Ratio Calculator
Simplify any ratio to its lowest terms or solve a proportion for the missing number.
Example
Simplify 12 : 18. The GCD of 12 and 18 is 6, so divide both:
12 / 6 = 2
18 / 6 = 3
12 : 18 → 2 : 3
Solve the proportion 2 : 3 = 10 : x. Use x = B×C/A = 3×10/2 = 15.
How it works
Pick Simplify to reduce A:B by their greatest common divisor, or pick Proportion to solve A:B = C:x for x. Values recompute live as you type.
Good to know
The Ratio Calculator handles two distinct jobs from a single screen. In Simplify mode it reduces a ratio A:B to its lowest terms by dividing both sides by their greatest common divisor, and in Proportion mode it solves A:B = C:x for the missing fourth value using cross-multiplication. It is built for anyone who works with proportional quantities by hand: cooks scaling a recipe, students checking equivalent fractions, builders mixing concrete or fuel, hobbyists working at model scale, and designers matching aspect ratios.
Reach for Simplify when you have two raw numbers and want the cleanest equivalent form, such as turning a 1920:1080 screen into 16:9, or expressing a 12:18 mix as 2:3. Reach for Proportion when you already know a working ratio and need to scale one side, for example "if 2 parts hardener go with 3 parts resin, how much resin do I need for 10 parts hardener?" Both modes recompute the moment you type, so you can sweep through several values quickly.
Read the headline result first: it is either the reduced "A : B" or the solved value of x. The supporting stats add context. In Simplify mode the GCD tells you exactly what factor was divided out, and the two decimal readouts (A/B and B/A) give you the ratio as a single multiplier in each direction; a zero denominator shows as the infinity symbol. In Proportion mode you also see the scale factor C/A, which is how many times bigger the second pair is than the first.
- Decimal inputs are accepted but rounded to 6 places, then scaled to whole numbers before reducing, so very long decimals or fractions lose precision past that point.
- Proportion mode requires A to be non-zero; if A is 0 the answer is mathematically undefined and the tool will say so rather than guessing.
Frequently asked questions
How does it simplify ratios with decimals?
Decimal values are scaled to whole numbers (up to 6 decimal places) by multiplying both sides by a power of 10, then the pair is reduced by its greatest common divisor.
What formula solves the proportion A:B = C:x?
Cross-multiplication gives A×x = B×C, so x = B×C / A. The tool needs A to be non-zero, otherwise x is undefined.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What does a ratio like 2:3 actually mean?
A ratio of 2:3 means that for every 2 units of the first quantity there are 3 units of the second, a total of 5 parts. It describes relative amounts, not absolute ones, so 2:3, 4:6, and 20:30 all represent the same relationship.
How do I convert a ratio to a fraction or percentage?
For the part-to-whole view, add the terms and divide each by the total: in 2:3 the first part is 2/5 = 40% and the second is 3/5 = 60%. To express one term relative to the other as a fraction, just write A over B, so 2:3 is the fraction 2/3.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 2:3. A proportion is a statement that two ratios are equal, such as 2:3 = 10:15, and solving a proportion means finding the value that makes both sides equal.
How do I scale a recipe up or down using ratios?
Keep the ingredient ratio fixed and treat the new amount as the unknown in a proportion. If a recipe uses 2:3 flour to water and you now have 10 cups of flour, solve 2:3 = 10:x to find x = 15 cups of water.
Can a ratio have three or more terms?
Yes, ratios such as 1:2:3 are common for mixing several ingredients, and they are simplified by dividing every term by the greatest common divisor of all of them. This particular calculator works with two-term ratios and two-ratio proportions.
What is the greatest common divisor and why is it used to simplify ratios?
The greatest common divisor (GCD) is the largest whole number that divides both terms exactly. Dividing both sides of a ratio by their GCD produces the smallest equivalent whole-number ratio, which is the definition of lowest terms.
How do I simplify a ratio that contains decimals?
Multiply both terms by the same power of 10 until they are whole numbers, then divide by their GCD. For example, 1.5:2 becomes 15:20 after multiplying by 10, which reduces to 3:4.
What does it mean if a proportion has no solution?
In A:B = C:x the answer x = B×C/A only fails when A is zero, because dividing by zero is undefined. In that case the proportion has no defined value for x and you need a non-zero first term.
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