Ratio Calculator
Simplify ratios to lowest terms, solve proportions (A:B = C:X) for any missing value, and scale ratios up or down by any factor.
About the Ratio Calculator
This ratio calculator handles the three ratio tasks that come up in school, cooking, mixing and design. First, it simplifies any ratio to lowest terms — 12:18 becomes 2:3. Second, it solves proportions: enter three of the four values in A:B = C:D and it finds the missing one by cross-multiplication. Third, it scales a ratio by any factor, ideal for resizing recipes or mixes.
Ratios express how two quantities relate, and equivalent ratios keep that relationship while changing scale. The proportion solver uses the cross-multiplication rule A×D = B×C, the same method used for map scales, currency conversion, paint mixing and unit-rate problems.
Whether you are converting a 16:9 screen resolution, mixing concrete at 1:2:4, adjusting a recipe for more guests or checking aspect ratios for images, the answers update live as you type — no submit button, no rounding surprises for whole-number ratios.
How to Use the Ratio Calculator
- 1To simplify: enter both parts of the ratio in the first section.
- 2To solve a proportion: fill three of the four A, B, C, D boxes and leave the unknown blank.
- 3To scale: enter a ratio and the factor to multiply both sides by.
- 4Each section works independently and updates as you type.
Frequently Asked Questions
How do you simplify a ratio?
Divide both parts by their greatest common divisor. For 12:18 the GCD is 6, so the simplified ratio is 2:3. If the parts are not whole numbers, the calculator instead expresses the ratio in the form n:1 by dividing the first part by the second — for example 2.5:1.5 becomes 1.6667:1 — which is standard for comparing rates.
How do you solve a proportion like 2:3 = 8:x?
Cross-multiply: in A:B = C:D, the products A×D and B×C are equal. For 2:3 = 8:x, that gives 2x = 24, so x = 12. In this calculator, type 2, 3 and 8 into the A, B and C boxes, leave D blank, and the missing value appears instantly. Any one of the four positions can be the unknown.
How do I scale a recipe using ratios?
Work out the scaling factor first: cooking for 10 instead of 4 means a factor of 10 ÷ 4 = 2.5. Then multiply every ingredient by that factor — the scale section does this for a ratio pair directly. Because scaling multiplies both sides equally, the underlying ratio between ingredients stays identical, which is what keeps the recipe balanced.
What is the difference between a ratio and a fraction?
A fraction is a part-to-whole comparison, while a ratio is usually part-to-part. If a class has 12 boys and 18 girls, the boy:girl ratio is 2:3, but boys are 12/30 = 2/5 of the class. You can convert: a ratio a:b corresponds to fractions a/(a+b) and b/(a+b) of the total. Our fraction calculator handles the fraction side.
Can ratios have more than two parts?
Yes — concrete mixes (1:2:4) and screen ratios are common examples — but proportions are solved pairwise. To simplify a three-part ratio, divide all three terms by their common GCD (this tool simplifies two parts at a time). To scale a three-part ratio, apply the same factor to each part using the scale section repeatedly.