Ratio Simplifier Calculator
Simplify a ratio to its lowest terms.
Results update as you type.
How it works
A ratio compares two quantities, and simplifying it to lowest terms makes it clearer and easier to work with, which this calculator does. You enter two whole numbers, and it returns the simplified ratio and the decimal value of the first divided by the second. Simplifying works exactly like reducing a fraction: you find the greatest common divisor (GCD) of the two numbers — the largest whole number that divides both without a remainder — and divide each by it. For example, the ratio 6:4 has a GCD of 2, so it simplifies to 3:2, and 100:25 simplifies to 4:1. The simplified ratio expresses the same proportion in the smallest whole numbers, which is easier to understand and compare. Ratios appear everywhere — recipes (2 parts flour to 1 part sugar), maps and scale models, mixing paint or chemicals, aspect ratios, odds, and financial comparisons — and putting them in simplest form is standard practice. The decimal value is useful for direct comparison or when you need a single number. This calculator requires whole numbers; for ratios with decimals, first scale both up to whole numbers (for example, 1.5:2 becomes 3:4 by multiplying both by 2). Simplifying ratios is a foundational math skill used from grade school through everyday life. Enter two numbers to simplify the ratio.
Divide both numbers by their greatest common divisor (GCD)
To simplify a ratio, find the greatest common divisor (GCD) of the two numbers — the largest number that divides both evenly — and divide each by it. This reduces the ratio to its lowest terms while keeping the same proportion, like reducing a fraction.
Source:Number theory (GCD)
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Worked example
How to use this calculator
- 1
Enter your values
Enter first number and second number.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Simplified ratio updates instantly as you type — no button to press.
Frequently asked questions
How do you simplify a ratio?
Find the greatest common divisor (GCD) of the two numbers — the largest number that divides both evenly — and divide each by it. For 6:4, the GCD is 2, giving 3:2. This reduces the ratio to its lowest terms while keeping the same proportion, exactly like simplifying a fraction to its simplest form.
What is the greatest common divisor?
The greatest common divisor (GCD), also called the greatest common factor, is the largest whole number that divides two or more numbers without leaving a remainder. For 12 and 18, it is 6. Dividing both numbers of a ratio by their GCD simplifies it fully in one step, which is how this calculator reduces the ratio.
Why simplify ratios?
A simplified ratio uses the smallest whole numbers that express the same proportion, making it easier to understand, compare, and use. Saying a recipe is 3:2 is clearer than 6:4, and simplified ratios make scaling and comparison straightforward. It is standard mathematical practice, the same reason fractions are reduced to lowest terms.
Can I simplify a ratio with decimals?
This calculator uses whole numbers, so first convert a decimal ratio to whole numbers by multiplying both parts by the same power of ten. For example, 1.5:2 becomes 15:20 (times 10), which simplifies to 3:4. Once both numbers are whole, you can simplify normally by dividing by their greatest common divisor.
Where are ratios used?
Ratios appear in cooking recipes, map and model scales, mixing paint, chemicals, or concrete, screen aspect ratios, gambling odds, financial analysis, and countless other contexts. Anywhere two quantities are compared proportionally, a ratio describes the relationship, and simplifying it to lowest terms makes that relationship clearest and easiest to apply.