Ratio Calculator: Solve, Compare and Split
Enter A, B and C to solve the proportion A : B = C : D. The calculator returns D, the ratio A : B in lowest terms, and A ÷ B as a decimal. Use it to scale a recipe or a drawing when you know one side of the new ratio. Two more modes compare two ratios and split a total into parts, so a ratio can scale to any total you set.
Solve: A : B = C : D
How to use the Ratio Calculator
- Enter your numbers in the Ratio Calculator above.
- Press the Solve, Compare or Split button to see the result.
- To try other numbers, change any value and press the button again.
Solving and simplifying a ratio
D = B × C ÷ A · · · Lowest terms: divide A and B by their greatest common divisor · · · Decimal = A ÷ B · · · Compare: A × D with B × C · · · Share = total × part ÷ sum of the parts
Two ratios A : B and C : D are equal when A × D = B × C, which is where the formula for D comes from. Decimals scale up to whole numbers before the calculator finds the common divisor, so 1.5 : 2.5 becomes 15 : 25 and then 3 : 5. To compare, the calculator works out A × D and B × C. When they match the ratios are equal, and otherwise the larger side belongs to the larger ratio. To split, it adds up the parts and gives each part its share of the total.
Worked example
For 3 : 4 = 6 : D, D = 4 × 6 ÷ 3 = 8. The ratio is already in lowest terms, 3 : 4, and the decimal is 0.750000. Enter 18, 24 and 6 and D is again 8, with 18 : 24 simplified to 3 : 4. To compare 3 : 4 with 9 : 12, pick Compare two ratios. It cross-multiplies: 3 × 12 = 36 and 4 × 9 = 36, so they are equal. To split 35 in the ratio 2 : 5, pick Split a total. There are 2 + 5 = 7 parts of 5, which gives 10 and 25.
Frequently asked questions
What's the difference between ratio and proportion?
A ratio is a comparison of two quantities (3:4). A proportion is an equation showing two ratios are equal (3:4 = 9:12).
How do I scale a recipe?
Keep the ratio and scale both ingredients. A recipe with 2 cups of flour to 1 cup of sugar becomes 4 cups of flour when doubled. Enter A = 2, B = 1 and C = 4, and the calculator gives D = 2 cups of sugar.
How do I compare two ratios?
Pick Compare two ratios and enter A : B and C : D. The calculator multiplies across and says which is larger, so 3 : 4 is larger than 5 : 8, because 3 × 8 = 24 beats 4 × 5 = 20. As decimals they are 0.750000 and 0.625000.
How do I scale a ratio to a total?
Pick Split a total, enter the total and the parts. A mix of 2 : 3 : 5 scaled to a total of 200 gives 40, 60 and 100, or 20%, 30% and 50%. The parts take up to 10 numbers, separated by colons or spaces, and a comma before three digits counts as a thousands comma, so 1,500 : 2 has two parts. A share with more than six decimals says it was rounded.
Can a ratio have more than two terms?
Yes, a ratio such as 2 : 3 : 5 has three terms, and Split a total takes up to 10. Solve for D takes two at a time. To scale 2 : 3 : 5 so the first term becomes C, enter A = 2 and B = 3 to get the second term, then A = 2 and B = 5 with the same C to get the third.
Which numbers can I enter?
A and B must be above 0, and C may also be 0, which makes D 0. Each takes a size from 0.000000000001 to 1,000,000,000,000,000. Negative numbers get a message. D shows up to six decimals and the line above it says when it was rounded, so 3 : 7 = 5 : D shows 11.666667, rounded to 6 decimals. A D of 1e15 or more, or too small for six decimals, prints in e-notation with four significant figures, and the line says so when that dropped digits. 1 : 123456789 = 123456789 : D shows 1.524e+16, rounded to 4 significant figures.