General
Ratio Calculator
Works ratios, where the parts and the whole are different questions.
Result
Simplification uses a greatest-common-divisor with a small tolerance so decimal ratios still reduce sensibly. Very long decimals may not reduce to neat whole numbers.
Get a Free Business AuditHow the calculation works
A ratio expresses relative quantities, simplified by dividing each part by their greatest common divisor. Converting a ratio to amounts requires knowing whether a given quantity is one part or the total, since a ratio of two to three divides a total into five parts rather than into two and three of something.
What moves the number
- Whether a known quantity is a part or the whole.
- Number of terms in the ratio.
- Whether the ratio is a proportion or a rate.
- Units, which must be consistent across terms.
Where this one goes wrong
A two to one ratio means one part in three rather than one in two, which is the confusion that ruins mixing instructions and dilution calculations, and the consequences are real when the mixture is a chemical or a concrete mix. Count the total parts. Units also have to match across the terms, since a ratio of a volume to a weight is not a ratio at all unless the densities are known.
Before you quote
- Count the total parts before dividing a quantity.
- Keep units consistent across every term.
- State whether the known figure is a part or the total.
Questions
About this calculator
Does a 2:1 ratio mean half?
No, it means two parts in three. That confusion ruins mixing and dilution calculations, and the consequences are real when the mixture is a chemical, a fertiliser or a concrete mix rather than an abstraction.
How do I split a total by a ratio?
Add the parts to get the total number of parts, divide the quantity by that, then multiply by each part. For 2:3 across 100, five parts of 20 gives 40 and 60. The common error is dividing by the individual terms.
Can a ratio mix units?
Not meaningfully. A ratio of a volume to a weight is not a ratio unless the densities are known, which is why mixing instructions specify whether they are by volume or by weight, and the two give different mixtures.
The formula
A : B = C : D → D = (B × C) ÷ A
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How to use this calculator
- Ratio: first term (A). Enter your own figure; the page starts at 16.
- Ratio: second term (B). Enter your own figure; the page starts at 10.
- Scale A up to. The proportion A : B = C : ? is solved below.
The result updates as you type, so you can try a figure, see what it does to simplified ratio, and change it back. Nothing you enter is sent anywhere or saved.
A worked example
These are the figures the calculator opens with. Every number in the results column below is produced by the same calculation the page runs, so you can follow it through before putting your own figures in.
What goes in
| Input | Value |
|---|---|
| Ratio: first term (A) | 16 |
| Ratio: second term (B) | 10 |
| Scale A up to | 40 |
What comes out
| Result | Value |
|---|---|
| Simplified ratio main result | 8 : 5 |
| Missing term (?) | 25 |
| A ÷ B | 1.6 |
| A as a share of the total | 61.54% |
16 : 10 simplifies to 8 : 5. Scaled so the first term is 40, the second becomes 25.
How sensitive the answer is
Holding everything else steady and changing only ratio: first term (a), this is what happens to simplified ratio. It is worth knowing which of your inputs the answer actually hinges on, and which barely move it.
| Ratio: first term (A) | Simplified ratio |
|---|---|
| 8 | 4 : 5 |
| 12 | 6 : 5 |
| 16 example above | 8 : 5 |
| 24 | 12 : 5 |
| 32 | 16 : 5 |
Every other input is held at the example value while this one changes, which is not how a real job behaves. Treat it as a guide to which number matters most, not as five separate quotes.
What each figure means
- Ratio: first term (A)
- A number, starting at 16.
- Ratio: second term (B)
- A number, starting at 10.
- Scale A up to
- The proportion A : B = C : ? is solved below.
What the results tell you
| Result | What it is |
|---|---|
| Simplified ratio | The headline result. A category or planning selection, rather than a measured quantity. |
| Missing term (?) | A number. |
| A ÷ B | A number. |
| A as a share of the total | A percentage. |
Keep going
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