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.
How to use this 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.
Formula and method
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
| 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%) |
Real-world applications
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.
Frequently asked questions
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%).