Ratio Calculator
Ratios and proportional splits of two values.
① Simplify to the lowest ratio
Simplest ratio
2 : 3
② Proportion A:B = C:x
Value of x
15
What is the Ratio Calculator?
A ratio compares two values in the form A:B. This tool simplifies a ratio to its lowest integer form and solves the unknown x in a proportion A:B = C:x.
How to use it
Section ① reduces two values to the simplest integer ratio using their GCD. Section ② keeps the same ratio as A:B and solves for x given C — useful for scaling recipes, map scales, and aspect ratios.
Formulas
| Type | Formula | Example |
|---|---|---|
| Simplest ratio | A÷gcd(A,B) : B÷gcd(A,B) | 12:18 → 2:3 |
| Proportion | x = B×C ÷ A | 2:3=10:x → x=15 |
Where Ratios Show Up — Scaling Recipes, Map Scales, and Screen Aspect Ratios
Say a recipe for 2 servings calls for 100g sugar to 300g flour, and you want to scale it to 5 servings. Reducing 100:300 by their GCD of 100 first reveals the underlying ratio, 1:3. The serving multiplier is 5 ÷ 2 = 2.5, so scaling both amounts by 2.5 gives 250g sugar and 750g flour — reduce 250:750 and you get 1:3 again, so the original ratio is preserved. Simply adding a flat amount to both ingredients, or scaling only one of them, breaks the ratio; you must multiply the original ratio by the same factor.
Maps rely on ratios too. A map at scale 1:50,000 means 1cm on the map equals 50,000cm (500m) in reality. Entering A=1, B=50000, C=2 into this calculator's ② Proportion tab returns x=100,000cm, i.e. 1km — so a 2cm distance measured on the map is actually 1km on the ground.
The familiar 16:9 screen aspect ratio is another example. Reducing the common Full HD resolution 1920×1080 by its GCD of 120 gives 16:9 (1920÷120=16, 1080÷120=9) — the exact reduction behind the term "widescreen 16:9" used for TVs, monitors, and video editing.
Outer and Inner Terms — the Mistake of Multiplying the Wrong Pair
In a proportion A:B = C:D, A and D (the outermost values) are called the outer terms, and B and C (the innermost values) are the inner terms. Because the product of the outer terms always equals the product of the inner terms (A×D = B×C), you can solve for an unknown — but pairing the wrong two numbers gives a completely different answer.
Take 2:3 = 6:9: the outer terms are 2 and 9, and the inner terms are 3 and 6. Multiplying correctly, outer × outer gives 2×9=18 and inner × inner gives 3×6=18 — they match. But mixing them up — multiplying the two numbers on the same side, 2×6=12 and 3×9=27 — gives mismatched values that make the proportion look broken. Always multiply diagonally (outer with outer, inner with inner) to avoid this error.