Continued Fraction Calculator
Convert a decimal into a continued fraction and a fraction.
Result
How to use
- Enter your values in the fields above.
- Press Calculate to see your result instantly.
- Use the Share button to copy a link to your result.
About this calculator
This calculator expands a decimal number into its continued fraction representation — a sequence of integer terms [a₀; a₁, a₂, a₃, …] found by repeatedly taking the integer part and inverting the remainder — and shows the convergents, the best rational (fraction) approximations obtainable at each step.
Number theory students and programmers use it to find the simplest fraction that closely approximates a decimal (useful for gear ratios, musical tuning, and calendar systems), and it's a classic way to demonstrate why some numbers like π have infinite non-repeating continued fractions while rational numbers terminate. Enter a decimal to see its continued fraction terms and best convergent fraction.
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