Finding Rationals that Approximate Irrationals

For the irrationals: π, φ, e, & √2


The calculator uses an iterative process to find a rational approximation that is within the input difference. The algorithm proceeds by selecting successively larger denominators and then exploring a few numerators to find the closest match. The process is repeated until the difference between the rational and the irrational is within the acceptable difference specified.

Select an irrational to approximate, enter an acceptable difference, and press the "Approximate" button.




Approximations for Irrationals: