Decimal to Percent Calculator

A decimal to percent calculator turns a decimal into a percent by multiplying it by 100, and it runs the same idea backwards and sideways for fractions. Example: 0.625 becomes 62.5%, and the same value written as a fraction is 5/8. This page handles all six conversions between decimals, fractions and percents, and shows every step.

Three sister tools cover the neighboring questions. The Percentage Calculator answers "what is 15% of 200" and "45 is what percent of 180", the Decimal to Fraction Calculator focuses on turning long decimals into clean fractions, and the Percentage Change Calculator compares two values over time. Use this page when the number itself is fine and you only need it written in a different form.

How the conversion works

The word percent comes from "per hundred", so a percent is nothing more than a fraction whose denominator is 100. That single definition produces every formula on this page:

Multiplying by 100 moves every digit two places to the left of the decimal point, which is why the practical shortcut is "slide the point two places right" going into a percent and "two places left" coming back out. Nothing about the value changes, only the way it is written. 0.5, 50% and 1/2 are the same quantity in three costumes.

Worked example: 0.4567 as a percent

Suppose a spreadsheet reports a conversion rate of 0.4567 and you need it as a percent for a report.

1. Start with the decimal: 0.4567.
2. Multiply by 100: 0.4567 x 100 = 45.67.
3. Add the percent sign: 45.67%.
4. As a check, slide the decimal point two places to the right: 0.4567 becomes 45.67. Same answer.

Writing the same value as a fraction takes one more thought. There are four decimal places, so the denominator is 10 to the fourth power, which is 10,000, and the numerator is the digit string 4567. That gives 4567/10,000. The numerator 4567 is a prime number, so nothing cancels and 4567/10,000 is already in lowest terms. Three ways to write one number: 0.4567 = 45.67% = 4567/10,000.

The six conversions at a glance

Every route between the three forms is two steps or fewer. The table lists all six with the example the calculator opens on:

Second worked example: 5/8 as a percent

Fraction to percent is the conversion people get wrong most often, because it is two operations instead of one. Take 5/8, the width of a common wrench or the share of a class that passed a quiz:

1. The fraction bar means divide: 5 / 8 = 0.625.
2. Multiply the decimal by 100: 0.625 x 100 = 62.5.
3. Add the percent sign: 62.5%.

A second route avoids decimals entirely. Scale the fraction so the denominator is 100: multiply top and bottom by 12.5, and 5/8 becomes 62.5/100, which reads directly as 62.5%. That trick is fastest when the denominator already divides 100 cleanly, as with 4, 5, 10, 20, 25 and 50. For a denominator such as 8, 3 or 7, dividing first is easier.

Third worked example: 62.5% back to a fraction

Going the other way shows why the calculator prints a greatest common divisor. Start from 62.5%:

1. Percent means per hundred, so write it over 100: 62.5/100.
2. A fraction cannot keep a decimal on top, so multiply top and bottom by 10: 625/1000.
3. The greatest common divisor of 625 and 1000 is 125.
4. Divide both by 125: 5/8.

The same procedure works for any percent. 8.25% becomes 825/10,000, and dividing both by 25 gives 33/400. A percent with no decimal is easier still: 25% is 25/100, which reduces to 1/4 by dividing both by 25.

Common fractions, decimals and percents

These are the values worth memorizing. Once you know them, most conversions become recognition rather than arithmetic. The last column flags the fractions whose decimals repeat forever:

Notice the eighths. Each step of 1/8 is exactly 12.5 percentage points, which is why 1/8, 3/8, 5/8 and 7/8 land on 12.5%, 37.5%, 62.5% and 87.5%. Sixths and thirds never land cleanly, because their denominators contain the prime factor 3.

Percent to decimal and percent to fraction reference

Formulas almost always want the decimal form, not the percent form. This table gives the decimal and the exact reduced fraction for the percents that turn up most often in money and measurement:

Turning a score into a percent

Grades are the most common everyday use of fraction to percent. Points earned go on top, points possible on the bottom, and the two-step conversion does the rest:

Only 38 out of 45 fails to land on a clean number, because 45 contains the factor 3 and 9. That is the row where rounding matters, and where a gradebook and a spreadsheet can disagree in the second decimal place.

How to use this calculator

1. Pick the direction from the six buttons at the top. The small line under each label shows the example that direction produces.
2. Type the value. Decimal and percent modes take one field; the two fraction modes take a numerator and a denominator.
3. Read the headline number in the colored card. It answers the exact conversion you chose.
4. Check the three tiles below it. They always show the same quantity as a decimal, a percent and a reduced fraction, so you never have to run a second conversion.
5. Follow the numbered steps if you need to show your work, for homework or for a document someone else will check.
6. Tap Use on any row of the common-values table to load that value into every mode at once.

The result updates as you type, and the whole calculation runs in your browser.

Who this calculator is for

• Students doing fraction, decimal and percent homework who need the intermediate steps, not just the answer.
• Teachers and tutors turning raw points into a percent score, or building a worksheet of equivalent values.
• Spreadsheet users who exported a rate as 0.0825 and need 8.25% for a report, or the other way around for a formula.
• Shoppers and budgeters converting a tax rate, a tip, or a discount between the form printed on the receipt and the form a formula needs.
• Trades and makers moving between the fractional inch on a tape measure and the decimal a machine or a drawing expects.
• Anyone reading statistics who wants to sanity-check whether 0.08 in a chart means 8% or 0.08%.

Key terms explained

• Percent: a number of hundredths. The symbol % stands for the factor 0.01, so 45.67% means 45.67 x 0.01.
• Decimal: a number written with a decimal point, where each place to the right is a tenth of the place before it.
• Numerator and denominator: the top and bottom of a fraction. The numerator counts the parts you have, the denominator says how many parts make a whole.
• Lowest terms: a fraction whose top and bottom share no common factor other than 1. 625/1000 is not in lowest terms; 5/8 is.
• Greatest common divisor: the largest whole number that divides both the numerator and the denominator. Dividing by it reduces the fraction in one move.
• Improper fraction: a fraction whose numerator is larger than its denominator, such as 5/4. It converts to a percent above 100%.
• Terminating and repeating decimals: a decimal that ends, such as 0.625, versus one that cycles forever, such as 0.3333 and onward.
• Percentage point: the plain difference between two percents. Moving from 4% to 6% is 2 percentage points, not 2%.

Why some fractions repeat forever

A fraction in lowest terms turns into a terminating decimal only when its denominator is built from the primes 2 and 5, the two primes that divide 10. Denominator 8 is 2 x 2 x 2, so 5/8 stops after three places at 0.625. Denominator 20 is 2 x 2 x 5, so 17/20 stops at 0.85. Denominator 3, 6, 7, 9 or 45 brings in a prime that 10 does not contain, so the long division never closes and the digits cycle. 1/3 gives 0.3333 and onward, 1/6 gives 0.166666 and onward, and 38/45 gives 0.844444 and onward.

This is why the calculator keeps the exact fraction next to the rounded decimal. If you are going to feed the number into another calculation, carrying the fraction avoids compounding a rounding error; if you are going to print it, rounding the percent to one or two decimals is normal and expected.

What changes the result

• How many decimal places you type: 0.33 is 33%, 0.333 is 33.3%, and 0.3333 is 33.33%. Each extra digit is a real change in value, not just in precision.
• Where the rounding happens: rounding the decimal first and then multiplying by 100 can differ in the last digit from multiplying first and rounding after.
• Whether the value is above 1: anything above 1 becomes a percent above 100%, which surprises people who expect percents to stop at 100.
• The sign: a negative decimal produces a negative percent. The magnitude conversion is identical.
• The denominator you started from: a denominator built only from 2s and 5s gives a clean decimal; anything else repeats and has to be rounded.
• Very small values: 0.005 is 0.5%, not 5%. Values below 0.01 are the ones most often misread by a factor of ten.

Tips for doing it in your head

• Two places, always. Going to a percent, slide the decimal point right twice. Coming back, slide it left twice. Add zeros as placeholders when you run out of digits: 5% becomes 0.05, not 0.5.
• Scale to 100 when you can. If the denominator divides 100 evenly, just scale: 17/20 is 85/100, so 85%. No division needed.
• Learn the eighths. Every eighth is 12.5 percentage points, so 3/8 is 37.5% and 7/8 is 87.5%.
• Sanity-check against a half. If the fraction is bigger than 1/2, the percent must be above 50%. It catches most slips instantly.
• Watch the whole number. A decimal such as 1.35 has a 1 in front, so the percent is 135%, not 35%.

Where these conversions show up

The conversion looks like a classroom exercise until you notice how often software hands you one form and asks for the other. A spreadsheet stores 8.25% internally as the number 0.0825, so a cell that looks like a percent is really a decimal wearing a format. Interest, tax and tip formulas all want the decimal: to add 8.25% sales tax to a price you multiply by 1.0825, and to take 20% off you multiply by 0.80. Statistics reported as proportions, such as 0.86 of respondents, become 86% before anyone quotes them out loud. A tape measure reads in eighths and sixteenths while a drawing reads in decimal inches, so 3/16 and 0.1875 have to be the same number in your head. Each of those is the same conversion in a different costume.

Limitations and assumptions

• Repeating decimals are rounded for display. The exact value survives only in the fraction column.
• The decimal-to-fraction conversion reads up to nine decimal places. Longer inputs are truncated before the fraction is built.
• An exact fraction from a long decimal can look ugly, such as 4567/10,000. The calculator also offers the closest fraction with a denominator of 64 or less when the exact one is unwieldy.
• The calculator converts a value; it does not compute a percentage of something, a percent change, or a weighted grade. Use the sister tools for those.
• A denominator of zero is rejected rather than computed, because division by zero has no defined result.

How it compares to related calculators

This page answers "how do I write this number as a percent, a decimal, or a fraction?" A different question has a better-fitting tool:

• For "what is 15% of 200" or "45 is what percent of 180", use the Percentage Calculator.
• To compare two values over time, use the Percentage Change Calculator or the Percentage Increase Calculator.
• For long decimals and repeating patterns, the Decimal to Fraction Calculator goes deeper on the fraction side.
• To reduce a fraction you already have, use the Simplify Fractions Calculator; to add or multiply fractions, use the Fraction Calculator.
• To convert a grade point average into a percent scale, use the GPA to Percentage Calculator.
• To compare a measured value against an accepted one, use the Percent Error Calculator; to round a result to a set number of places, use the Rounding Calculator.

Sources

Every result on this page is deterministic arithmetic that follows from the definition of a percent, so there are no rates, prices or statistics to cite. Multiplying by 100, dividing a numerator by a denominator, and reducing a fraction by its greatest common divisor are exact operations. The one convention worth sourcing is the meaning of the percent symbol itself:

• National Institute of Standards and Technology (NIST) - Special Publication 811, Guide for the Use of the International System of Units, which defines the symbol % as the number 0.01 and covers the correct use of percent in reported values.