Quick answer
Add all three parts to get the total number of shares. Divide the quantity by total shares (unit share), then multiply each part by the unit share. For £600 in ratio 1:2:3: unit share = 600÷6 = £100. Shares: £100 : £200 : £300.
- The denominator is always the sum of all three parts - never one individual part. For 2:3:5, every percentage divides by 10.
- All three shares always add to exactly 100% - use this as a fast sanity check after any calculation.
- Multiplying or dividing all three parts by the same number keeps the ratio equivalent: 1:2:3 = 2:4:6 = 10:20:30.
- Standard concrete mix ratios (cement:sand:aggregate = 1:2:3) and three-partner profit splits are among the most common real-world uses.
- A ratio of 1:1:1 is the only three-part ratio where all three shares are equal - each receives exactly one third of the total.
How to use our 3 ratio calculator
Enter the three ratio parts (a, b, c). The calculator immediately shows the percentage each part represents of the whole. Optionally enter a total quantity to find the exact share for each part. All three percentages will always sum to 100%.
What is a 3-part ratio?
A three-part ratio (a:b:c) describes how a whole is divided into three proportional groups. Unlike a two-part ratio, it requires three values to define the proportional relationship. The ratio 2:3:5 means the whole is divided into 10 parts, with the three groups receiving 2, 3, and 5 parts respectively.
3-part ratio explained to a beginner
Imagine you and two friends split a $30 dinner bill based on how much each person ate - a small meal, a medium, and a large. You agree the split is 1:2:3. Add the parts: 1+2+3 = 6 total shares. Each share is worth $30 ÷ 6 = $5. Small pays 1 × $5 = $5. Medium pays 2 × $5 = $10. Large pays 3 × $5 = $15. Total: $5 + $10 + $15 = $30. Done.
That is the entire three-part ratio method. The formal version just replaces "dinner bill" with any quantity and 1:2:3 with whatever ratio fits your situation. The unit share ($5 here) is the pivot - every share is simply a multiple of it.
Formula and method for three part ratio calculation
To find the percentage each part represents:
$$\%A = \frac{a}{a+b+c} \times 100$$
To find each group's share of a total quantity:
$$\text{Share of A} = \frac{a}{a+b+c} \times \text{Total}$$
Example - 2:3:5 as percentages:
$$2{:}3{:}5 \implies \frac{2}{10} = 20\%,\;\frac{3}{10} = 30\%,\;\frac{5}{10} = 50\%$$
Example - £1000 split in ratio 2:3:5:
$$\$1000 \text{ split } 2{:}3{:}5 \implies \$200,\;\$300,\;\$500$$
Worked examples for three-part ratio
| Ratio | Total | Share A | Share B | Share C |
|---|---|---|---|---|
| 1:1:1 | 300 | 100 (33.3%) | 100 (33.3%) | 100 (33.3%) |
| 1:2:3 | 600 | 100 (16.7%) | 200 (33.3%) | 300 (50%) |
| 2:3:5 | 1000 | 200 (20%) | 300 (30%) | 500 (50%) |
| 1:2:2 | 100 | 20 (20%) | 40 (40%) | 40 (40%) |
| 3:3:4 | 500 | 150 (30%) | 150 (30%) | 200 (40%) |
| 1:3:6 | 2000 | 200 (10%) | 600 (30%) | 1200 (60%) |
When I use three-part splits for budget or profit-sharing work, I always verify the result by summing all three shares and confirming they equal the original total.
A rounding gap of even a cent can compound into a real discrepancy when the same ratio is applied across many months or line items - catching it at the calculation stage is far easier than reconciling it later.
Real-world applications for 3-part ratio
Business profit sharing - three partners in a 2:3:5 profit split on £80,000 annual profit receive £16,000, £24,000, and £40,000 respectively. The ratio reflects their investment, hours worked, or agreed contribution.
Inheritance and estate division - estates divided among three beneficiaries in specified proportions. A ratio ensures a fair and legally clear allocation without ambiguity.
Concrete and construction mixing - standard concrete mix ratios by volume: cement:sand:aggregate = 1:2:3 (general purpose) or 1:1.5:3 (structural). Converting to percentages helps when calculating bag quantities.
Investment portfolio allocation - allocating capital across three asset classes (e.g. equities:bonds:cash = 6:3:1) means 60%, 30%, and 10% of the portfolio respectively.
Cooking and chemistry - cocktail ratios, fertiliser NPK ratios, and chemical solution ratios all use three-part splits where precision matters.
One thing I consistently notice when working with three-part ratios is how often people accidentally use only one or two parts as the denominator.
In a 2:3:5 split, it is tempting to calculate Part A as 2/(2+3) = 40% - forgetting the third part entirely. The result looks correct at first glance, which is exactly what makes the mistake so persistent.
Always check that your denominator equals the sum of all three parts before doing anything else.
Frequently asked questions about 3-part ratio calculation
How do you divide a quantity in a 3-part ratio?
Add the three ratio parts to get total shares. Divide the quantity by total shares (unit share). Multiply each part by the unit share. For 600 in ratio 1:2:3: unit = 100; shares = 100, 200, 300.
What is a 2:3:5 ratio as a percentage?
Total = 10 parts. A = 20%, B = 30%, C = 50%.
How do you split 100 in a ratio of 1:2:2?
Total = 5. Unit share = 20. Shares: 20, 40, 40.
Do all three percentages add to 100%?
Yes - by definition the three parts together form the whole (100%).
Quiz: how well do you know 3-part ratios?
1. In the formula for converting Part A of an a:b:c ratio to a percentage, what is the denominator?
2. From the worked examples table: a ratio of 3:3:4 split across a total of 500 gives Part C a share of:
3. According to the key takeaways, which ratio is equivalent to 1:2:3?
4. In the beginner analogy, a $30 dinner bill split in ratio 1:2:3 means the largest portion pays:
5. For a 2:3:5 ratio, what mistake produces a plausible-looking but wrong answer for Part A?