Continued Fraction Calculator
Convert fractions to continued fraction representation and calculate convergents.
Enter Fraction
About Continued Fractions
A continued fraction has the form:
aâ + 1/(aâ + 1/(aâ + 1/(aâ + ...)))
Notation: [aâ; aâ, aâ, aâ, ...]
Continued Fraction
[3; 7, 16]
= 3.1415929204
Terms
3
Type
Finite
Convergents
| n | aâ | pâ/qâ | Value |
|---|---|---|---|
| 0 | 3 | 3/1 | 3.00000000 |
| 1 | 7 | 22/7 | 3.14285714 |
| 2 | 16 | 355/113 | 3.14159292 |
Properties
- Rational numbers have finite continued fractions
- Irrational numbers have infinite continued fractions
- Convergents give best rational approximations
- |x - pâ/qâ| < 1/(qâ * qâââ)
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
ðŸâĹĄ
Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
ðŸââLast reviewed: May 2026
âĹâFormula checks are based on standard references and internal QA review.