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Ratio Calculator

Simplify a ratio, solve a proportion, scale a ratio, split an amount by ratio, or convert a ratio to a fraction and percentage.

✓ Last reviewed: Sources: Euclidean algorithm — Wikipedia

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The first term of the ratio (a:b).

The second term of the ratio.

The third term of the ratio, or the third value of the proportion.

The fourth term of the ratio, or the unknown value of the proportion.

Your result

Fill in the fields above to see your result.

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What the ratio calculator does

The ratio calculator is five tools in one: it simplifies a ratio, solves the missing value in a proportion, scales a ratio up or down, splits an amount by ratio, and converts a ratio to a fraction and a percentage. Pick a mode at the top, type in your numbers, and the result updates instantly — no separate page for each job.

That range matters because ratios show up everywhere in ordinary life, not just in maths class:

  • Recipes. Scaling a sauce from 4 to 10 servings, or checking that a doubled recipe keeps the same flavour balance.
  • Maps and models. A 1:50000 map scale, or a 1:32 scale model kit — working out real-world distances from a drawing.
  • Mixing ratios. Concrete (cement:sand:gravel), paint thinner, or two-part epoxy that has to be mixed in an exact ratio to cure properly.
  • Money. Splitting a bonus, rent, or profit between partners in an agreed ratio, or reading investment allocations expressed as a ratio.

Whatever the job, it comes down to the same handful of operations below — and this ratio calculator covers all of them under one roof, which is more than most single-purpose tools do.

How to use it

  1. Choose a mode. Simplify, solve a proportion, scale, split, or convert to fraction/percentage.
  2. Enter the values. Every mode shares the same four fields — a first and second value (required), plus an optional third and fourth for ratios with more than two terms (e.g. 2:3:5 for a concrete mix). Leave the third and fourth blank if your ratio only has two terms.
  3. Add the mode-specific number. Solving a proportion needs one value left blank (that’s the unknown); scaling needs a multiplier; splitting needs the total amount to divide.
  4. Read the result. It appears immediately, with a short explanation of what happened to the numbers.

Ratios in this calculator are non-negative — enter values of zero or more. Ratios that compare quantities in real life (ingredients, distances, money) don’t have a meaningful negative form, so negative input is rejected rather than silently flipped in sign.

How the ratio calculator works

Simplifying a ratio (proportion calculator basics)

A ratio is in its simplest form when its terms share no common factor bigger than 1. To simplify, divide every term by their greatest common divisor (GCD), found with the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is 0 — the last non-zero value is the GCD.

For three or more terms, the calculator finds the GCD pairwise: first between the first two terms, then between that result and the next term, and so on.

Example: simplify 12 : 18 : 30.

  • GCD(12, 18) = 6, then GCD(6, 30) = 6.
  • Divide every term by 6: 12 ÷ 6 = 2, 18 ÷ 6 = 3, 30 ÷ 6 = 5.
  • Result: 2 : 3 : 5.

Decimal terms work too: the calculator scales every term by a power of 10 first (enough to make them whole numbers), finds the GCD on those integers, and simplifies from there — so 2.5 : 3.75 becomes 250 : 375 internally, GCD 125, and simplifies to 2 : 3. If a term is 0, that’s fine (0 : 5 simplifies to 0 : 1); if every term is 0, there’s no ratio to simplify and the calculator flags it rather than guessing.

Solving a proportion (a:b = c:X)

A proportion states that two ratios are equal: a : b = c : d. Cross-multiplication turns that into a·d = b·c, which you can rearrange to find any missing term.

Example: solve 3 : 4 = 9 : X.

  • Cross-multiply: 3 × X = 4 × 9 = 36.
  • Divide: X = 36 ÷ 3 = 12.
  • So 3 : 4 = 9 : 12.

Leave exactly one of the four values blank — that’s the one the calculator solves for. If solving would require dividing by zero (for instance, the known term on the same side as the unknown is 0 while the opposite product isn’t), there’s no valid answer, and the calculator says so instead of returning an undefined number.

Scaling a ratio

Scaling multiplies every term of a ratio by the same factor, which keeps the proportion — and therefore the relationship between the quantities — unchanged. This is exactly what you do when resizing a recipe or a mixing ratio for a bigger batch.

Example: scale 2 : 3 by a factor of 5.

  • 2 × 5 = 10, 3 × 5 = 15.
  • Result: 10 : 15 — still the same ratio as 2:3, just bigger.

Splitting an amount by ratio

To divide a total into parts that follow a given ratio, add up all the ratio’s terms (the “shares”), then give each part its fraction of the total: partᵢ = total × (its share) ÷ (sum of all shares).

Example: split 1200 in the ratio 2 : 3 : 5.

  • Sum of shares: 2 + 3 + 5 = 10.
  • Part 1: 1200 × 2/10 = 240. Part 2: 1200 × 3/10 = 360. Part 3: 1200 × 5/10 = 600.
  • Check: 240 + 360 + 600 = 1200. ✓

When the shares don’t divide evenly, the parts can come out with recurring decimals — splitting 100 in a 1:1:1 ratio gives three parts of 33.333…, shown rounded to two decimals (33.33 each). Because of that rounding, the displayed parts can be a fraction of a unit off from the total; the calculator flags this with a short note rather than hiding it.

Converting a ratio to a fraction and a percentage

A ratio like 3:2 can answer two different questions, and it’s easy to mix them up:

  • Share of the whole (part-to-whole): what fraction of the total does each term represent? For 3:2, the whole is 3 + 2 = 5, so the shares are 3/5 = 60% and 2/5 = 40%.
  • One term relative to the other (part-to-part): simply term ÷ term. For 3:2, that’s 3 ÷ 2 = 1.5.

Both are correct — they just answer different questions, so the calculator labels them separately instead of showing a single ambiguous number. The part-to-part figure is undefined when the second term is 0 (you can’t divide by it), and the calculator shows a note instead of an error-looking result.

Frequently asked questions

What is the difference between a ratio and a proportion?

A ratio compares two or more quantities, like 3:2 or 2:3:5. A proportion is a statement that two ratios are equal, like 3:4 = 9:12. In other words, a ratio is a single comparison; a proportion is an equation built from two ratios. This calculator’s “solve” mode works with proportions — it finds the missing value that makes two ratios equal.

How do you simplify a ratio to its simplest form?

Divide every term of the ratio by their greatest common divisor (GCD), found with the Euclidean algorithm. For example, 12:18:30 has a GCD of 6, so dividing each term by 6 gives 2:3:5, which can’t be reduced any further. The “simplify” mode above does this instantly for two, three, or four terms, including decimals.

How do you solve a proportion (find the missing value in a:b = c:d)?

Cross-multiply: a·d = b·c. Rearrange for whichever term is unknown. For 3:4 = 9:X, cross-multiplying gives 3 × X = 4 × 9 = 36, so X = 36 ÷ 3 = 12. The “solve” mode lets you leave any one of the four values blank and calculates it for you.

How do you divide or split a number by a given ratio?

Add up the ratio’s terms to get the total number of shares, then multiply the amount by each term’s share of that sum. Splitting 1200 in a 2:3:5 ratio (10 total shares) gives 240, 360, and 600 — each part is the amount times its share divided by 10. The “split” mode does this for two to four terms and flags any rounding difference from the total.

How do you scale a ratio up or down (e.g. for a recipe)?

Multiply every term by the same factor. Scaling 2:3 by 5 gives 10:15 — still the same proportion, just larger numbers. This is the standard way to resize a recipe, a mixing ratio, or a model’s dimensions while keeping every ingredient or part in the same balance.

How do you convert a ratio to a percentage?

Add the ratio’s terms to get the whole, then divide each term by that whole and multiply by 100. For 3:2, the whole is 5, so the shares are 3/5 = 60% and 2/5 = 40%. This ratio to percentage conversion is what the “convert” mode calculates automatically, alongside the ratio expressed as a fraction.

How do you convert a ratio to a fraction or decimal?

As a share of the whole, each term becomes term ÷ (sum of all terms) — for 3:2 that’s 3/5 and 2/5. As a direct comparison of the two terms (part-to-part), it’s simply the first term divided by the second — 3 ÷ 2 = 1.5. The “convert” mode shows both, since they answer different questions.

How do you convert a fraction or percentage back into a ratio?

Use the “simplify” mode with the two numbers as terms. A 60%/40% split, for example, is the same as entering 60 and 40 and simplifying — the calculator reduces it to 3:2. A fraction like 3/8 can be read directly as the ratio 3:8 (part-to-whole) or simplified the same way if it isn’t already in lowest terms.

How do you know if two ratios are equivalent?

Two ratios are equivalent ratios if they simplify to the same lowest terms, or if cross-multiplying gives equal products (a·d = b·c). Simplify both ratios in this calculator and compare the results — if 4:6 and 10:15 both reduce to 2:3, they’re equivalent.

How do you work with a ratio of three or more numbers (a:b:c)?

The same rules apply with more terms: simplifying divides all of them by their combined GCD, scaling multiplies all of them by the same factor, and splitting shares an amount across all of them proportionally. This calculator supports a:b:c ratio input (and a fourth term) in every mode, covering common cases like a 1:2:2 concrete mix or a three-way profit split.

Sources