Ratio Calculator for 3 Numbers

Built for the three-part share-out: divide a total between three shares in the ratio A : B : C, or work back to the total from any one known share. The simplified ratio, the value of one part and each share's percentage all come with it.

Formula A : B : C

The ratio

A
B
C
Try an example
Method

The value of one part does all the work

Every three-part share-out reduces to finding one number, then multiplying by it three times.

Write down which term belongs to whom

A three-part ratio has three positions and they are not interchangeable. Note that A is Alice, B is Ben, C is Chris — or cement, sand, gravel — before you touch the numbers. Reassigning them halfway through is the most common error in these problems.

Add the terms for the total number of parts

2 + 3 + 4 = 9. The whole has been divided into 9 equal parts, and each person's share is a count of those parts. This is the step people skip when they mistakenly divide by 3 because there are three people.

Divide the total by the number of parts

450 ÷ 9 = 50. One part is worth £50. Keep this number — every share and every follow-up question comes from it.

Multiply each term by the value of one part

2 × 50 = £100, 3 × 50 = £150, 4 × 50 = £200. Three multiplications and you are done.

Add the shares back up

100 + 150 + 200 = 450 ✓. If the shares do not sum to the original total, something has gone wrong — usually the number of parts. This check costs nothing and catches almost every mistake.

one part = total ÷ (A + B + C)

The key quantity. Compute it once and every share follows. It also gives you a unit to reason in — "each part is worth £50".

share = term × one part

Each share. Equivalently total × term / (A+B+C), which avoids an intermediate rounding if the value of one part is not exact.

Not divided by three

Three recipients does not mean dividing by 3. In a 2 : 3 : 4 split you divide by 9, the total parts. Dividing £450 by 3 gives £150 each, which happens to be B's correct share and is wrong for the other two — a mistake that can pass a casual glance.

Worked examples

Three-part splits in practice

Sharing money

Divide £450 between three people in the ratio 2 : 3 : 4.

Total parts
2 + 3 + 4 = 9
One part
450 ÷ 9 = £50
Share A
2 × 50 = £100
Share B
3 × 50 = £150
Share C
4 × 50 = £200
Check
100 + 150 + 200 = 450 ✓

£100 / £150 / £200

Concrete mix

Mix 700 kg of concrete as 1 : 2 : 4 cement to sand to gravel.

Total parts
1 + 2 + 4 = 7
One part
700 ÷ 7 = 100 kg
Cement
1 × 100 = 100 kg
Sand
2 × 100 = 200 kg
Gravel
4 × 100 = 400 kg

100 / 200 / 400 kg

Working backwards

In a 2 : 3 : 4 split the largest share is £200. What was the total?

Known share
C = £200, term 4
One part
200 ÷ 4 = £50
Total parts
9
Total
50 × 9 = £450
Other shares
£100 and £150

£450 in total

Awkward remainder

Split £100 equally three ways, 1 : 1 : 1.

Total parts
3
One part exactly
100/3 = £33.333…
Rounded down
£33.33 each
Paid out
3 × 33.33 = £99.99
Left over
1 penny to allocate

£33.33 each, 1p remaining

Reference

Common three-part ratios

Ratio Total parts Percentages Typical use
1 : 1 : 1333.33 / 33.33 / 33.33An equal three-way split
1 : 2 : 3616.67 / 33.33 / 50A simple graded split
1 : 2 : 4714.29 / 28.57 / 57.14Standard concrete mix
1 : 3 : 61010 / 30 / 60Lean concrete, foundations
2 : 3 : 4922.22 / 33.33 / 44.44Graded profit or inheritance split
2 : 3 : 51020 / 30 / 50Portfolio allocation — clean percentages
3 : 4 : 51225 / 33.33 / 41.67Also the Pythagorean triple
4 : 3 : 31040 / 30 / 30Macronutrient splits
5 : 3 : 21050 / 30 / 20Time or budget allocation
12 : 18 : 306020 / 30 / 50Same as 2 : 3 : 5 unsimplified
Background

Why three parts is the awkward case

Two-part ratios are easy to reason about intuitively — you can picture the split. Three parts is where intuition starts to fail and the arithmetic has to be trusted instead, which is why it is the shape that appears most in exam questions and most in real disputes over how something was divided. The failure mode is nearly always the same: dividing by the number of recipients rather than by the number of parts.

The other difficulty is that three-part ratios frequently do not divide cleanly. A 2 : 3 : 4 split of £450 works out beautifully because 450 is a multiple of 9. Change the total to £500 and you get £111.11, £166.67 and £222.22, with a rounding decision to make. Showing the exact fractions — 1000/9, 1500/9, 2000/9 — makes it clear exactly how much is being rounded and in which direction.

Handling the remainder fairly

When money will not divide evenly there is no mathematically correct answer, only conventions. The common ones are: give the remainder to the largest share, give it to the smallest, rotate it if the split repeats, or round each share down and hold the remainder back. Contracts that specify a ratio split usually also specify the rounding rule, and for good reason — a penny per transaction over a million transactions is a real amount.

Ratios that give clean percentages

A three-part ratio converts to whole-number percentages only when its total parts divide 100 — so totals of 2, 4, 5, 10, 20, 25, 50 and 100. That is why 2 : 3 : 5 (total 10) is so popular for portfolio and budget allocations: it maps exactly onto 20%, 30% and 50%. A total of 9 or 7 parts never will, which is worth knowing when you are choosing a ratio rather than being given one.

Related tools

For longer ratios, the 4, 5 and 6-number ratio calculator takes the same approach with a term-count selector. For two-part ratios and for solving A : B = C : D, use the ratio calculator. To reduce a three-part ratio to lowest terms, the simplify ratio calculator handles up to six terms, and the ratio to percentage calculator gives the percentage breakdown on its own.

Questions

Three-part ratios — questions

The parts-versus-people distinction, plus what to do when the shares will not divide evenly.

How do you divide an amount in the ratio A : B : C?
Add the three parts to get the total number of parts, divide the amount by that to get the value of one part, then multiply each ratio term by it. To split £450 in the ratio 2 : 3 : 4: the total is 9 parts, one part is 450 ÷ 9 = £50, and the shares are £100, £150 and £200. They add back to £450, which is the check.
What is the "value of one part" and why does it matter?
It is the amount each single unit of the ratio is worth — the total divided by the number of parts. Once you have it, every share is one multiplication away, and it is the number to keep if you have several questions about the same split. It also makes the arithmetic checkable: if one part is £50 and the ratio has 9 parts, the total must be £450.
How do I work out the total if I only know one share?
Divide the known share by its ratio term to get the value of one part, then multiply by the total number of parts. If the largest share in a 2 : 3 : 4 split is £200, then one part is 200 ÷ 4 = £50 and the total is 50 × 9 = £450. This calculator has a mode for exactly that.
Can a three-part ratio be simplified?
Yes, by dividing all three terms by their greatest common divisor. 12 : 18 : 30 has a GCD of 6, giving 2 : 3 : 5. Importantly you must use the GCD of all three — you cannot cancel two terms and leave the third alone, which would change the ratio.
What if the shares do not come out as whole numbers?
That is normal and usually fine. Splitting £100 in the ratio 1 : 1 : 1 gives £33.33 each with a penny left over. For money you have to decide where the remainder goes; conventionally it is added to the largest share or split by agreement. This calculator shows exact fractions alongside the decimals so you can see precisely how much is being rounded.
Is 2 : 3 : 4 the same as 4 : 3 : 2?
No. The order maps each term to a specific recipient or ingredient, so reversing it reassigns the shares. Both ratios have 9 parts and the same set of share values, but who gets which changes completely. Always write down which term belongs to which quantity before you calculate.
How do I find one term when the others are known and the ratio is scaled?
If you know that 2 : 3 : 4 has been scaled so the second term is 12, the factor is 12 ÷ 3 = 4, so the terms are 8 : 12 : 16. That is the same as finding the value of one part and multiplying through. The share-out mode here does it in one step when you give it a known share.
Where are three-part ratios used?
Concrete mixes (cement : sand : gravel, often 1 : 2 : 4), inheritance and profit splits between three parties, portfolio allocations across asset classes, paint and dye mixing, nutritional macronutrient splits, and any recipe with three main components. Anywhere a fixed whole has to be divided three ways in a set proportion.