundred, one of the two came from somewhere else.
Worked examples
37.5 percent as a decimal
- Write the percentage without its sign: 37.5
- Divide by a hundred: 37.5 ÷ 100 = 0.375
- The same number per thousand is ten times the percentage: 37.5 × 10 = 375
The default case. Read the two lines together and the ratio is ten to one, which is the check that catches almost every mistake on this page.
7 percent entered into a spreadsheet
- Write the percentage without its sign: 7
- Divide by a hundred: 7 ÷ 100 = 0.07
- Per thousand: 7 × 10 = 70
This is the case the page exists for. A cell formatted as a percentage would show 7 percent for a stored value of 0.07, so a formula that was handed 7 rather than 0.07 returns a hundred times too much, and the number still looks like a plausible rate.
12.3457 percent, with all four decimals used
- Divide by a hundred: 12.3457 ÷ 100 = 0.123457
- Per thousand: 12.3457 × 10 = 123.457
- Check the ratio: 0.123457 × 1000 = 123.457
The decimal needs six places to hold a percentage that used four, because dividing by a hundred moves the point two places. The per thousand figure needs three, because multiplying by ten moves it one place the other way. Those two numbers are chosen to match, not copied from each other.
A negative percentage
- Keep the sign: -25
- Divide by a hundred: -25 ÷ 100 = -0.25
- Per thousand: -25 × 10 = -250
Every reading keeps the sign, so all three stay on the same side of zero. A price fall of 25 percent and a temperature of -25 degrees both arrive here as a negative percentage, and neither should come back positive.
Limitations
The decimal is displayed to six places and the per thousand figure to three, so a percentage below five hundred-thousandths of a percent reads as zero on the first line and as zero on the second. 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 six places. A percentage that carries more than four decimals is not rounded on the way in, but the readings themselves are rounded to the places just named, so a value near the last printed digit can come back one step off. No distinction is drawn between a positive and a negative base: a percentage is read as a pure number, so the sign is carried through without asking what it was a percentage of, and a rate that fell from a negative base needs the arithmetic of the change rather than this page. The page has no notion of a percentage point, a basis point or any other named unit, and it does not round the percentage you typed to something tidier first.
Frequently asked questions
- How do I convert a percentage to a decimal?
- Divide by a hundred, which is the same as moving the decimal point two places to the left: 37.5 percent becomes 0.375, 7 percent becomes 0.07. The sign goes away at the same time, because it was standing in for the division rather than marking a unit.
- Why does 7 percent become 0.07 and not 7?
- Because a percentage is a count of hundredths. Seven percent means seven hundredths, and seven hundredths written as a plain number is 0.07. Dropping the sign without dividing is the single most common mistake in this direction, and it multiplies any answer by a hundred.
- When do I need the decimal form instead of the percentage?
- Whenever something else does the arithmetic. A spreadsheet cell, a script and most formulas take a rate as a plain number, so 5 percent has to arrive as 0.05; a cell that is formatted to display percentages will still show it as five percent once it is stored that way.
- What is the per thousand figure for?
- It is the same quantity written with a thousand in the denominator, and it is ten times the percentage. Rates that are awkward as percentages are often quoted that way, and having it on the panel means a figure given per thousand can be read off without a second calculation. It also acts as a check, since it must be exactly ten times the first line.
- Why do the decimal and the per thousand figure carry a different number of decimals?
- Because they are the percentage scaled by a hundred and by ten respectively, so the point moves a different number of places in each. The percentage is printed to four places, the decimal to six and the per thousand figure to three, which is the set that lets a percentage using all four of its places come back exact on both other lines.
- What happens to a very small percentage?
- It is converted exactly and then rounded for display. Below five hundred-thousandths of a percent both readings print as zero, not because the value was taken to be zero but because six places and three places are not enough to show it. A percentage of 0.0001 still survives as 0.000001.
- Can the decimal be larger than one?
- Yes, whenever the percentage is above a hundred. Two hundred and fifty percent is 2.5, and that is the correct decimal for a quantity that grew to more than double. Nothing on this page treats a value above a hundred as a mistake.
References
- NIST Special Publication 811, Chapter 7, section 7.10.2 — the percent sign stands for the number 0.01, which is what makes division by a hundred the conversion rather than a convention — National Institute of Standards and Technology (United States)
- Decimal fraction — an arithmetical fraction whose denominator is an integral power of ten, which is why dividing by a hundred is a shift of the decimal point and not a calculation — Encyclopedia of Mathematics, European Mathematical Society (international)
- Percent — a ratio or fraction is converted to a percentage by multiplying by a hundred, and the same definition runs the other way as a single division — Wolfram MathWorld (United States)