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Egyptian fraction calculator

Every proper fraction can be written as a sum of distinct unit fractions (1/2 + 1/3 …), the way ancient Egyptian scribes did. This runs Fibonacci's greedy algorithm and shows the decomposition.

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The Egyptian fraction calculator turns Numerator, Denominator into Egyptian fraction, Number of terms, instantly and for free. For instance, with Numerator = 5 and Denominator = 8 it returns Egyptian fraction = 1/2 + 1/8 and Number of terms = 2.

How to use it

  1. Enter your values: Numerator, Denominator.
  2. Read the result instantly: Egyptian fraction, Number of terms.

Frequently asked questions

What does the Egyptian fraction calculator actually compute?

It takes Numerator and Denominator and derives Egyptian fraction and Number of terms from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

2 values: Numerator and Denominator. Nothing else is required — no account, no file upload.

Can you show a worked example?

With Numerator = 5 and Denominator = 8, the calculator returns Egyptian fraction = 1/2 + 1/8 and Number of terms = 2. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

What is the difference between the Egyptian fraction calculator and the Decimal to fraction calculator?

This one returns Egyptian fraction and Number of terms; the Decimal to fraction calculator returns Fraction. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Continued fraction calculator is the closest one after this: Expand a number into its continued fraction [a₀; a₁, a₂, …] and list the convergents — the best rational approximations at each step. Feed it a decimal, an exact fraction a/b, or a square root √k: rationals terminate, √k is periodic, and irrationals stream on to the term cap. Continued fractions give the closest fractions for a given size of denominator and reveal the hidden structure of numbers like the golden ratio and π.

What else is worth having open alongside it?

Fraction Calculator and Multiple fraction calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from, and how current are they?

Base conversion and number-theory results are exact. Roman numerals follow the standard subtractive form used since the Middle Ages, which is not the only one the Romans themselves used.

Further reading

All guides →
How-toHow to Convert a Fraction to a DecimalDivide the top number by the bottom. Here's the rule, why some fractions repeat, how to round them, and how to turn the result into a percentage.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Convert a Percentage to a Fraction: Over 100, Then ReduceA percentage is just a fraction out of 100. Put the number over 100, reduce to lowest terms, and handle decimal percentages like 12.5% by clearing the decimal first. With examples.How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.How-toHow to Find Prime Factors: Factor Trees and the Division MethodBreak any whole number into its prime building blocks with a factor tree or repeated division — and write the result as a clean prime factorization with exponents.