Ratio Calculator
Proportions are the workhorse of everyday math: scale a recipe from 4 servings to 6, convert a map distance, mix paint at 3:2, work out screen aspect. All of it is one sentence - A is to B as C is to x - and one move: x = C × B ÷ A. Enter the three known values and this calculator fills in the fourth, then shows the ratio simplified, as a decimal and as a percentage, with the cross-multiplication check written out so the answer verifies itself.
The worked line is the point: 3:4 = 15:x resolves to x = 20 with the cross-products shown (3 × 20 = 60, 4 × 15 = 60), which is exactly the check a teacher wants to see. Values persist on your device for multi-step scaling sessions, and the page sits naturally beside the fraction calculator for the same students.
How to use
- Enter the three known values of your proportion - A, B and C.
- Read x, plus the ratio simplified, decimal and percentage views.
- Check the cross-multiplication line, then share or keep the values for the next step.
Frequently asked questions
How do I solve a proportion?
Cross-multiply and divide: A:B = C:x means A·x = B·C, so x = B·C ÷ A. For 3:4 = 15:x: x = 15 × 4 ÷ 3 = 20. The note line shows this arithmetic - and its reverse check - with your numbers.
How do I simplify a ratio?
Divide both sides by their greatest common divisor: 12:18 shares a GCD of 6, so the ratio is 2:3. The calculator reduces whatever you enter, including decimals (scaled to integers first), so 1.5:2 becomes 3:4.
How do I scale a recipe with ratios?
Treat servings as one side of the proportion. A recipe serving 4 with 2 cups of rice scales to 6 servings via 4:6 = 2:x - x = 3 cups. Enter recipe servings, target servings and the known quantity in the A, B, C slots in that order.
What's the difference between a ratio and a rate?
A ratio compares like quantities (3 cups to 2 cups); a rate compares unlike ones with units kept (60 miles per hour). The math here solves both, but keep units explicit for rates - mixing numerators and denominators is the classic proportion error.