Simplify ratios, scale them, and solve A:B = C:D.
Ratios come up in recipes, maps, mixing paint and concrete, sharing money and scaling drawings. This ratio calculator does the three ratio jobs people need most: simplifying a ratio like 24:36, solving a proportion like 3:4 = 15:?, and sharing a total in a ratio like 2:3:5. Every answer shows its working.
Quick answer: to simplify a ratio, divide every part by the greatest common factor: 24:36 = 2:3. To share an amount in a ratio, divide it by the total number of parts, then multiply by each part: $1,200 in 2:3:5 is $240, $360 and $600.
How to Use the Ratio Calculator
Simplify: enter A and B. You get the simplified ratio, the ratio as 1 : n and n : 1, and A’s share of the total. Decimals such as 1.5:2.5 are converted to whole numbers first.
Solve A:B = C:?: enter A, B and C to find the missing fourth value.
Share a total: enter the total and the ratio, such as 2:3 or 2:3:5. You get each person’s share, and a chart of the split.
Ratio Formulas
- Simplify: divide both parts by their greatest common factor.
- Solve a proportion: if A : B = C : D, then D = B × C ÷ A.
- Share a total: one part = Total ÷ sum of the ratio numbers, then multiply each ratio number by one part.
Ratio Examples
Simplify 24:36. The GCF is 12, so 24:36 = 2:3. As 1 : n, that is 1 : 1.5. A is 40% of the total.
Solve 3:4 = 15:? D = 4 × 15 ÷ 3 = 20. If 3 cups of flour need 4 eggs, 15 cups need 20 eggs.
Share $1,200 in the ratio 2:3:5. The parts add up to 10, so one part is $120. The shares are $240, $360 and $600.
Ratios in Everyday Life
- Recipes: a 1:2 ratio of rice to water means 2 cups of water for every cup of rice.
- Map scales: at 1:50,000, 1 cm on the map is 50,000 cm, or 500 m, on the ground.
- Mixing: concrete is often mixed around 1:2:3 of cement, sand and gravel. Check the product’s own instructions for your job.
- Screens and photos: a 16:9 screen is 16 units wide for every 9 units tall.
- Sharing costs or profits: partners who invest $20,000 and $30,000 might share profit 2:3.
Ratios, Fractions and Percentages
A ratio of 2:3 means the total has 5 parts. So the first share is 2/5 of the total, or 40%, and the second is 3/5, or 60%. Notice that 2:3 does not mean 2/3. To work with the fractions, use the fraction calculator. For percentages, use the percentage calculator.
Mistakes to Avoid
- Mixing up the order. 2:3 of boys to girls is not the same as 3:2.
- Using different units. Convert 50 cm : 2 m to the same unit first: 50 : 200, which simplifies to 1:4.
- Dividing by the wrong total. When sharing, divide by the sum of the parts, not by the number of people.
Ratio Calculator FAQs
How do you simplify a ratio?
Divide both numbers by their greatest common factor. 24:36 ÷ 12 = 2:3. The simplify fractions calculator uses the same method for fractions.
Can a ratio have decimals?
Yes, but ratios are usually written with whole numbers. Multiply both sides by 10, 100 or 1,000 to remove the decimals, then simplify. 1.5:2.5 becomes 15:25, which is 3:5.
How do you split money in a ratio?
Add the ratio numbers, divide the total by that sum to get one part, then multiply. $90 in the ratio 1:2 is 30 and 60.
Can I use a ratio with more than two parts?
Yes. In “Share a total”, enter ratios like 2:3:5 or 1:1:2:4.
How we checked this page: every example was worked by hand and matches the calculator, including the three-way share.