Ratio Calculator
The ratio calculator simplifies a ratio to lowest terms, solves a proportion for the missing term, scales a ratio, and splits a total in a given ratio.
Simplified ratio
- Original Divided both terms by their greatest common factor, 6.
- 18 : 24
- As a fraction
- 3/4
- As a decimal
- 0.75 to 1
- As percentages of the whole
- 42.86% and 57.14%
How the Ratio Calculator works
A ratio compares two quantities by division. 18 : 24 means 18 of one thing for every 24 of another, and like a fraction it simplifies: divide both terms by their greatest common factor of 6 to get 3 : 4. Scaling both terms by the same number never changes a ratio, which is why 18 : 24, 3 : 4 and 0.75 : 1 are all the same statement.
A ratio compares the parts to each other, not each part to the whole. Mixing concrete at 1 : 3 cement to sand means one bucket in every four is cement.
A proportion is two ratios set equal, and it is solved by cross-multiplication. 3 : 4 = 30 : x is the equation 3/4 = 30/x, and multiplying both sides by 4x clears both denominators. This is the workhorse of scaling: recipes, map distances, drug dosages, model dimensions and unit conversions are all one proportion.
Ratios can have more than two terms, and they work the same way. Concrete at 1 : 2 : 3 cement, sand and gravel is six parts; a cubic yard of concrete needs a sixth of a yard of cement. The simplification rule is the same: divide every term by the GCF of all of them.
Two conventions worth getting right.
Order matters, and the units go with the position. A ratio of 3 : 4 teachers to students is not the same claim as 4 : 3, and writing the ratio without saying which quantity comes first makes it useless. An aspect ratio of 16 : 9 is width to height.
A ratio and a rate are different. A ratio compares quantities of the same kind and has no units; 3 : 4 teachers to students is a bare number. A rate compares different kinds and carries units: 60 miles per hour, $4 per pound. Dividing one by the other gives a unit rate, which is what makes prices comparable: $6 for 3 pounds and $9 for 5 pounds are $2.00 and $1.80 a pound.
The golden ratio is the number phi, (1 + sqrt(5)) / 2, about 1.618, defined by the property that a : b = (a + b) : a. It is irrational, so no whole-number ratio equals it; 8 : 5 and 13 : 8 are the nearest small approximations, and they are consecutive Fibonacci numbers, whose ratios converge on phi.
Ratio Calculator FAQ
How do I simplify a ratio?
Divide both terms by their greatest common factor. 18 : 24 has a GCF of 6, so it simplifies to 3 : 4. For decimal terms, multiply both by a power of ten first: 1.5 : 2.5 becomes 15 : 25, which reduces to 3 : 5.
How do I split an amount in a ratio?
Add the terms to get the number of parts, divide the total by that, then multiply by each term. $4,200 in the ratio 3 : 4 is 7 parts, so $600 a part, giving $1,800 and $2,400. Dividing the total by 3 and by 4 separately is the common error and does not add back to the total.
Is a ratio of 1:3 the same as one third?
No. A ratio of 1 : 3 means one part to three parts (four parts in total), so the first part is a quarter of the whole. One third would be a ratio of 1 : 2. This is the most frequent mistake made with ratios and it matters for anything being mixed.
How do I solve a proportion?
Cross-multiply and divide. For 3 : 4 = 30 : x, multiply 4 x 30 = 120 and divide by 3 to get x = 40. It works because a proportion is two equal fractions, so their cross products are equal. That is the basis of every scaling calculation from recipes to map distances.