Ratio Calculator: Simplify a Ratio Like 12:18
Reduces the ratio of two positive numbers a and b to its simplest whole-number form by dividing both sides by their greatest common divisor, and echoes the original values so you can compare 12:18 with the simplified 2:3.
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Formula
How the calculation works
The calculator finds the greatest common divisor of the two positive numbers you enter, which is the largest whole number that divides both of them exactly with no remainder.
It then divides each side of the ratio by that divisor, so 12 and 18, whose greatest common divisor is 6, are returned as 2 and 3 while keeping their original order.
The values you typed come back unchanged as ratioA and ratioB, and the reduced pair is returned as simplifiedA and simplifiedB, so the input and the answer sit side by side.
Common mistakes
- Entering zero or a negative number is rejected with a CalcError, because a ratio in this tool is only defined for two positive quantities.
- Swapping the order of the two numbers changes the meaning of the ratio, even though the simplified pair may look familiar in reverse.
- Forgetting that a greatest common divisor of one leaves the ratio unchanged, so a pair like 7:9 is already in its simplest whole-number form.
When to use it
- Scale a recipe or a mixing chart written as 12:18 down to the tidy pair 2:3 before you measure out each ingredient.
- Check whether two gear or pulley sizes share a common factor so you can describe them as one simple whole-number ratio.
Worked example
With a = 12 and b = 18, the greatest common divisor is 6, so the ratio 12:18 simplifies to 2:3.
Common questions
What do ratioA and ratioB contain?
They echo the two positive numbers you entered, so with 12 and 18 the fields hold 12 and 18 exactly as typed.
How is the simplified ratio computed?
Both sides are divided by the greatest common divisor, so 12:18 becomes 2:3 because 6 divides both 12 and 18.
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