Continued Fraction Calculator
Convert fractions to continued fraction representation and calculate convergents.
Enter Fraction
About Continued Fractions
A continued fraction has the form:
a₀ + 1/(a₁ + 1/(a₂ + 1/(a₃ + ...)))
Notation: [a₀; a₁, a₂, a₃, ...]
Continued Fraction
[3; 7, 16]
= 3.1415929204
Terms
3
Type
Finite
Convergents
| n | aₙ | pₙ/qₙ | 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 - pₙ/qₙ| < 1/(qₙ * qₙ₊₁)
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
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Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.