Ratio Calculator
Work with ratios in three ways: simplify a ratio to lowest terms, solve a proportion by finding the missing value in a : b = c : d, or split a total in a given ratio. Example: 18 : 24 simplifies to 3 : 4; in 3 : 4 = 9 : x the missing x is 12; and 120 split 3 : 2 : 1 gives 60, 40 and 20.
Type the problems from this lesson and check each step.
Third part (simplify / split) or c in a : b = c : d.
Show steps
How to use the Ratio Calculator
- Choose a mode: simplify, solve a proportion, or split a total.
- Simplify: enter a and b (and c for three parts). Proportion: fill three of a, b, c, d and leave one empty. Split: enter the ratio parts and the total.
- Press Calculate to see the result, a check and the steps.
Formula and method
Simplify: divide every part by their greatest common divisor. 18 : 24 ÷ 6 = 3 : 4.
Proportion a : b = c : d means a/b = c/d, so a·d = b·c (cross-multiplication). The missing value is d = b·c / a, and so on.
Split a total T in the ratio p : q : r: one part = T ÷ (p + q + r), and the shares are p, q and r times that.
Example: 3 : 4 = 9 : x gives x = 4 × 9 / 3 = 12. 120 split 3 : 2 : 1 gives one part = 20, so 60, 40, 20.
What is a ratio?
A ratio compares two or more quantities of the same kind. It can be written a : b, a to b or the fraction a/b. Ratios have no units: 2 cups to 3 cups is the same ratio as 4 cups to 6 cups.
Simplifying ratios
Divide all parts by their greatest common divisor. If the parts are decimals, multiply by a power of ten to make them whole numbers first: 1.5 : 2.5 becomes 15 : 25, then 3 : 5. A ratio in lowest terms has a GCD of 1.
Equivalent ratios and proportions
Two ratios are equivalent when their fractions are equal. The statement a : b = c : d is a proportion. Cross-multiplication is a quick test: 3 : 4 and 9 : 12 are equivalent because 3 × 12 = 4 × 9.
Worked example: recipe scaling
A recipe uses 2 cups of flour for 3 cups of milk. How much milk for 5 cups of flour? Solve 2 : 3 = 5 : x. x = 3 × 5 / 2 = 7.5 cups.
Worked example: splitting money
Three partners share a profit of $9,000 in the ratio 5 : 3 : 1. One part is 9,000 / 9 = $1,000, so they get $5,000, $3,000 and $1,000.
Ratio, fraction and percent
| Ratio | Fraction of whole | Percent |
|---|---|---|
| 1 : 1 | 1/2 | 50% |
| 1 : 3 | 1/4 | 25% |
| 2 : 3 | 2/5 | 40% |
| 3 : 7 | 3/10 | 30% |
The percent column is the first part’s share of the whole.
Common mistakes
Mixing units (hours with minutes), reversing the order of the terms, and adding the same number to both parts (which changes the ratio). To keep the ratio, multiply or divide, never add.
Accuracy and limits
Results are shown to four decimals. Decimal inputs are converted to integers up to 8 decimal places before simplifying.
Frequently asked questions
How do I simplify a ratio?
Divide each part by their greatest common divisor.
How do I solve a proportion?
Cross-multiply: a·d = b·c, then solve for the unknown.
How do I split an amount in a ratio?
Add the parts, divide the total by that sum to find one part, then multiply.
Is a ratio the same as a fraction?
A ratio of a to b is related to the fraction a/b, but ratios can compare more than two parts.
Can ratios have decimals?
Yes. The calculator converts them to whole numbers before simplifying.
Sources
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