Ratio calculator

How do I simplify a ratio?

Divide both numbers by their greatest common factor. 12 : 18 — both divide by 6 — becomes 2 : 3. For decimals, multiply both sides by 10 or 100 first: 1.5 : 2.5 = 15 : 25 = 3 : 5.

How do I find a missing number in a ratio?

Scale the ratio by the same factor on both sides. If A : B = 3 : 4 and A is 9, the factor is 9 ÷ 3 = 3, so B is 4 × 3 = 12. Switch to "Scale" and enter the known side.

What is the aspect ratio of 1920 × 1080?

16 : 9 — both divide by 120. For a 16 : 9 picture 1280 pixels wide, the height is 1280 × 9 ÷ 16 = 720 pixels.

How do I write a ratio as 1 : x?

Divide both sides by the first number. 4 : 10 is 1 : 2.5. It is handy for comparing mixes and scales, such as a 1 : 2.5 cement-to-sand mix.

What is the difference between a ratio and a fraction?

A ratio compares parts with each other; a fraction compares a part with the whole. In a class with 2 boys for every 3 girls, the ratio is 2 : 3, but boys are 2/5 of the class.

Can a ratio have more than two numbers?

Yes. A ratio such as 36 : 48 : 60 simplifies by dividing every term by their greatest common factor, 12, to 3 : 4 : 5. It is read as three quantities in fixed proportion, as in a concrete or paint mix.

Simplifying and scaling

A ratio keeps its meaning when every term is multiplied or divided by the same nonzero number. To simplify, divide by the greatest common factor; for decimals, first multiply every term by a power of 10 to clear the decimal point. 2.4 : 3.6 becomes 24 : 36 and then 2 : 3. To scale, find the factor from the known pair and apply it to the other term: if the ratio is 5 : 7 and the first term must be 40, the factor is 8 and the second term is 56.

A worked example with a mix

A mix is specified as 1 part cement to 2.5 parts sand by volume. If you use 18 buckets of cement, the sand is 18 × 2.5 = 45 buckets. The cement is 1 ÷ 3.5 = 28.6% of the dry mix, and the sand is 71.4%. Notice that the ratio compares the parts with each other, so the percentage of the whole needs the total of the parts, 1 + 2.5 = 3.5.

Common mistakes

Reversing the order is the most frequent one: 3 : 4 and 4 : 3 describe opposite situations, so keep track of which quantity comes first. Mixing units, such as minutes in one term and hours in the other, gives a ratio that is wrong by the unit factor; convert first. Treating a ratio as a fraction of the whole is the third: 2 boys for every 3 girls is the ratio 2 : 3, and boys are 2/5 of the class. Last, simplifying only one term instead of dividing both by the same number changes the ratio.

Sources: OpenStax Prealgebra 2e, the sections on ratios, rates and proportions; the greatest-common-factor method as in OpenStax Elementary Algebra. Related: proportion calculator, aspect ratio calculator, LCM and GCF calculator and golden ratio calculator.