Ratio Simplify Calculator
A ratio compares two quantities, and the same proportion can be written many ways: 18:24, 9:12 and 3:4 all describe the same relationship. The clearest form uses the smallest whole numbers, found by dividing both terms by their greatest common divisor. This calculator reduces any two-term ratio to its lowest terms and also shows its decimal value. Enter the two terms to see the simplified ratio instantly.
Ratio simplification formula
g = GCD(A, B) via the Euclidean algorithm
simplified ratio = (A / g) : (B / g)
decimal value = A / B
The greatest common divisor is found by repeatedly taking the remainder of the larger term divided by the smaller until the remainder reaches zero. Dividing both terms by this value yields the lowest-terms ratio.
Worked example
Simplify 18:24. The GCD of 18 and 24 is 6. Dividing both terms: 18 / 6 = 3 and 24 / 6 = 4, so the simplified ratio is 3:4. The decimal value is 18 / 24 = 0.75.
Ratio simplification: frequently asked questions
How do you simplify a ratio?
Divide both terms of the ratio by their greatest common divisor (GCD), the largest whole number that divides both exactly. For example, the ratio 18:24 has a GCD of 6, so dividing both terms by 6 gives 3:4. The simplified ratio expresses the same proportion using the smallest whole numbers.
What is the greatest common divisor?
The greatest common divisor, also called the greatest common factor, is the largest positive integer that divides two or more integers without leaving a remainder. It is found efficiently using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is zero. The last nonzero value is the GCD.
Can a ratio with decimals be simplified?
Yes. First multiply both terms by the same power of ten until they are whole numbers, then simplify using the GCD. For example, 1.5:2 becomes 15:20 after multiplying by 10, which simplifies to 3:4. This calculator works with whole-number inputs, so convert any decimal terms to integers first.
What does the decimal value of a ratio mean?
The decimal value is simply the first term divided by the second, showing the ratio as a single number. For 3:4 the decimal value is 0.75, meaning the first quantity is 0.75 times the second. This is useful for comparing ratios: a higher decimal value means a larger first term relative to the second.
Official sources
- National Institute of Standards and Technology: NIST Digital Library of Mathematical Functions.
- National Institute of Standards and Technology: NIST mathematics and statistics.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.