The Ratio Calculator does the two ratio jobs that come up everywhere: simplify a pair of numbers to their cleanest ratio (24:36 becomes 2:3), and solve a proportion, finding the missing fourth value in A:B = C:D. Fill in two values to simplify, or any three values of a proportion to solve for the fourth.
How It Works
Simplification divides both terms by their greatest common divisor, the same operation as reducing a fraction. Solving a proportion uses cross-multiplication: in A:B = C:D, the products A x D and B x C are equal, so the missing term is the product of the two values diagonal to it divided by the remaining known value. The calculator validates against zero denominators and asks for at least two values (to simplify) or three (to solve).
Worked examples
24:36 simplifies by a GCD of 12 to 2:3. A photo printed at 24 cm by 36 cm shares its shape with every 2:3 print size, which is why ratio, not size, is the right language for scaling. For the proportion 2:3 = 8:D, cross-multiplication gives D = (3 x 8) / 2 = 12: a recipe that uses 2 cups of flour to 3 of milk needs 12 parts of milk scaled against 8 of flour. Solve for a middle term instead: in 4:B = 10:15, B = (4 x 15) / 10 = 6.
Scaling is the everyday use
Ratios earn their keep in scaling: map scales (1:50,000 turns 3 cm on paper into 1.5 km on the ground), model kits, ingredient ratios in baking (the baker's percentage system is ratios all the way down), gear ratios, screen dimensions, and mixture problems such as fuel-to-oil or concrete mixes. The working pattern is always the same: fix the ratio in simplest form first (small numbers, fewer slips), then scale to the quantity you actually have by solving the proportion with the known side entered here.
Ratio versus fraction versus percent
A ratio compares two quantities and can compare part to part (2 boys to 3 girls) where a fraction compares part to whole (2/5 of the class). Percentages are ratios standardized to a whole of 100. Converting between them is mechanical: A:B as a fraction of the total is A/(A+B). Many errors in mixture and probability problems are really this single confusion, part-to-part read as part-to-whole; the calculator's A:B = C:D framing keeps the parts explicit.
Limitations
The solver handles one proportion with positive, finite values as entered; a zero in a denominator position is rejected because the proportion is undefined there, and negative values, while arithmetically accepted in some positions, rarely mean anything in scaling problems and should be sanity-checked. It simplifies integer ratios exactly; decimal inputs simplify by the same GCD logic applied to the values given, so 2.5:5 returns 1:2 only insofar as the decimal GCD resolves, which for tidy decimals it does.
Frequently Asked Questions
How is a ratio different from a fraction?
Notation and emphasis: 2:3 and 2/3 encode the same relationship when the comparison is part to part of two quantities, but a fraction usually reads as part of a whole. The calculator treats A:B as A/B for the proportion math.
Can I solve for any of the four positions?
Yes. Leave exactly one of A, B, C, D empty and provide the other three; each missing position has its own rearrangement of the cross-multiplication, and the calculator applies the right one with its zero checks.
Why simplify a ratio at all?
Small numbers are easier to compare, remember, and scale mentally. 2:3 communicates instantly what 24:36 or 200:300 also say, and errors in later scaling steps shrink with the numbers.