Continued Fraction Calculator

[a₀; a₁, a₂, ...]

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Number

CF Representation

[3; 7, 15, 1, 288, 1, 2, 1, 3, 1, 7, 3, 1, 11, 12]

Convergents

p/q3/1= 3.00000000001.42e-1

p/q22/7= 3.14285714291.26e-3

p/q333/106= 3.14150943408.32e-5

p/q355/113= 3.14159292042.70e-7

p/q102573/32650= 3.14159264936.89e-10

p/q102928/32763= 3.14159265022.46e-10

p/q308429/98176= 3.14159264996.52e-11

p/q411357/130939= 3.14159265001.26e-11

p/q1542500/490993= 3.14159265002.95e-12

p/q1953857/621932= 3.14159265003.22e-13

p/q15219499/4844517= 3.14159265001.07e-14

p/q47612354/15155483= 3.14159265003.11e-15

p/q62831853/20000000= 3.14159265000.00e+0

p/q738762737/235155483= 3.14159265000.00e+0

p/q8927984697/2841865796= 3.14159265000.00e+0

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About Continued Fraction Calculator

A continued fraction calculator that converts any real number into its continued fraction representation [a₀; a₁, a₂, ...]. Shows convergents (p/q rational approximations), detects periodic patterns for quadratic irrationals, and finds the best rational approximation for any denominator bound. All calculations are client-side.

Continued Fraction Calculator Features

CF expansion
Convergents
Best approx
Periodic detect
Custom input

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