Ratio & Proportion Calculator
Simplify a ratio to lowest terms or solve A : B = C : x, with the steps shown.
How it works
To simplify, divide both terms by their GCD. To solve a proportion, multiply across the equals sign: A × D = B × C, then divide both sides by the number that sits next to the unknown.
Simplify: A : B → (A ÷ GCD) : (B ÷ GCD)
Proportion: A × D = B × C
D = B × C / AExample
24 : 36 has GCD 12, so it simplifies to 2 : 3. To scale that ratio up so the first term is 8, solve 2 : 3 = 8 : x. Cross-multiply: 2 × x = 3 × 8 = 24, so x = 24 ÷ 2 = 12, and 8 : 12 is the same ratio.
Common mistakes
- Adding instead of multiplying to scale a ratio. Adding 2 to both terms of 2 : 3 gives 4 : 5, which is a different ratio. 4 : 6 is the equivalent one.
- Putting quantities in different positions. If A and C are both kilometres and B and D both hours, keep that order on both sides.
- Treating a 0 in the second term as fine. A : 0 has no fraction value, so the solver rejects a zero B or D.
About this calculator
The ratio simplifier takes two terms, A and B, and divides both by their greatest common divisor. Decimals are allowed: both terms are scaled by the same power of ten to whole numbers first, so 2.4 : 3.6 becomes 24 : 36 and then 2 : 3. A zero term is handled (0 : 5 is 0 : 1) and 0 : 0 has no simplified form.
The proportion solver reads A : B = C : D as the fractions A/B = C/D and cross-multiplies (A × D = B × C). Pick which of the four terms is unknown and fill in the other three. The second terms, B and D, are denominators, so they cannot be 0. If a division by zero would be needed, the tool says whether every value or no value works.
Frequently asked questions
How do I simplify a ratio with decimals?
Multiply both terms by the same power of ten until both are whole numbers, then divide by their GCD. For 2.5 : 4, multiplying by 10 gives 25 : 40, the GCD is 5, and the simplified ratio is 5 : 8. The calculator does this on exact decimals, up to 6 decimal places.
What is cross-multiplication?
For A : B = C : D, the products across the equals sign are equal: A × D = B × C. Solving for the unknown means dividing that product by the term next to the unknown. For 2 : 3 = 8 : x, x = (3 × 8) ÷ 2 = 12.
What happens with zero terms?
In the simplifier, 0 : 5 becomes 0 : 1 and 5 : 0 becomes 1 : 0, while 0 : 0 has no simplest form. In the solver, B and D cannot be 0. If the term you divide by is 0, the tool reports that every value works (when the other side is also 0) or that none does.
How are negative terms handled?
If exactly one term is negative, the minus sign is written on the first term, so 24 : −36 becomes −2 : 3. If both are negative the signs cancel, so −24 : −36 becomes 2 : 3.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, like 2 : 3. A proportion is a statement that two ratios are equal, like 2 : 3 = 8 : 12. The simplifier works on one ratio; the solver finds a missing term of a proportion.