Continued Fraction Calculator

To find the generalized continued fraction, write the fraction and hit calculate button

r = a0+ 1a1+1

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Continued Fraction Calculator

Continued fraction calculator is used to calculate the continued fraction representation of simple fractional numbers. It converts the simple fraction into a sequence of numbers and the reciprocal of a simple fraction.

What is a Continued Fraction?

Continued fractions are a unique way of representing real numbers as an infinite sequence of numbers where each number is the sum of an integer and the reciprocal of a simple fraction. A continued fraction is used to approximate the real numbers to their simple form.


The formula to find the continued fraction is:

r = a0 + 1/a1+1


  • a0 = first term.
  • a1 = next term.

How to calculate the Continued Fraction?

Example 1:

Find the Continued fraction when the simple fraction is “7/8”.


Step 1: Write the given fraction.

Simple fraction = 7/8, Continued fraction =?

Step 2: Write the formula to find continued fraction

r = a0 + 1/a1+1

Step 3: Write the given fraction in the above expression.

Simple fraction = 7/8

Simple fraction = 1/(8/7)

Simple fraction = 1/[1 + 1/7] ----------> (i)

Continued fraction formula.

r = a0 + 1/a1+1 ---------> (ii)

Compared the equation (i) & (ii) then get the answer.

Generalized continued fraction = [0; 1, 7]

More results

Here are some other results of the continued fraction.

Simple Fraction

Generalized Continued Fraction


[1; 2]


[3; ]


[2; 3, 1, 1]


[1; 1, 6]




[37; 1, 1, 1]

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