Ratio Calculator
Simplify ratios, solve for an unknown ratio term, or scale a ratio up — with the full step-by-step working.
Ratio Calculator — input your values
What does this math calculator do?
The ratio calculator performs three common tasks: simplifying a ratio to its lowest terms (for example 12:18 becomes 2:3), solving a proportion for the missing term (a : b = c : x), and scaling a ratio by a factor. Three- and four-term ratios like a : b : c : d are supported when simplifying.
Ratios compare quantities without units, and two ratios are equivalent when they reduce to the same simplest form. The calculator uses the greatest common divisor to simplify and cross-multiplication to solve proportions, showing each step so the math is fully transparent.
Formula and variables
Cross-multiplication works because the two ratios are equal, so the product of the outer terms equals the product of the inner terms.
| Symbol | Meaning |
|---|---|
| a : b | The first ratio |
| c : x | The second ratio (x is unknown) |
| gcd | Greatest common divisor of the ratio terms |
Worked example
A recipe needs flour and sugar in the ratio 3 : 2. If you use 12 cups of flour, how much sugar do you need?
- Write the proportion: 3 : 2 = 12 : x.
- Cross multiply: 3 × x = 2 × 12 = 24.
- Divide by 3: x = 24 ÷ 3 = 8.
Answer: You need 8 cups of sugar.
Tips and common mistakes
Tips
- A ratio with no common unit is a pure comparison — 2 : 3 means 'two parts to three parts', whatever the unit.
- To check if two ratios are equivalent, compare their cross products: a : b = c : d exactly when a × d = b × c.
- When scaling a recipe or a model, multiply every ingredient or dimension by the same factor to preserve the ratio.
- Ratios can also be written with a colon, as a fraction (a/b), or as 'a to b' — they all mean the same thing.
Common mistakes to avoid
- Simplifying only one term of the ratio instead of dividing both by the same number.
- Cross multiplying in the wrong order, which flips the answer in a proportion.
- Dividing by zero when term a is zero in the solve mode.
Ratio Calculator — frequently asked questions
How do I simplify a ratio?
Divide every term by their greatest common divisor. For 12:18, gcd is 6, so the ratio simplifies to 2:3.
How do I solve for x in a proportion?
Cross multiply and divide: in a : b = c : x, x = b × c ÷ a. For 3 : 2 = 12 : x, x = 2 × 12 ÷ 3 = 8.
What does it mean to scale a ratio?
You multiply both terms by the same factor, which produces an equivalent ratio. For example, scaling 2:3 by 4 gives 8:12.
Can ratios involve decimals?
Yes, and the calculator supports them in solve and scale modes. For simplification, whole numbers are used so the result stays exact.
Are ratios the same as fractions?
Closely related: the ratio a : b can be read as the fraction a/b. Ratios compare parts, while fractions describe a part of a whole.
Why do recipes give ratios instead of exact amounts?
Because a ratio scales automatically: the same 3:2 mixture works for a single serving or a banquet, as long as every ingredient is scaled equally.