Free Ratio Calculator
Simplify exact decimal ratios, compare shares or solve a missing term in A:B = C:D. Use advanced options and copy or download your results. Browser-based and no signup required.
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How to use the ratio calculator
Simplify exact decimal ratios, compare shares or solve a missing term in A:B = C:D. No signup required.
- Choose exact ratio simplification or a missing-term proportion.
- For simplification, enter non-negative A and B values with up to six decimal places.
- For a proportion, select the missing term in A:B = C:D and enter the other three values.
- Review the simplified ratio, shares or solved term and copy or download the calculation.
Everyday situations that call for a ratio
Ratios appear in recipes, mixing instructions, map scales, budgets and school homework. A cleaning product may ask for 1 part concentrate to 4 parts water. A recipe for 4 people may need scaling for 6. A business may want to compare 120 online sales to 80 store sales.
This calculator has two modes. Simplify A:B reduces a ratio to its lowest whole-number terms and shows the decimal value of A divided by B and each term's share of the total. Solve a proportion finds one missing value in A:B = C:D.
Students can use it to check homework steps, and anyone scaling quantities can use it to avoid mental arithmetic errors.
Worked examples with real numbers
Simplify 12:18. The greatest common divisor of 12 and 18 is 6, so the simplified ratio is 2:3. A divided by B is about 0.667. A's share of the total is 12 divided by 30, or 40 percent, and B's share is 60 percent.
Simplify decimals: 2.5:0.75. The tool scales both terms by 100 so they become whole numbers, 250 and 75. Their greatest common divisor is 25, which gives 10:3.
Solve a proportion: a recipe uses 3 cups of flour for 4 servings, and you want 9 cups. Enter A as 3, B as 4, C as 9 and choose D as the missing term. Cross multiplication gives D = B times C divided by A, which is 4 times 9 divided by 3, or 12 servings. The result row shows the full proportion 3:4 = 9:12.
How the calculator works
Simplification uses exact integer arithmetic. It finds the largest number of decimal places among the two terms, up to six, multiplies both terms by the same power of ten, and divides them by their greatest common divisor using the Euclidean algorithm. Because no rounding happens, a ratio like 0.1:0.3 becomes exactly 1:3.
Proportions rely on the rule that A:B = C:D means A times D equals B times C. Each missing term is found by rearranging that equation, for example A = B times C divided by D. Proportion results use normal floating-point arithmetic, so long decimals may be rounded in the display.
Terms for simplification must be non-negative, with up to 12 digits before the decimal point and up to 6 after it.
Common mistakes to avoid
Keep the order consistent. If A:B is flour to servings, then C:D must also be flour to servings. Mixing the order gives a wrong answer that still looks reasonable.
Use the same units on both sides of a proportion. Do not compare cups on one side with milliliters on the other unless you convert first.
Remember that B and D act as denominators and cannot be zero, and a ratio of 0:0 cannot be simplified. Also, a simplified ratio describes proportions, not amounts: 2:3 does not tell you whether you have 2 liters or 200.
Useful tips and limitations
- Ratio simplification uses exact integer arithmetic after scaling decimal places.
- Proportion denominators B and D must be nonzero; some zero combinations do not have a unique solution.
- To split an amount in a ratio, use the share percentages: for 2:3, the first part gets 40 percent and the second gets 60 percent.
- Use the copy or download option to keep your calculation with homework or project notes.
Common questions
Can the ratio simplifier handle decimal values exactly?
Yes, for supported decimal inputs with up to six fractional digits. It scales the terms to integers and reduces them using their greatest common divisor.
How do I solve a missing proportion value?
Select Solve a proportion, choose A, B, C or D as missing, and enter the other terms. The calculator uses A times D equals B times C.
Why is my zero-valued proportion rejected?
A zero denominator is invalid, and some zero combinations give no solution or infinitely many solutions. Only a unique valid proportion is shown.
Can the ratio calculator handle negative numbers?
No. Simplification accepts non-negative decimal terms only, with up to six decimal places.
Why is 1.5:2.25 shown as 2:3?
Both terms are scaled to whole numbers, 150 and 225, and divided by their greatest common divisor, 75, which gives 2:3.
Can I solve for A or B instead of D?
Yes. Choose any of A, B, C or D as the term to solve, then enter the other three values.
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