Ratio Calculator
Simplify a ratio
Solve A : B = C : D — leave one blank
About Ratio Calculator
Simplify a ratio to its lowest whole-number terms, or solve a proportion for whichever value is missing.
A ratio like 8:12 and its simplified form 2:3 describe the exact same relationship, but the simplified version is what most contexts actually want — a recipe, a mixing instruction, an aspect ratio. This reduces any ratio of two or more whole numbers to its lowest terms the same way a fraction gets simplified.
The second section solves the classic "A is to B as C is to what" proportion — leave one of the four fields blank and it works out that value by cross-multiplication, the same method taught for solving a proportion by hand.
Both tools work on whole numbers — a ratio's own convention is integer terms, so a decimal input is flagged rather than silently scaled to some arbitrary precision.
Simplifying a ratio
Divide every part by the largest number that divides them all. 8:12 reduces to 2:3, and 8:12:20 reduces to 2:3:5. If the parts share no common factor, the ratio is already as simple as it gets. Two ratios are equivalent when they simplify to the same form: 6:9 and 10:15 both reduce to 2:3.
Solving a proportion
A proportion sets two ratios equal, A:B = C:D, and cross-multiplication gives A × D = B × C. If 3 cups of rice serve 4 people and you need to serve 12, enter 3, 4, a blank and 12 in the right fields: the missing value is 9 cups. Enter exactly three values and leave the one you want blank.
The same method handles map and model scales. If 1 cm on a map is 25 km and two towns are 7 cm apart, the distance is 175 km. Keep both ratios in the same order, for example map to ground on both sides, or the answer will be inverted.
Limits and common mistakes
Ratios here use whole numbers; decimals are flagged, so multiply through first if you have one (1.5:2 becomes 3:4). The most frequent error is mixing the order of a proportion so one side reads rice to people and the other people to rice. If the answer looks the wrong way round, check that the same quantity is on the same side in both ratios.
What you can use it for
- Simplify a mixing ratio, like paint or concrete, to its lowest terms.
- Scale a recipe up or down while keeping the same proportions.
- Solve a map-scale or model-scale proportion for a missing distance.
- Check whether two ratios are actually equivalent.
- Find a fourth proportional value given three known ones.
How it works, step by step
- 1
Simplify a ratio
Enter two or more parts separated by a colon, like 8:12.
- 2
Or solve a proportion
Fill in three of the four A:B = C:D fields and leave the one you want solved blank.
Frequently asked questions
Does this support decimal ratios?
Not currently — ratios are treated as whole numbers, matching the convention most ratio problems actually use.
How does the proportion solver work?
By cross-multiplication: A × D = B × C. Leave one field blank and it solves for that one using the other three.
What if I leave more than one field blank, or none at all?
It asks for exactly one blank field — that's what makes it clear which value you're solving for.
Is my data sent anywhere?
No. Both calculations run entirely in your browser.