Ratios have no fixed measurement unit. For quantities of the same kind, convert to matching units before entering values. Currency and unit preferences do not convert these inputs.
How to use this ratio calculator
Choose Simplify and enter A and B, or choose Scale and add the new second value D to solve A:B = C:D. Results update as you type.
How to simplify and scale a ratio
A ratio compares two quantities in a fixed order. In 12:18, the first value is 12 and the second is 18. For quantities of the same kind, convert them to the same unit before entering them: 1 meter to 50 centimeters is 100:50, or 2:1.
To simplify a ratio, find the greatest common divisor (GCD) of its two whole-number terms, then divide both by it. For 12:18, the GCD is 6, so (12 ÷ 6):(18 ÷ 6) = 2:3. Dividing both terms by the same positive number preserves the ratio.
For decimal ratios, first multiply both values by the same power of ten. For example, 1.5:2 becomes 15:20 after multiplying by 10, then 3:4 after dividing by 5. This calculator does that conversion for you.
To find an equivalent ratio with a known second value, write A:B = C:D. The scale factor is D ÷ B; multiply A by this factor to find C. Equivalently, C = A × D ÷ B. Open Calculation steps below the results to see the substitution for your inputs.
A:B also represents the fraction A/B. A’s share of a combined total is different: A ÷ (A + B). For a 2:3 ratio, A/B is 2/3, while A is 2/5, or 40%, of the total.
Ratio examples: simplest form, recipes, and dimensions
Simplify: 24:36 → divide both terms by 12 → 2:3. Recipe: a flour-to-water ratio of 3:2 with 500 g of water needs 3 × 500 ÷ 2 = 750 g of flour. Dimensions: at 16:9, a height of 1,080 pixels needs a width of 16 × 1,080 ÷ 9 = 1,920 pixels. Keep each quantity in the same position when scaling.
Equivalent ratio: scale both quantities by the same factor
An equivalent ratio compares quantities in the same proportion at a different scale. Multiply or divide both terms by the same positive factor: A:B = (A × k):(B × k). For example, 2:3, 4:6, and 10:15 are equivalent ratios because they all simplify to 2:3.
If the new second quantity D is known, write A:B = C:D and calculate C = A × D ÷ B. Example: 3:8 = C:72 gives C = 3 × 72 ÷ 8 = 27, so the equivalent ratio is 27:72. Choose Scale mode and enter A = 3, B = 8, and D = 72 to check the result and its calculation steps.
Keep each quantity in the same position and use matching units. To check whether two ratios are equivalent, simplify each pair separately and compare their lowest terms. The form above solves for C; it does not automatically solve an unknown in any of the four positions.
Ratio simplifier: reduce whole numbers and decimals
A ratio simplifier writes the same comparison in its lowest whole-number terms. Use matching units before simplifying: 1 m to 50 cm becomes 100:50, not 1:50.
Formula: let g = GCD(A, B). The simplified ratio is (A ÷ g):(B ÷ g). Example: GCD(24, 36) = 12, so 24:36 = (24 ÷ 12):(36 ÷ 12) = 2:3.
For decimals, multiply both terms by the same power of ten first. Example: multiplying both terms of 1.5:2.5 by 10 gives 15:25; divide both terms by 5 to get 3:5. Enter 1.5 and 2.5 in Simplify mode, then open Calculation steps to see the working.
Limits and assumptions
Two-term, nonnegative ratios only. A can be zero; B and D must be positive. Inputs are limited to 1 billion and six decimal places. Simplification is exact for accepted inputs; scaled and percentage displays are rounded. Scale mode solves for C in A:B = C:D, not for any of the four positions. Fractions, negative ratios, three-part ratios, and automatic unit conversion are not supported.
Frequently asked questions
How do I simplify a ratio?
Enter its first and second values in Simplify a ratio mode. For example, 12 and 18 reduce to 2:3. Open Calculation steps to see the common divisor and both divisions.
Can I enter a ratio with decimals?
Yes. Enter decimals directly, such as 1.5 and 2, to get 3:4. Up to six decimal places are supported. Use a decimal point; commas are accepted only as thousands separators, as in 1,500.
How do I find a missing value in a proportion?
Choose Scale a ratio / find missing C. Arrange the proportion as A:B = C:D, then enter A, B, and D. For 3:8 = C:72, the result is C = 27. This mode solves the first value of the second ratio only.
Are 2:3 and 4:6 equivalent ratios?
Yes. Both simplify to 2:3. You can check two ratios by entering each pair in Simplify mode and comparing their lowest whole-number terms.
What is the difference between a ratio and a percentage?
A part-to-part ratio compares A with B. A part-to-whole percentage compares one part with their total. With 2 parts concentrate and 3 parts water, concentrate is 2 ÷ 5 = 40% of the mixture, not 2 ÷ 3.
Can I use this as an aspect ratio calculator?
Yes. Choose Scale mode, enter width as A and height as B, then put your new height in D. The result C is the corresponding width. Keep width and height in the same units.
Can a ratio contain zero?
A can be zero: 0:5 simplifies to 0:1. B cannot be zero because this tool also evaluates A divided by B. It does not accept 0:0 or a zero second term.