Continued Fraction Approximation Calculator
Find a close rational approximation to an entered numeric value under a maximum denominator.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the bounded-denominator continued-fraction method on the entered JavaScript numeric value.
Build continued-fraction convergents and compare the final admissible semiconvergent with the last convergent
Worked example
π approximated with maximum denominator 1000 gives 355/113≈3.14159292; its absolute numeric error is about 2.67×10⁻⁷.
Assumptions and input details
Input is a floating-point numeric approximation, not an exact symbolic constant or arbitrary-length decimal. Denominator ≤1e6 and |value|≤1e9 keep numerator within safe integer range. Near floating-point ties can affect which equally close fraction is returned.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Add, subtract, multiply or divide fractions and mixed numbers. Follow exact fraction steps, simplification and a number-line diagram.
Convert a repeating decimal block to an exact fraction, or find a fraction’s terminating prefix and complete repeating cycle.
Add, subtract, multiply or divide two real radical terms. Simplify square factors, combine matching radicals and rationalize a radical denominator.
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