Simplify ratios to lowest terms, solve proportions, scale values, and convert any ratio to a fraction, decimal or percentage.
Results update live as you type.
Simplified ratio
As fraction
2/3
a / b
As decimal
0.6667
a ÷ b
As percentage
66.67%
(a ÷ b) × 100
GCD
6
greatest common divisor
| Ratio | Fraction | Decimal | Percent |
|---|---|---|---|
| 1 : 1 | 1/1 | 1.0 | 100% |
| 1 : 2 | 1/2 | 0.5 | 50% |
| 1 : 4 | 1/4 | 0.25 | 25% |
| 2 : 3 | 2/3 | 0.667 | 66.7% |
| 3 : 4 | 3/4 | 0.75 | 75% |
| 16 : 9 | 16/9 | 1.778 | widescreen |
| 1.618 : 1 | φ | 1.618 | golden ratio |
The Method
To simplify a ratio, divide every term by their greatest common divisor
(GCD), found with the Euclidean algorithm. The ratio
12 : 18 has GCD 6, so it reduces to 2 : 3 — its lowest terms.
To solve a proportion a : b = c : d, use cross-multiplication:
because a/b = c/d, it follows that a × d = b × c, which you can rearrange to find any
missing term. Scaling simply multiplies a value by the scale ratio while
preserving every internal proportion.
Working for 12 : 18
About This Tool
A ratio calculator compares quantities and puts them into their simplest, most useful form. It can simplify a ratio to lowest terms, handle three-part ratios (a : b : c), solve proportions for a missing value, and scale any quantity up or down by a chosen ratio. It also converts every ratio to its equivalent fraction, decimal, and percentage.
Ratios are one of the most practical ideas in everyday mathematics. They appear in cooking (a 1 : 2 ratio of rice to water), finance (debt-to-equity, price-to-earnings), maps and models (a 1 : 50,000 scale), screen and image dimensions (16 : 9 widescreen, 4 : 3 classic), mixing and dilution (1 : 10 concentrate to water), betting odds, and aspect ratios in design. Understanding ratios lets you keep proportions correct whenever you scale something up or down.
The mathematical engine here is the Euclidean algorithm for the greatest common divisor — the same elegant method Euclid described around 300 BC — used to reduce ratios to lowest terms, and cross-multiplication for solving proportions. Both are exact for whole numbers; for decimal inputs the calculator rounds sensibly to avoid floating-point artefacts. Everything runs in your browser.
Use this free ratio calculator for homework, recipes, scale drawings, financial analysis, dilutions, and any situation where you need to keep two or more quantities in proportion. No sign-up, no tracking — every calculation is local.
Simplify Ratios
Reduce any 2-part or 3-part ratio to its lowest terms via the GCD.
Solve Proportions
Find the missing value in A : B = C : D by cross-multiplication.
Scale Values
Multiply any quantity up or down by a ratio while keeping proportions.
Multi-Format Output
See each ratio as a fraction, decimal and percentage at once.
Visual Proportion Bar
A live bar shows each part's share of the whole at a glance.
100% Free & Private
No account, no tracking — every calculation runs locally in your browser.
Four modes cover every everyday ratio problem.
Choose Simplify, 3-part, Proportion, or Scale depending on what you need. The input fields change to match.
Type the terms of your ratio. The colon (:) separators show how the values relate. Decimals are accepted and rounded sensibly.
The summary card shows your simplified ratio (or solved value), plus its fraction, decimal and percentage equivalents.
The coloured proportion bar shows each part as a share of the whole — perfect for visualising how a ratio divides a quantity (e.g. splitting profit 2 : 3).
In Proportion mode, fill three of the four boxes in A : B = C : D and leave one blank. The calculator cross-multiplies to find the missing value.
In Scale mode, enter a value and a scale ratio (e.g. 3 : 2). The result multiplies the value by 3/2 — ideal for resizing recipes, drawings and budgets.
Everything you need to know about ratios, proportions, scaling, and how to interpret your result.
A ratio compares two or more quantities by division, showing how many times one value contains another. The ratio 3 : 2 means for every 3 units of the first quantity there are 2 of the second. Ratios can be written three ways: with a colon (a : b), as a fraction (a/b), or in words ("3 to 2"). They are the foundation of proportion, scaling, and rates.
Divide every term by their greatest common divisor (GCD). For 12 : 18, the GCD is 6, so the ratio simplifies to 2 : 3. A ratio is in lowest terms when the only common factor of its terms is 1. This is the same process as reducing a fraction — find the GCD, then divide top and bottom by it.
A proportion is an equation stating two ratios are equal: a/b = c/d. To find a missing value, cross-multiply: a × d = b × c, then solve for the unknown. For example, 3/4 = 9/? gives ? = 4 × 9 / 3 = 12. Cross-multiplication works because multiplying both sides of a/b = c/d by bd cancels the denominators.
A fraction expresses a part of a whole (3/4 of a pizza). A ratio compares two separate quantities (3 boys to 4 girls = 3 : 4). Mathematically they are computed the same way, but in a ratio the second term need not represent a whole — in "3 boys to 4 girls" the total is 7, not 4. A ratio a : b can always be written as the fraction a/b, but the interpretation differs.
Multiply each ingredient by the same scale factor. To double a recipe, scale by 2/1; to make 1.5× the amount, scale by 3/2; to halve it, scale by 1/2. The ratio between ingredients stays constant — that's what keeps the recipe balanced. Use the Scale mode of this calculator: enter the quantity and the scale ratio, and read off the new amount.
A three-part ratio (a : b : c) compares three quantities at once — for example, a concrete mix of 1 : 2 : 4 (cement : sand : aggregate). To simplify, divide all three terms by their common GCD. To split a total amount in this ratio, add the terms to get the total parts (1 + 2 + 4 = 7), then give each item its share: cement gets 1/7, sand 2/7, aggregate 4/7.
For a two-part ratio a : b, divide a by b and multiply by 100 to express the first as a percentage of the second: 3 : 4 → (3 ÷ 4) × 100 = 75%. To express each part as a percentage of the whole, divide by the total: in 3 : 4 the whole is 7, so the parts are 3/7 ≈ 42.9% and 4/7 ≈ 57.1%. This calculator shows both interpretations.
The golden ratio (φ, "phi") is approximately 1.618 : 1 and has the unique property that the whole relates to the larger part exactly as the larger part relates to the smaller. It appears in art, architecture, the Fibonacci sequence, and natural patterns like spiral shells and sunflower seeds. Its exact value is (1 + √5) / 2.
Aspect ratio is the ratio of width to height of an image or screen. Common ones: 16 : 9 (modern widescreen TVs and monitors), 4 : 3 (classic TVs and older monitors), 21 : 9 (ultrawide / cinema), 1 : 1 (square, used on Instagram), and 3 : 2 (35 mm photography). Keeping the aspect ratio constant when resizing prevents distortion.
Yes. A ratio like 2.5 : 1 is perfectly valid and often appears in finance and engineering. To express it in whole-number terms, multiply both sides by the same factor to clear the decimals: 2.5 : 1 = 25 : 10 = 5 : 2. This calculator handles decimal inputs and rounds carefully to avoid floating-point artefacts when finding the GCD.