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Continued Fraction Convergent Approximation Calculator

[a₀; a₁, a₂, a₃] — evaluate nested continued fraction.

Evaluates a simple continued fraction [a₀; a₁, a₂, a₃] and reports the convergent value as a decimal approximation.

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Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

[a₀; a₁, a₂, a₃] = a₀ + 1/(a₁ + 1/(a₂ + 1/a₃))

In depth

Evaluates a simple continued fraction [a₀; a₁, a₂, a₃] and reports the convergent value as a decimal approximation.