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Ratio Calculator

Simplify, scale and split ratios. Find equivalent ratios with the cross-multiply method.

Simplified
2 : 3
16:24 = 2:3
Simplified ratio
2 : 3
16:24 = 2:3
Decimal (a/b)
0.6667

Dividing both sides by gcd(16, 24) = 8 gives the simplified ratio 2:3 (decimal 0.6667).

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How to use the Ratio Calculator

  1. 1

    Choose your mode

    Pick simplify, scale, split or solve-equivalent. Simplify reduces a ratio to lowest terms; scale resizes one part proportionally; split divides a total in the given ratio; solve-equivalent finds the missing term.

  2. 2

    Enter the ratio terms

    Type the two (or three) terms separated by colons. Use whole numbers wherever possible — convert any decimals or fractions to integers first by multiplying through (0.5:1 becomes 1:2).

  3. 3

    Add the scaling or split value

    For scale mode, enter the new value for one side; for split mode, enter the total to divide. The calculator preserves the proportion exactly using GCD-based reduction so the parts always reconcile.

  4. 4

    Read the simplified ratio plus decimal

    The result shows the answer in lowest terms (e.g. 16:24 → 2:3) along with the decimal equivalent (a/b) and the percentage breakdown for split mode. Worked steps reveal the GCD reduction.

  5. 5

    Cross-check or share the result

    For split or scale mode, sum-check the parts (they should equal the original total). Copy the share link to send the exact ratio problem to someone else, preserving every input value.

What this calculator does

A ratio is a comparison of two quantities by division, written a:b (read "a to b"). It says nothing about absolute size — only about proportion. A ratio is closely related to a fraction: the ratio 3:4 has the same simplification rules and decimal value (0.75) as the fraction 3/4. The difference is intent: fractions denote part-of-a-whole; ratios denote part-to-part (or part-to-whole when the total is implicit). 3:4 of boys-to-girls in a class of 21 means 3 parts boys and 4 parts girls (7 parts total − 9 boys, 12 girls). Three-term ratios extend the idea: 2:3:5 means three quantities in those proportions; the operations generalise naturally.

Formula

simplify: a:b → (a/g):(b/g) where g = gcd(a,b). scale: a:b with new a = a' gives b' = b × a'/a. split T in a:b: parts = (a/(a+b))×T : (b/(a+b))×T.
a, b
The two parts of the ratio
g
Greatest common divisor of a and b
T
Total to be split in the ratio a:b
a', b'
New values after scaling that preserve the ratio

Simplifying a ratio is the same operation as simplifying a fraction — divide both sides by the GCD. Scaling preserves the proportion: the multiplier you apply to one side must apply to the other. Splitting a total T means treating each part as a fraction of the sum: a/(a+b) of T goes to the first, b/(a+b) goes to the second. For equivalent ratios a:b = c:d, the cross-product is constant: a × d = b × c.

Worked examples

Example: simplify 16:24

GCD(16, 24) = 8. Divide both sides by 8. 16 ÷ 8 = 2; 24 ÷ 8 = 3.

Simplified: 2:3. Decimal (a/b): 16/24 = 0.6667.

You can verify by multiplying back: 2 × 8 = 16, 3 × 8 = 24. ✓

Example: scale a recipe — 2:3 flour:water, now using 5 cups flour

Original ratio: 2:3 (2 cups flour, 3 cups water). Multiplier: 5 ÷ 2 = 2.5. New water = 3 × 2.5 = 7.5 cups.

So 5 cups flour pairs with 7.5 cups water to keep the 2:3 proportion. Cross-check: 5/7.5 = 0.6667, same as 2/3. ✓

Example: split $1,000 between partners 3:7

Sum of parts: 3 + 7 = 10. Partner A gets: (3 ÷ 10) × 1,000 = $300. Partner B gets: (7 ÷ 10) × 1,000 = $700.

Sum check: 300 + 700 = 1,000 ✓. This generalises to any number of parts — "split $1,200 in ratio 1:2:3" → divide by 6, then multiply by each part: $200, $400, $600.

Common use cases

  • Cooking — scaling recipes up or down while keeping flavour proportions
  • Construction — mixing concrete (typical 1:2:3 cement:sand:gravel) or mortar
  • Painting — primer-to-thinner ratios for sprayers
  • Photography and design — aspect ratios (4:3, 16:9, 21:9, 1:1, 9:16)
  • Finance — splitting profits, costs or returns between partners or LPs
  • Map scales — 1:50,000 means 1 cm on the map = 50,000 cm in reality
  • Engineering — gear ratios, leverage, mechanical advantage
  • Chemistry — stoichiometric mole ratios in reactions
  • Education — boy-to-girl ratios, student-to-teacher ratios, dose-to-weight ratios
  • Sports betting — odds expressed as ratios (3:1 against = 25% implied probability)

What affects the result

  • Order matters — 3:5 is not the same as 5:3 unless reading "ratio of A to B" vs "ratio of B to A"
  • Units must match — comparing 1 metre to 50 centimetres is 100:50 = 2:1, not 1:50
  • Whole numbers preferred — ratios are typically expressed as integers; 0.5:1 should be written as 1:2
  • Three-or-more-term ratios — simplification uses the GCD of all terms, not pairwise
  • Ratios vs proportions — a proportion is an equation between two ratios (a:b = c:d)
  • Part-to-part vs part-to-whole — be clear which you mean before doing math on the total

Tips

  • Always simplify the final ratio to lowest terms — easier to read and compare
  • For scaling, find the multiplier first (new ÷ old on one side), then apply to the other side
  • For three-or-more-term ratios (a:b:c), divide all terms by their common GCD
  • When comparing two ratios, convert both to the same denominator: 3:4 vs 5:7 → 21:28 vs 20:28, so 3:4 is bigger
  • To convert ratio to percentages: divide each part by the sum and multiply by 100 (3:7 → 30%, 70%)
  • For aspect ratios on screens, divide both width and height by the GCD: 3840:2160 → 16:9 (divide by 240)

Mistakes to avoid

  • Confusing 3:5 (part-to-part) with 3/5 (part-to-whole) — in 3:5 the total is 8, not 5
  • Adding ratios instead of preserving proportion — combining 1:2 and 1:3 by adding terms gives a meaningless ratio
  • Scaling only one side when adjusting a recipe — both sides must be multiplied by the same factor
  • Forgetting to convert units before forming a ratio (kg vs g, cm vs m, etc.)
  • Reducing ratios to decimals too early — keep them as integers until the final step where possible
  • Computing odds backwards — "3:1 odds against" means probability 1/(3+1) = 25%, not 1/3 = 33%

Frequently asked questions

How do I simplify a ratio?

Find the GCD of all terms and divide each term by it. 12:18 → GCD = 6 → 2:3. For three-term ratios like 6:9:15, GCD = 3 → 2:3:5.

How do I split an amount in a given ratio?

Add the parts to get the total number of "units". Divide the amount by that total to get the value of one unit. Multiply by each part. Split £600 in 2:3 → total parts = 5, one unit = £120, → £240 and £360.

What is the difference between a ratio and a fraction?

They use the same arithmetic but mean different things. A fraction 3/4 means "3 parts out of 4 (the whole)". A ratio 3:4 means "3 parts of A for every 4 parts of B" — the total is 7, not 4. Same numbers, different totals.

How do I find an equivalent ratio?

Multiply both sides by the same number. 2:3 = 4:6 = 6:9 = 20:30 (all the same ratio). For "2:3 = ?:15", divide 15 by 3 to get the multiplier (5), then multiply 2 by 5: answer is 10:15.

How do I convert a ratio to a percentage?

Compute each part as a fraction of the sum, then multiply by 100. For 3:5: total = 8 − 3/8 = 37.5%, 5/8 = 62.5%. The two percentages always add to 100%.

What does a ratio of 1:50,000 mean on a map?

1 unit on the map represents 50,000 of the same units in reality. 1 cm on the map = 50,000 cm = 500 m in real life. This is a "scale ratio" and is the standard way map scales are expressed.

How do I work with three-term ratios like 1:2:3?

Treat each part as a unit. For "split $600 in 1:2:3" → total units = 6, one unit = $100, parts get $100, $200, $300. For scaling, multiply every term by the same factor. For simplifying, divide every term by the GCD of all three.

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Sources & references

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