Egyptian Fraction Calculator

About this calculator

An Egyptian fraction is a sum of distinct unit fractions — fractions with a numerator of 1, like ½, ⅓, or 1/17 — and takes its name from the fact that ancient Egyptian mathematicians, as recorded in documents like the Rhind Papyrus, represented all fractions this way rather than using a general numerator over a denominator. Every positive rational number less than 1 can be written as a finite sum of distinct unit fractions.

This calculator expands a proper fraction into its Egyptian fraction form using the greedy algorithm (also called the Fibonacci–Sylvester method), which repeatedly subtracts the largest possible unit fraction at each step. It's a classic topic in recreational and number theory, used in math education to illustrate greedy algorithms and number representation, and it's a fun way to explore how differently ancient mathematical systems could express the same quantities we now write as simple numerator/denominator fractions.