How to use it
- Pick a mode: proportion, direct, inverse, split or simplify.
- Enter the known values or the ratio, such as 3 : 2 : 1.
- For splitting, enter the total amount.
- Read the missing value or the parts.
Five ratio tools in one
- a : b = c : x finds the missing term of a proportion.
- Direct proportion scales a value up or down: more items, higher price.
- Inverse proportion handles cases where one quantity goes up as the other goes down: more workers, fewer days.
- Split by ratio divides a total into shares, for example $120,000 in the ratio 3 : 2 : 1.
- Simplify ratio reduces a ratio to the smallest whole numbers, even with decimals.
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Solving a proportion
In a proportion a : b = c : x, the cross products are equal, so a · x = b · c and x = b · c / a.
Example: 3 : 4 = 9 : x, so x = 4 × 9 / 3 = 12.
Map scale: if 1 inch on a map is 25 miles, then 3.5 inches is 25 × 3.5 / 1 = 87.5 miles.
Direct and inverse proportion
Direct proportion: when one quantity doubles, the other doubles too. If 4 gallons of gas cost $13.60, then 10 gallons cost 13.60 × 10 / 4 = $34.00.
Recipe scaling: 2 cups of flour make 12 cookies. For 30 cookies: 2 × 30 / 12 = 5 cups.
Inverse proportion: when one quantity doubles, the other halves, because their product stays the same. If 3 painters need 12 days for a job, 4 painters need 3 × 12 / 4 = 9 days (assuming everyone works at the same pace).
Another inverse example: at 60 mph a trip takes 2 hours, so at 50 mph it takes 60 × 2 / 50 = 2.4 hours.
Splitting an amount by a ratio
To divide a total in the ratio 3 : 2 : 1, add the parts (3 + 2 + 1 = 6), divide the total by that sum to get one share, then multiply.
Example: split $120,000 of business profit 3 : 2 : 1.
| Partner | Shares | Amount |
|---|---|---|
| A | 3 | $60,000 |
| B | 2 | $40,000 |
| C | 1 | $20,000 |
The same method mixes concrete or paint in a given ratio, or divides a shared bill by how much each person used.
Simplifying ratios
A ratio is in simplest form when its terms are whole numbers with no common factor. Divide each term by the greatest common factor: 12 : 18 = 2 : 3. If a ratio has decimals, first multiply every term by the same power of ten: 1.5 : 2 = 15 : 20 = 3 : 4.
Common simplified ratios include screen aspect ratios: 1920 × 1080 pixels is 16 : 9, and 1024 × 768 is 4 : 3. For percentages of a total, try the percentage calculator.
Common mistakes
- Mixing up the order. A ratio of boys to girls of 3 : 2 is not the same as girls to boys. Keep the terms in the same order on both sides of a proportion.
- Using direct proportion when it is inverse. Ask whether doubling one quantity should double or halve the other. More workers means fewer days, not more.
- Different units. Convert everything to the same unit first: 2 feet : 8 inches is 24 : 8 = 3 : 1, not 2 : 8.
- Assuming proportion where there is none. Cooking time for a turkey, for example, does not double when the weight doubles.
- Rounding shares too early. When splitting money, round only the final amounts, then adjust one share by a cent if the total is off.
Frequently asked questions
How do I solve a proportion?
Cross-multiply: in a : b = c : x, x = b × c / a.
What is the difference between direct and inverse proportion?
In direct proportion both quantities change in the same direction. In inverse proportion, one goes up as the other goes down and their product is constant.
How do I split money by a ratio?
Add the ratio parts, divide the total by that sum, then multiply by each part. $120,000 in 3 : 2 : 1 gives $60,000, $40,000 and $20,000.
Can I simplify a ratio with decimals?
Yes. The calculator scales decimals to whole numbers first, so 1.5 : 2 becomes 3 : 4.
How do I enter a ratio?
Separate the parts with colons, for example 3 : 2 : 1.
Last updated: November 12, 2026