Ratio Calculator
Enter two numbers and get the ratio in simplest form, plus its decimal value, with the GCF steps shown.
How to use this calculator
Enter the two quantities being compared and press Calculate. The calculator divides both by their greatest common factor, shows the simplified ratio, and gives the decimal equivalent so you can compare it with other ratios at a glance.
How it works
Simplifying a ratio works exactly like simplifying a fraction: find the greatest common factor (GCF) of both terms and divide each term by it. A ratio is in lowest terms when its two numbers share no common factor besides 1.
Worked example
Example: simplify 12 : 18
Step 1, GCF: the greatest common factor of 12 and 18 is 6.
Step 2, Divide: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
Answer: 2 : 3, which as a decimal is about 0.667.
Common mistakes
- Simplifying only one side: both terms must be divided by the same GCF, or the relationship changes.
- Reading 2:3 as the fraction 2/3 of a whole: a ratio compares parts to each other; 2:3 means 2 parts to 3 parts (5 parts total), not 2 out of 3.
- Order matters: the ratio 2:3 is not the same as 3:2, keep the quantities in the order the question gives them.
When to use it
Ratios describe mixtures (2 parts concentrate to 3 parts water), odds, map scales, aspect ratios of screens and images, and any “for every X there are Y” situation. Simplified form makes comparisons instant: 2:3 and 4:6 are the same ratio, which is obvious only after simplifying.
Frequently asked questions
A ratio compares two quantities by division, written a:b and read “a to b”. It tells you how many times one quantity contains the other.
Divide both terms by their greatest common factor. For 12:18, the GCF is 6, giving 2:3. The calculator above finds the GCF and shows the division.
They use the same division idea, but a ratio a:b compares part to part, while a fraction a/b usually means part of a whole. The ratio 2:3 corresponds to the fraction 2/5 of the total.
Yes, but simplest form uses whole numbers. A ratio like 1.5:2 is usually cleared to 3:2 by doubling both terms first.