basic

Continued Fraction First Convergents Calculator

[a₀; a₁, a₂] — rational approximations via convergents.

Computes the first two convergents of a continued fraction from three partial quotients. Convergents are the best rational approximations to the underlying real number.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

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

p₀=a₀, q₀=1; p₁=a₁·a₀+1, q₁=a₁; p₂=a₂·p₁+p₀, q₂=a₂·q₁+1

In depth

Computes the first two convergents of a continued fraction from three partial quotients. Convergents are the best rational approximations to the underlying real number.