Scale a ratio into a table you can keep
Applies one sequence of multipliers to both sides of a ratio, shows the exact simplified base ratio, and turns every equivalent pair into a downloadable CSV table for recipes, mixtures, drawings and repeated batches.
Equivalent ratio table
| 1 | 0.5 | 1 | 1.5 |
| 2 | 1 | 2 | 3 |
| 3 | 1.5 | 3 | 4.5 |
| 4 | 2 | 4 | 6 |
| 5 | 2.5 | 5 | 7.5 |
| 6 | 3 | 6 | 9 |
| 7 | 3.5 | 7 | 10.5 |
| 8 | 4 | 8 | 12 |
| 9 | 4.5 | 9 | 13.5 |
| 10 | 5 | 10 | 15 |
| 11 | 5.5 | 11 | 16.5 |
| 12 | 6 | 12 | 18 |
How it works
What this works out
A ratio is easy to state once and tedious to scale repeatedly. This makes the repetition explicit: choose the first multiplier, how much it grows by, and how many rows you need. Both quantities, the multiplier and the complete sequence then become one table you can download rather than a succession of calculator answers.
The method
Every row has one multiplier. The first row uses the starting value; row two adds one step; row three adds two. That value is applied to both base parts. Nothing more complicated is needed—and applying it to both is the property that must never be lost.
The simplified label needs more care than the table. Decimal values such as 2.5 and 0.75 are not simplified by asking whether floating-point quotients are close. They are read as the exact decimal fractions 25/10 and 75/100, moved to a common denominator, and reduced as whole integers. That produces 10:3 exactly.
Before you read on
A mix is 1:4. If the first quantity is 0.5, what is the second quantity?
2. Multiplying both parts of 1:4 by 0.5 gives 0.5:2. The combined amount is 2.5, and dividing either quantity by its original part recovers the same multiplier of 0.5.
A worked example
Start with 2:3, begin at a multiplier of 0.5, add 0.5 per row, and make twelve rows:
| Row | Multiplier | First | Second |
|---|---|---|---|
| 1 | 0.5 | 1 | 1.5 |
| 2 | 1 | 2 | 3 |
| 3 | 1.5 | 3 | 4.5 |
| 4 | 2 | 4 | 6 |
| 12 | 6 | 12 | 18 |
The final pair is 12:18, which divides by six to return to 2:3. The quotient is also unchanged: 2/3, 4/6 and 12/18 are the same number. These exact default rows and the separate 2.5:0.75 → 10:3 decimal simplification are asserted in the formula tests.
Parts are not percentages
A 1:4 mix has five total parts. The first therefore makes up one fifth, or 20%, and the second makes up four fifths, or 80%. If somebody says “one in four” and means 25% of the total, the two-column ratio is 1:3 instead. The distinction is language, not arithmetic, and it is why the table keeps the two quantities visible instead of showing only a quotient.
The formula
multiplier[row] = start + (row - 1) x step
firstQuantity[row] = firstPart x multiplier[row]
secondQuantity[row] = secondPart x multiplier[row]
To simplify decimal parts:
write both parts as base-10 integers over powers of ten
cross-multiply to one common denominator
divide both resulting integers by their greatest common divisor
The same multiplier is always applied to both parts.
What it assumes
- Both base parts and both multiplier controls are positive. A zero-part relationship can be written, but it does not make a useful scale table and is refused here.
- Parts are dimensionless until the visitor assigns a unit. A row can mean grams, litres, pixels or people only when both columns are interpreted consistently.
- The simplified headline is exact for the decimal spelling accepted by the number control. Table quantities use JavaScript numbers and are shortened to twelve significant digits to remove binary display tails.
- A ratio names quantities alongside each other. A ratio of 1:4 contains five total parts; it does not mean one part out of four total.
Common questions
What makes two ratios equivalent?
Both parts must be multiplied or divided by the same non-zero number. If one side changes independently, the quotient changes and the new pair is not equivalent to the original ratio.
Why simplify the base ratio when every row still works?
Simplifying exposes the smallest whole-number relationship. A table based on 4:6 is mathematically sound, but 2:3 makes the relationship easier to recognise and compare with another table.
Can a ratio table mix different units?
It can only if the intended relationship does. Two litres to three litres is dimensionless after cancellation; two litres to three kilograms is a recipe relationship whose units must stay attached to their columns.
Why do some decimal calculations show a long trail of nines?
Most decimal fractions have no finite binary representation in a JavaScript Number. The table shortens results to twelve significant digits, while simplification separately uses base-10 integers so its ratio is not inferred from a floating-point near-equality.