Continued Fraction Calculator
Convert a fraction to its continued fraction representation. Shows coefficients, convergents, and approximation error.
Inputs
Results
Continued Fraction
[3; 7, 16]
Number of Terms3
Final Convergent355/113
Approximation Error0
How to Use This Calculator
- Enter Numerator and Denominator.
- Review the Continued Fraction result.
- Use Number of Terms and Final Convergent to inform your decision.
- Use the chart to visualize the results and explore different scenarios by adjusting inputs.
What each input means
- Numerator
- Numerator of the fraction (e.g., 355 for the classic pi approximation 355/113)
- Denominator
- Denominator of the fraction
How this is calculated
Worked example, using the default values
- Identify Input ParametersNumerator = 355, Denominator = 113 = 2 input(s) provided
- Calculate Continued FractionContinued Fraction[3; 7, 16] = [3; 7, 16]
- Calculate Number of TermsNumber of Terms3 = 3
- Calculate Final ConvergentFinal Convergent355/113 = 355/113
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators.
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