Ratio of 3 Numbers Calculator
Enter three numbers to form the ratio A : B : C. Choose whether to simplify the ratio to its lowest terms, scale it up or down by a factor, or divide a total amount according to the ratio. You get the simplified form, the greatest common factor, and a step-by-step breakdown of the working. Results update instantly as you type.
What is a ratio of 3 numbers?
A ratio of three numbers, written A : B : C, describes a proportional relationship between three quantities. It tells you how much of each part there is relative to the others. For example, a concrete mix of 1 : 2 : 3 (cement : sand : gravel) means for every 1 unit of cement you use 2 units of sand and 3 units of gravel, whatever the unit is. Unlike a fraction, a 3-part ratio does not reduce to a single number; it captures a three-way split. Ratios can describe anything from ingredient proportions and profit splits to colour mixtures and chemical concentrations.
How to simplify a ratio of 3 numbers
Simplifying a three-part ratio means finding the smallest whole-number form that preserves the proportional relationship. The steps are: (1) List the factors of each number. (2) Find the greatest common factor (GCF) shared by all three numbers. (3) Divide every term by that GCF. The result is the simplified ratio. For instance, 4 : 6 : 10 has a GCF of 2, so dividing each term gives 2 : 3 : 5. If the GCF is 1, the ratio is already in its simplest form. Decimal ratios such as 0.5 : 1 : 1.5 can be simplified by multiplying all terms by a power of 10 to make them integers first (giving 1 : 2 : 3), then dividing by the GCF.
How to divide an amount in a ratio of 3 numbers
To split a total quantity in the ratio A : B : C, add the three parts to get the total number of shares (A + B + C), then divide the total amount by that sum to find the value of one share, and finally multiply each term by the unit share value. For example, to divide 200 in the ratio 2 : 3 : 5: the parts sum to 10, one share is 200 / 10 = 20, so the three portions are 40, 60, and 100 respectively. As a check, 40 + 60 + 100 = 200. This approach works for any quantity: money, weight, area, time, or anything else.
Scaling and equivalent ratios
A ratio is scale-invariant: multiplying or dividing all three terms by the same non-zero number produces an equivalent ratio. The scaled version describes the exact same proportional relationship. If a recipe calls for ingredients in the ratio 1 : 2 : 3 and you want to triple the batch, you scale by 3 to get 3 : 6 : 9. For equivalent ratios, you know one term of the new ratio (say D, the equivalent of A) and you want to find E and F. Divide D by A to get the multiplier k, then multiply B and C by k to get E and F. For example, if A : B : C = 2 : 3 : 5 and D = 10, then k = 10 / 2 = 5, so E = 15 and F = 25, giving the equivalent ratio 10 : 15 : 25.
Common ratio examples and their simplified forms
| Original ratio | GCF | Simplified | Context |
|---|---|---|---|
| 4 : 6 : 10 | 2 | 2 : 3 : 5 | Dividing amounts proportionally |
| 10 : 15 : 25 | 5 | 2 : 3 : 5 | Scaling ingredients |
| 6 : 9 : 15 | 3 | 2 : 3 : 5 | Cement mortar mix |
| 1 : 2 : 3 | 1 | 1 : 2 : 3 | Concrete mix (cement : sand : gravel) |
| 2 : 3 : 5 | 1 | 2 : 3 : 5 | Finance (profit sharing) |
| 3 : 4 : 5 | 1 | 3 : 4 : 5 | Right triangle sides (Pythagorean triple) |
| 12 : 16 : 20 | 4 | 3 : 4 : 5 | Scaled Pythagorean triple |
| 6 : 4 : 2 | 2 | 3 : 2 : 1 | Descending proportion |
| 25 : 50 : 25 | 25 | 1 : 2 : 1 | Nutrient macros (equal ends, double middle) |
| 30 : 20 : 10 | 10 | 3 : 2 : 1 | Business cost allocation |
Everyday 3-part ratios found in cooking, construction, finance, and science.
Frequently asked questions
How do I simplify a 3-part ratio?
Find the greatest common factor (GCF) of all three numbers, then divide each term by that GCF. For example, 6 : 9 : 15 has a GCF of 3, so it simplifies to 2 : 3 : 5. If the GCF is 1, the ratio is already fully simplified. This calculator finds the GCF and simplified form automatically.
How do I divide a sum of money in a ratio of 3 numbers?
Add the three ratio parts to get the total number of shares. Divide the amount of money by that total to find the value of one share. Multiply each ratio part by the unit share to get each person's allocation. For example, to split $50 in the ratio 2 : 3 : 5: total parts = 10, one share = $5, so the three amounts are $10, $15, and $25. Use the "Divide an amount" mode above to do this instantly.
What is the greatest common factor (GCF) and why does it matter?
The GCF of a set of numbers is the largest positive integer that divides all of them without a remainder. For simplifying ratios, the GCF tells you the single number you can divide every term by to reach the lowest-terms form. A GCF of 1 means the ratio cannot be simplified further. A GCF greater than 1 means there is a simpler equivalent ratio.
Can a 3-part ratio include decimals or fractions?
Yes. A ratio like 0.5 : 1.5 : 2 is valid. To simplify it, multiply all terms by a power of 10 to clear the decimals (giving 5 : 15 : 20), then divide by the GCF (5) to get 1 : 3 : 4. This calculator accepts decimal inputs and handles the arithmetic for you.
How are equivalent ratios different from the simplified ratio?
The simplified ratio is the lowest-terms form you get by dividing by the GCF; it is unique. An equivalent ratio is any ratio that describes the same proportional relationship, including scaled-up versions. For example, 2 : 3 : 5, 4 : 6 : 10, and 10 : 15 : 25 are all equivalent, but only 2 : 3 : 5 is the simplified form.
What is the sum of parts and why is it useful?
The sum of parts (A + B + C) tells you how many equal shares the whole is divided into. When you know this total, dividing any given amount by it gives the value of one share, which you then multiply by each ratio term to get the allocation. It is the key step in proportional division.