Ratio Calculator
Simplify ratios and solve proportions.
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A ratio compares two or more quantities. This tool does the two things people actually need: reduce a ratio to its simplest whole-number form (like 1920 : 1080 → 16 : 9), and solve a proportion when one value is missing (like 3 : 4 = 9 : ?). It also shows the ratio as a decimal and scaled to '1 : n'.
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How to Simplify a Ratio & Solve a Proportion — The Quick Answer
To simplify a ratio, divide every term by their greatest common divisor (GCD). To solve a proportion with a missing term, cross-multiply: in A : B = C : D the products A×D and B×C are always equal.
Shortcut
Simplify: divide each term by GCD | Proportion A : B = C : D → A × D = B × C
Fact-Checking Claims You May Have Seen Online
A ratio and a fraction are the same thing
Closely related
The ratio 3 : 4 and the fraction 3/4 share the same arithmetic, but a ratio can compare more than two parts (3 : 4 : 5) and usually describes 'part to part', while a fraction describes 'part to whole'.
To scale a recipe you add the same amount to each part
False
Ratios scale by multiplying, not adding. Doubling 2 : 3 gives 4 : 6, not 3 : 4. Adding the same number to each term changes the ratio entirely.
16 : 9 and 1920 : 1080 are different aspect ratios
False
They are the same ratio: 1920 : 1080 both divide by 120 to give 16 : 9. Equivalent ratios simplify to the same lowest terms.
Simplifying: divide both terms by their GCD
| Ratio | GCD | Simplest form |
|---|---|---|
| 20 : 60 | 20 | 1 : 3 |
| 18 : 24 | 6 | 3 : 4 |
| 1920 : 1080 | 120 | 16 : 9 |
| 50 : 100 : 150 | 50 | 1 : 2 : 3 |
Solving a proportion by cross-multiplication
| Proportion | Cross-multiply | Missing value |
|---|---|---|
| 3 : 4 = 9 : ? | ? = (4 × 9) ÷ 3 | 12 |
| 2 : 5 = ? : 20 | ? = (2 × 20) ÷ 5 | 8 |
A quick sanity check for any proportion: the two ratios should give the same decimal. 3 : 4 = 0.75 and 9 : 12 = 0.75, so the solution is correct.
How It Works
The Method
GCD reduction and cross-multiplication
Formula
Simplify: a : b → (a ÷ g) : (b ÷ g), where g = GCD(a, b) Proportion: a : b = c : d ⟺ a × d = b × c
Variables
Greatest common divisor
The largest whole number that divides every term exactly. Dividing each term by the GCD gives the smallest equivalent whole-number ratio. For 20 : 60 the GCD is 20, so the simplest form is 1 : 3.
Ratios with decimal terms
If you enter decimals, the calculator scales every term up to whole numbers first (for example 1.5 : 2 becomes 15 : 20), then reduces by the GCD to 3 : 4 — so the result is still an exact whole-number ratio.
Cross-multiplication
Two ratios are equal when their cross-products match. Given three of the four terms, rearrange this identity to find the fourth: for example a missing d equals (b × c) ÷ a.
Note: Ratios describe relative size, so they stay the same when every term is multiplied or divided by the same number (2 : 3 = 4 : 6 = 20 : 30). That is exactly why simplifying and scaling work.
Worked Example
Simplifying 1920 : 1080, and solving 3 : 4 = 9 : ?
Simplify 1920 : 1080 — find the GCD
The greatest common divisor of 1920 and 1080 is 120.
Divide each term by the GCD
1920 ÷ 120 = 16 and 1080 ÷ 120 = 9, so 1920 : 1080 = 16 : 9 — the widescreen aspect ratio.
Solve 3 : 4 = 9 : ? — cross-multiply
A × D = B × C means 3 × ? = 4 × 9, so ? = (4 × 9) ÷ 3.
Compute the missing value
(4 × 9) ÷ 3 = 36 ÷ 3 = 12. Check: 3 ÷ 4 = 0.75 and 9 ÷ 12 = 0.75. Correct.
Reference Guide
| unit | value | note |
|---|---|---|
| 20 : 60 | 1 : 3 | Divide by GCD 20 |
| 18 : 24 | 3 : 4 | Divide by GCD 6 |
| 1920 : 1080 | 16 : 9 | Divide by GCD 120 |
| 3 : 4 = 9 : ? | 12 | Cross-multiply |
| 2 : 5 = ? : 20 | 8 | Cross-multiply |
Key Features
💡 Pro Tips
- →Scale ratios by multiplying, never by adding. To go from 2 : 3 to a recipe for 6 people, multiply both parts by 3 → 6 : 9, keeping the proportion identical.
- →To compare two ratios quickly, turn each into a decimal (first ÷ second). The larger decimal is the 'richer' ratio in the first quantity.
- →Aspect ratios, gear ratios, map scales, and mixing ratios are all the same maths — reduce by the GCD to compare them on equal footing.
- →When solving a proportion, double-check by confirming both sides give the same decimal. If they don't, a value was entered in the wrong box.
Common Mistakes
Adding to each term instead of multiplying
Ratios represent relative size, so they only stay equivalent under multiplication or division. Changing 2 : 3 to 3 : 4 by adding 1 to each term produces a completely different ratio (0.667 vs 0.75).
Confusing part-to-part with part-to-whole
A ratio of 2 : 3 means 2 parts to 3 parts — a total of 5 parts. The first quantity is 2/5 (40%) of the whole, not 2/3. Mixing these up is the most common ratio error in recipes and budgets.
Forgetting to simplify before comparing
20 : 30 and 40 : 60 look different but are the same ratio (both reduce to 2 : 3). Always reduce to lowest terms before deciding whether two ratios are equal.
Last updated: October 5, 2026
Creators
Computer Scientist & Developer Tools Author
Reviewers
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Frequently Asked Questions
How do I simplify a ratio?
Divide every term by their greatest common divisor (GCD) — the largest whole number that divides them all exactly. For 20 : 60, the GCD is 20, so dividing both terms gives 1 : 3. This calculator finds the GCD and reduces the ratio for you, including three-term ratios like 50 : 100 : 150 → 1 : 2 : 3.
How do I solve a proportion with a missing value?
Cross-multiply. In A : B = C : D, the products A × D and B × C are always equal, so you can rearrange to find any missing term. For 3 : 4 = 9 : ?, the missing value is (4 × 9) ÷ 3 = 12. Enter the three values you know and leave the unknown box blank.
What is the difference between a ratio and a fraction?
They use the same arithmetic but describe different things. A fraction like 3/4 usually compares a part to a whole. A ratio like 3 : 4 compares one part to another part, and can extend to more than two quantities (3 : 4 : 5). For two-term part-to-part ratios, the maths of simplifying is identical to reducing a fraction.
Can I simplify a ratio that has decimals?
Yes. The calculator first scales decimal terms up to whole numbers — for example 1.5 : 2 becomes 15 : 20 — and then divides by the greatest common divisor to give an exact whole-number ratio, here 3 : 4.
What is an aspect ratio, and how is it calculated?
An aspect ratio compares width to height. A 1920 × 1080 screen has a ratio of 1920 : 1080, which simplifies (dividing both by their GCD of 120) to 16 : 9 — the standard widescreen ratio. Any resolution that reduces to 16 : 9 has the same shape.