How it works
A ratio compares two or more quantities of the same kind, written A : B. A proportion says two ratios are equal, like 3 : 5 = 12 : 20. Ratios show up everywhere: recipes, concrete and paint mixes, screen sizes, map scales and splitting profits or rent. This calculator handles the three jobs people actually need in one place.
Simplify: divide every term by the greatest common factor Proportion: A : B = C : D → D = B × C ÷ A Split: share = total × (part ÷ sum of parts)Worked examples. Simplify: 12 : 18 : 24 has a GCF of 6, so it becomes 2 : 3 : 4. Solve: if 3 : 5 = 12 : D, then D = 5 × 12 ÷ 3 = 20. Split: three partners invested in the ratio 2 : 3 : 4 and share a profit of 90,000. The parts add to 9, so they receive 20,000, 30,000 and 40,000.
Simplifying ratios with decimals
Multiply every term by 10, 100 or 1,000 until they are whole numbers, then simplify. 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5. The calculator does this automatically.
Everyday uses
- Splitting money fairly: profits by investment, rent by room size, shared bills by usage.
- Mixes: a common concrete mix is 1 : 2 : 4 (cement : sand : gravel); many concentrates are 1 : 10 with water.
- Scaling recipes: a recipe for 4 scaled to 10 multiplies every ingredient by 10 ÷ 4 = 2.5.
- Aspect ratios: 16 : 9 means a 1920-pixel-wide image is 1080 pixels tall.
- Map scales: 1 : 50,000 means 1 cm on the map is 500 m on the ground.
Ratio vs percentage
A ratio compares part to part; a percentage compares part to whole. In 2 : 3, the first part is 2 of 5 — 40% of the whole — while its ratio to the second part is 2 ÷ 3 = 66.67%. The “first ÷ second” line in the results shows that second figure.
Direct and inverse proportion
In direct proportion both quantities rise together (twice the guests, twice the food). In inverse proportion one rises as the other falls (twice the workers, half the time). This tool solves direct proportions; for both kinds with the reasoning shown, use the rule of three calculator.
To simplify fractions use the fraction calculator, and to find the GCF of a list of numbers try the GCF and LCM calculator.