Ratio Calculator for 4, 5 & 6 Numbers

For ratios longer than three terms — recipe blends, alloy compositions, multi-way budget splits. Pick how many terms you have, then simplify, scale by a factor, or divide a total between the shares.

Formula A : B : C : D …

Try an example
Method

More terms, same three rules

Nothing changes mathematically when a ratio gets longer. What changes is how easy it is to apply an operation to some terms and forget the rest.

Label every position before you start

With six terms it is genuinely easy to lose track of which is which. Write down the mapping — A is nitrogen, B is phosphorus, C is potassium — and keep the order fixed for the whole calculation.

To simplify, use the GCD of all terms

Compute it pairwise: gcd(8, 12) = 4, then gcd(4, 20) = 4, then gcd(4, 32) = 4. Divide every term by that 4 to get 2 : 3 : 5 : 8. A single term that shares no factor with the others forces the GCD to 1 and the ratio cannot be reduced at all.

To scale, multiply every term by the factor

1 : 2 : 3 : 4 times 25 is 25 : 50 : 75 : 100. This is what you do when you know one actual quantity and need the rest — divide it by its ratio term to get the factor, then apply it across.

To share a total, divide by the sum of the terms

1 + 2 + 3 + 4 = 10 parts. £2000 ÷ 10 = £200 per part, so the shares are £200, £400, £600 and £800. As always, it is the number of parts you divide by, not the number of recipients.

Check the total, every time

Shares must sum to the original amount; percentages must sum to 100%. With four to six terms this check is the only practical way to catch an arithmetic slip, because there are too many numbers to eyeball.

gcd(a,b,c,d) = gcd(gcd(gcd(a,b),c),d)

Pairwise GCD. Reduce two at a time. Order does not affect the result, so start with whichever pair is easiest.

shareᵢ = total × termᵢ / Σterms

Direct share formula. Skipping the intermediate "value of one part" avoids compounding a rounding error when the division is not exact.

Rounding gets worse with more terms

Six shares each rounded to the nearest penny can leave up to three pence unallocated. The exact fractions are shown in their own column so you can see the true values and decide where any remainder goes.

Worked examples

Four, five and six terms

Simplifying four terms

Simplify 8 : 12 : 20 : 32

gcd(8, 12)
4
gcd(4, 20)
4
gcd(4, 32)
4
Divide all four
8÷4 : 12÷4 : 20÷4 : 32÷4
Result
2 : 3 : 5 : 8

2 : 3 : 5 : 8 — GCD was 4

Sharing four ways

Split £2000 in the ratio 1 : 2 : 3 : 4.

Total parts
1 + 2 + 3 + 4 = 10
One part
2000 ÷ 10 = £200
Shares
£200, £400, £600, £800
Percentages
10%, 20%, 30%, 40%
Check
200+400+600+800 = 2000 ✓

£200 / £400 / £600 / £800

Cannot be reduced

Simplify 2 : 3 : 5 : 7 : 11

All five are prime
and all different
gcd(2, 3)
1
Once the GCD is 1
it stays 1
Total parts
2+3+5+7+11 = 28
First share
2/28 = 7.14%

Already simplest — GCD 1

Scaling a blend

A six-part glaze is 6 : 9 : 12 : 15 : 18 : 21. Simplify it, then make 140 g.

GCD of all six
3
Simplified
2 : 3 : 4 : 5 : 6 : 7
Total parts
27
One part
140 ÷ 27 = 5.185 g
First component
2 × 5.185 = 10.37 g

2 : 3 : 4 : 5 : 6 : 7, one part 5.185 g

Reference

Multi-term ratios and their parts

Ratio Terms GCD Simplest Total parts Percentages
1 : 2 : 3 : 4411 : 2 : 3 : 41010 / 20 / 30 / 40
8 : 12 : 20 : 32442 : 3 : 5 : 81811.1 / 16.7 / 27.8 / 44.4
2 : 2 : 3 : 3412 : 2 : 3 : 31020 / 20 / 30 / 30
1 : 1 : 1 : 1411 : 1 : 1 : 1425 each
10 : 20 : 30 : 40 : 505101 : 2 : 3 : 4 : 5156.7 / 13.3 / 20 / 26.7 / 33.3
2 : 3 : 5 : 7 : 11512 : 3 : 5 : 7 : 11287.1 / 10.7 / 17.9 / 25 / 39.3
4 : 4 : 2 : 1 : 1514 : 4 : 2 : 1 : 11233.3 / 33.3 / 16.7 / 8.3 / 8.3
6 : 9 : 12 : 15 : 18 : 21632 : 3 : 4 : 5 : 6 : 7277.4 / 11.1 / 14.8 / 18.5 / 22.2 / 25.9
1 : 1 : 2 : 2 : 4 : 4611 : 1 : 2 : 2 : 4 : 4147.1 / 7.1 / 14.3 / 14.3 / 28.6 / 28.6
5 : 10 : 15 : 20 : 25 : 30651 : 2 : 3 : 4 : 5 : 6214.8 / 9.5 / 14.3 / 19 / 23.8 / 28.6
Background

Where long ratios actually appear

Ratios with four or more terms are almost always compositions rather than divisions. A four-part ratio splitting money between four people is possible but uncommon; a four-part ratio describing the composition of a bronze alloy, a fertiliser blend, a ceramic glaze or a feed mix is routine. The distinction matters because compositions are usually specified per unit of total mass, which is exactly the share-a-total calculation.

Formulations also tend to arrive unsimplified, because the numbers came from measured quantities rather than from a designed ratio. A glaze recipe listed as 6 : 9 : 12 : 15 : 18 : 21 grams simplifies to 2 : 3 : 4 : 5 : 6 : 7, which is far easier to scale to a different batch size and reveals the structure of the recipe — each component one step up from the last.

Why more terms means more care, not more maths

The formulas are identical for two terms and for six. What increases is the number of places to make a mistake: six divisions instead of two, six multiplications, six percentages to sum. There is no clever shortcut for longer ratios — the reliable approach is to compute the value of one part once, apply it mechanically, and then verify the total. That last step is what catches errors, and it becomes more important the more terms you have.

Rounding across many shares

If a total does not divide evenly by the number of parts, every share inherits a rounding error and they accumulate. Splitting £100 six ways as 1 : 1 : 1 : 1 : 1 : 1 gives £16.666… each; rounded to £16.67 the six shares total £100.02, which is two pence over. Rounding down to £16.66 leaves four pence short. Neither is wrong — you simply have to decide, which is why the exact fractions are shown.

Related tools

For exactly three terms, the three-number ratio calculator is laid out for that case and adds a work-back-from-one-share mode. For two terms use the ratio calculator. To simplify without any share-out, the simplify ratio calculator handles two to six terms, and the ratio to percentage calculator gives just the percentage breakdown.

Questions

Long ratios — questions

Mostly about the GCD across many terms and how rounding behaves when shares multiply.

How do you simplify a ratio with four or more terms?
Find the greatest common divisor of all the terms and divide every one of them by it. For 8 : 12 : 20 : 32 the GCD is 4, giving 2 : 3 : 5 : 8. The critical point is that the divisor must be common to every term — cancelling a factor that only some terms share breaks the ratio, and this becomes easier to get wrong the more terms there are.
How do you divide a total among four, five or six shares?
Exactly as with two or three: add all the terms to get the total number of parts, divide the amount by that to get the value of one part, then multiply each term by it. For 1 : 2 : 3 : 4 sharing £2000, the total is 10 parts, one part is £200, and the shares are £200, £400, £600 and £800.
Can I scale a long ratio by a factor?
Yes, and the rule is unchanged: multiply or divide every term by the same number. 1 : 2 : 3 : 4 multiplied by 25 gives 25 : 50 : 75 : 100. This is how you convert a recipe ratio into actual quantities when you know how much of one ingredient you have.
How do I find the GCD of five or six numbers?
Take them two at a time. Find the GCD of the first two, then the GCD of that answer with the third, and continue. The order does not matter — gcd(a, b, c) = gcd(gcd(a, b), c) — so you can start anywhere. In practice starting with the two smallest terms usually gets you to 1 fastest if the ratio cannot be reduced.
What if one term in a long ratio is zero?
A zero term simply gets zero of the total, and the remaining terms share the whole between them. 2 : 0 : 3 : 5 means the second recipient receives nothing. A zero term does not stop the calculation, but it does mean the ratio has an effectively unused position — you may as well drop it and use a shorter ratio.
Do longer ratios still convert to percentages?
Yes, using the same method: divide each term by the total of all terms and multiply by 100. The percentages still sum to 100%. With more terms you get more of them, and rounding gaps become more likely to show up in the total — six terms rounded to two places can leave the sum at 99.99% or 100.01%.
Are there real ratios with six parts?
Yes, though they usually describe compositions rather than divisions of money. Alloy and glaze formulations, fertiliser blends, animal feed mixes, pigment recipes and nutritional breakdowns all commonly run to five or six components. Budget allocations across departments and asset allocations across several classes are the financial equivalents.
Should I use this or the three-number calculator?
Use the three-number calculator if your ratio has exactly three terms — it is laid out for that case and includes a mode for working back from one known share. Use this one for four to six terms, where the term-count selector and the scaling mode matter more. For two-term ratios use the ratio calculator.