Everyday & Math

Fraction to Decimal & Percent Converter

Convert any simple or mixed fraction into a decimal, a percentage, its simplified form and its reciprocal, with an imperial inch chart.

Fraction Input

Number Format Region

Fraction Type

Common Imperial Fractions

Numerator (top number)

num

Denominator (bottom number)

den

The denominator is clamped to a minimum of 1, so a division by zero can never reach the result cards. Switch to “Mixed Number” to activate the whole-number row, for example 2 3/4.

Decimal Value

0.75

3/4 = 3/4 · terminating decimal

Breakdown

Percentage Value75.00 %

Simplified Fraction3/4

Simplified Fractional Part3/4

Improper Fraction3/4

Reciprocal Value (1 ÷ fraction)1.3333

Visual Share

75.00 % of a single whole unit is filled.

How do you convert a fraction into a decimal number and a percentage using one single online converter?

A fraction is a division that has not been carried out yet. The Fraction to Decimal & Percent Converter finishes that division for you: enter a numerator and denominator — optionally with a whole number for mixed values such as 2 and 3/4 — and the tool returns the exact decimal, the equivalent percentage, the reduced fraction in lowest terms, and the reciprocal. The circular chart on the right shows the fractional remainder as a filled slice, which makes the relationship between 3/4 and 75% immediately visible rather than abstract.

What are the exact formulas behind fraction, decimal, percentage and reciprocal conversion?

Improper numerator = whole x denominator + numerator
Decimal value      = improper numerator / denominator
Percentage value   = decimal value x 100
Simplified form    = (improper numerator / GCD) / (denominator / GCD)
Reciprocal         = 1 / decimal value            (undefined when decimal = 0)
Denominator        = clamp(value, 1, 1000)        (never zero)

GCD is the greatest common divisor, computed with the Euclidean algorithm. Reducing by the GCD is what turns 6/8 into 3/4 without changing the value.

What is the full conversion chart for imperial inch fractions from 1/16 up to 15/16?

Fraction	Reduced	Decimal (in)	Percent	Millimetres
1/16	1/16	0.0625	6.25 %	1.587
2/16	1/8	0.1250	12.50 %	3.175
3/16	3/16	0.1875	18.75 %	4.762
4/16	1/4	0.2500	25.00 %	6.350
5/16	5/16	0.3125	31.25 %	7.938
6/16	3/8	0.3750	37.50 %	9.525
7/16	7/16	0.4375	43.75 %	11.112
8/16	1/2	0.5000	50.00 %	12.700
9/16	9/16	0.5625	56.25 %	14.287
10/16	5/8	0.6250	62.50 %	15.875
11/16	11/16	0.6875	68.75 %	17.462
12/16	3/4	0.7500	75.00 %	19.050
13/16	13/16	0.8125	81.25 %	20.637
14/16	7/8	0.8750	87.50 %	22.225
15/16	15/16	0.9375	93.75 %	23.813

Which common fractions terminate cleanly and which ones repeat forever as decimals?

Fraction	Decimal	Percent	Behaviour
1/2	0.5	50.00 %	Terminates
1/3	0.333…	33.33 %	Repeats (3)
1/4	0.25	25.00 %	Terminates
1/5	0.2	20.00 %	Terminates
1/6	0.1666…	16.67 %	Repeats (6)
1/7	0.142857…	14.29 %	Repeats (142857)
1/8	0.125	12.50 %	Terminates
1/9	0.111…	11.11 %	Repeats (1)
1/16	0.0625	6.25 %	Terminates

How do you turn a mixed number into an improper fraction before dividing it out?

Multiply the whole number by the denominator, add the numerator, and keep the same denominator. Two and three quarters becomes eleven quarters, five and one half becomes eleven halves, and ten and seven sixteenths becomes one hundred and sixty seven sixteenths. Only after that single step does the division produce a correct decimal — dividing 3 by 4 and pasting a 2 in front of the result is a common shortcut that fails as soon as the fraction is improper to begin with.

Why does the calculator refuse a denominator of zero instead of showing an error value?

Division by zero has no defined result, so any downstream percentage, reciprocal, or chart geometry built on it would be meaningless. Instead of propagating NaN or Infinity through the interface, the denominator is clamped to a strict minimum of one and a validation alert replaces the result cards until a valid value is supplied. Every other input follows the same discipline: empty fields fall back to their minimum, and out-of-range values are clamped on blur.

Frequently Asked Questions

Start by converting the mixed number into an improper fraction: multiply the whole number by the denominator and add the numerator, so 2 and 3/4 becomes (2 × 4 + 3) / 4 = 11/4. Then divide the numerator by the denominator: 11 ÷ 4 = 2.75. To express the same value as a percentage, multiply the decimal by 100, giving 275%. The calculator performs the improper-fraction step internally, which is why the decimal, the percentage, and the reciprocal all stay consistent with each other.

Divide both the numerator and the denominator by their greatest common divisor. For 6/8 the greatest common divisor is 2, so the reduced form is 3/4. On a tape measure this matters because imperial rules are marked in halves, quarters, eighths, and sixteenths — a measurement written as 10/16 is physically the 5/8 mark, and reading it in reduced form removes a whole class of cutting errors. This tool reduces every fraction automatically and shows the reduced pair alongside the decimal equivalent.

A fraction in lowest terms terminates only when its denominator factors into nothing but 2s and 5s, because 2 and 5 are the prime factors of base ten. That is why 1/2, 1/4, 1/8, 1/16, 1/5, and 1/20 all terminate, while 1/3 = 0.333…, 1/6 = 0.1666…, and 1/7 = 0.142857142857… repeat forever. When a repeating decimal appears, round to the precision your work requires — three decimals is typical for machining, two for money, and four for engineering drawings.

Multiply the numerator by 100 and then divide by the denominator: 3/4 becomes (3 × 100) ÷ 4 = 75%. Mathematically this is identical to dividing first and multiplying afterwards, but it keeps the arithmetic in whole numbers longer, which is easier to do mentally. For mixed numbers, convert to an improper fraction first, so 2 and 3/4 becomes 11/4 and then (11 × 100) ÷ 4 = 275%.

The reciprocal is the fraction flipped upside down: the reciprocal of 3/4 is 4/3, or 1.3333 as a decimal. You need it whenever you divide by a fraction, because dividing by a fraction is the same as multiplying by its reciprocal. It also appears in gear ratios, lens optics, resistor networks in parallel, and unit conversions such as turning miles per gallon into gallons per mile. Zero has no reciprocal, which is why the reciprocal card is disabled when the fraction evaluates to zero.

Division by zero is undefined: there is no number that, multiplied by zero, produces a non-zero numerator. Rather than emitting NaN or Infinity into the result cards, this calculator clamps the denominator to a strict minimum of 1 and shows a validation alert if an empty or invalid value is typed. That guardrail keeps the decimal, percentage, reciprocal, and pie chart in a defined state at all times.

Multiply the decimal by the denominator you want to work in — usually 16 for a standard tape measure — then round to the nearest whole number and place it over that denominator. For 0.31 inches, 0.31 × 16 = 4.96, which rounds to 5, giving 5/16 of an inch. Reduce the result if possible: 8/16 collapses to 1/2. For finer machining work use 32 or 64 as the working denominator and accept the extra precision.

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