Simplify a ratio to its lowest terms, or find a missing value in an equivalent ratio.
Simplifying a ratio means dividing both sides by their greatest common divisor (GCD), the same way you'd reduce a fraction. A ratio of 24:36 and a ratio of 2:3 describe the exact same relationship between two quantities — the simplified form is just easier to read and compare at a glance.
Two ratios are equivalent when one is a scaled-up or scaled-down version of the other. Given A:B = C:D, you can find the missing value with cross-multiplication: D = (B × C) ÷ A. This is the same method used for recipe scaling, map distances, mixing concentrations, or converting between units that share a fixed proportion.
This calculator only handles simple two- and three-term numeric ratios — for unit conversions or currency, use a dedicated conversion calculator instead.
To simplify a ratio, enter the terms (like 24 and 36) and the calculator reduces them to lowest terms automatically. To solve for a missing value in an equivalent ratio, enter the three known values and leave the unknown blank — the calculator uses cross-multiplication to solve for it. Both modes work instantly, so you can quickly check whether two ratios are actually equivalent or find the exact value needed to keep a proportion balanced.
A ratio compares two or more quantities, showing their relative sizes to each other rather than their absolute values. A ratio of 3:2 could describe 3 cups of flour to 2 cups of sugar, or 300 grams to 200 grams, or 3 million to 2 million — the ratio itself only captures the proportion, not the specific scale. This is what makes ratios so useful for scaling: as long as you multiply or divide every term by the same number, the underlying relationship stays exactly the same, whether you're doubling a recipe or shrinking a blueprint to a smaller scale model.
Ratios, fractions, and percentages are closely related but used in different contexts. A ratio like 3:5 compares two separate quantities to each other. A fraction like 3/5 typically represents a part out of a whole (3 parts out of a total of 5). A percentage converts that same relationship to a value out of 100 — 3/5 becomes 60%. It's worth noting that a ratio of 3:5 (comparing two things) is subtly different from a fraction of 3/5 (a part of a whole) — in the ratio case, the "whole" would actually be 3+5=8, so 3 out of the total 8 parts is 3/8, not 3/5. Being clear on this distinction avoids a very common source of calculation errors.
When two ratios are equivalent, written as A:B = C:D, cross-multiplication provides a reliable way to solve for any single missing value. The relationship can be rewritten as A × D = B × C, and rearranged to isolate whichever value is unknown. For example, if 3:4 = 9:x, cross-multiplying gives 3 × x = 4 × 9, so 3x = 36, meaning x = 12. This method works because equivalent ratios represent the same underlying proportion scaled by a consistent factor, and cross-multiplication is simply a algebraic way of solving for that scaling relationship without needing to first figure out the scale factor explicitly.
While two-term ratios (A:B) are the most common, three-term ratios (A:B:C) show up in situations involving three related quantities at once — like mixing concrete (cement:sand:gravel), blending colors, or splitting a bill or profit three ways according to a set proportion. Simplifying a three-term ratio works the same way as a two-term one: divide all three terms by their greatest common divisor. Scaling a three-term ratio to hit a target total also follows similar logic, just distributed across three terms instead of two, which is exactly the kind of calculation this tool handles automatically.
Beyond simplifying and solving for a missing term, ratios are often used to split a total amount according to a set proportion — for example, splitting a $900 profit between two partners in a 2:1 ratio. This works by adding the ratio terms together (2+1=3), dividing the total by that sum ($900 divided by 3 equals $300), then multiplying each term by that unit value (2 times $300 equals $600, and 1 times $300 equals $300). This same method extends naturally to three-term ratios and any total amount that needs to be divided proportionally.
How do I know if two ratios are equivalent? Simplify both ratios to their lowest terms — if the simplified forms match, the ratios are equivalent, since they represent the same underlying proportion.
Can a ratio have a value of zero? A ratio term can be zero (like 0:5), but a ratio can't have zero as the value being divided by in a fraction form, since division by zero is undefined — this comes up if you're converting a ratio to a fraction or decimal.
Does the order of terms in a ratio matter? Yes — 3:5 and 5:3 describe different relationships. Always keep the terms in the same order as the quantities they represent to avoid inverting the intended proportion.
Can this calculator handle ratios with decimal numbers? Yes — decimal values are supported, though simplifying to a clean whole-number ratio may require first scaling the decimals up (for example, multiplying by 10 or 100) before reducing.
What is the difference between a ratio and a rate? A rate is a ratio that compares two different types of units, like miles per hour, while a standard ratio typically compares quantities of the same type or unit.
Can a ratio be simplified to a single number instead of two terms? Yes — dividing the first term by the second gives a single decimal value, sometimes useful for direct comparison, though the two-term form preserves more context about the original quantities.
How do I convert a ratio into a percentage? Divide the first term by the sum of all terms, then multiply by 100 — for a 3:5 ratio, that's 3 divided by 8, times 100, giving 37.5%.
Can ratios have more than three terms? Yes — while two and three-term ratios are most common, any number of related quantities can be expressed as a multi-term ratio, following the same simplification and scaling logic.
Last reviewed by Mehmed on July 11, 2026.