Ratio Calculator
Simplify ratios, find missing values, and scale ratios up or down.
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How to use this calculator
Divide both parts by their greatest common divisor to simplify. Use cross-multiplication to find missing values.
- 1
Enter the two values that form your ratio.
- 2
The simplified ratio appears automatically.
- 3
Optionally enter a scale factor to multiply the simplified ratio.
Frequently asked questions
What does it output for a ratio A : B?
The simplified ratio, the ratio multiplied by your scale factor, the fraction A/B in lowest terms, the decimal A ÷ B (up to 6 places) and each side as a share of A + B. For 12 and 8 you get 3 : 2, 3/2, 1.5, 60.0% and 40.0%.
How does the scale factor work?
It multiplies the simplified ratio, not your raw inputs. The inputs 16 and 9 with a factor of 60 return 960 : 540, and 3 : 4 with a factor of 2.5 returns 7.5 : 10. A factor of 0 or less hides the scaled line. The default of 1 simply repeats the simplified ratio.
Does it handle decimals?
Yes. Both values are shifted by the same power of ten, up to six decimal places, so that the greatest common divisor can be found on whole numbers. 1.5 and 2.5 simplify to 3 : 5, and 0.1 and 0.3 simplify to 1 : 3. Anything beyond six decimals is rounded before simplifying.
Why does it reject zero and negative values?
A ratio of 0 : 5 only says the first quantity is absent, and a negative amount has no meaning for a proportion, so both A and B must be above zero. Blank fields count as 0 and trigger the "Values must be greater than zero" message.
Can it find a missing term, such as 3 : 4 = 9 : ?
Not directly; it does not take a third and fourth value. Use the scale factor instead: the factor is 9 ÷ 3 = 3, so enter 3 and 4 with a factor of 3 and read 9 : 12. Decimal factors are fine, and the factor always applies to the reduced ratio, so for 6 and 8 (reduced to 3 : 4) the factor is still 3.
Are the percentages the same as the ratio?
They express the same split relative to the total. For 5 : 2, A is 71.4% and B is 28.6%, so the first part is a bit over 2.5 times the second. With extreme ratios like 1 : 50000 the share of A displays as 0.0% because it rounds to one decimal place.
Does it work with three-part ratios such as 2 : 3 : 5?
No, it handles two values. For a three-part ratio, simplify using the greatest common divisor of all three numbers by hand, or compare the parts in pairs.
Ratio calculator — reduce a ratio and scale it up or down
Reducing by the greatest common divisor
A ratio is in simplest form when both sides share no common factor except 1. The calculator finds the greatest common divisor with the Euclidean algorithm and divides it out: 12 : 8 becomes 3 : 2 and 1920 : 1080 becomes 16 : 9. Equal values, such as 7 and 7, reduce to 1 : 1. The same process works on lengths, quantities and prices, as long as both values are in the same unit and neither is zero. Comparing 150 cm with 2 m only makes sense after converting one of them.
Worked example: screen resolution to aspect ratio
Entering 1920 and 1080 returns 16 : 9, a decimal of 1.777778, and shares of 64.0% and 36.0%. To find a matching height for a new width of 960, set the scale factor to 60 using inputs 16 and 9: the scaled line shows 960 : 540. Every size in the 16 : 9 family follows the same rule, so any width times 9 ÷ 16 gives the matching height without redoing the reduction.
Worked example: scaling a mix
Suppose a mix needs 250 g of one ingredient to 750 g of another. The tool reduces this to 1 : 3, with shares of 25.0% and 75.0%. Because the scale factor multiplies the reduced ratio, a factor of 2 gives 2 : 6; a factor of 250 gives back 250 : 750 and a factor of 500 gives the doubled batch, 500 : 1500. Ratios built this way keep the proportions exactly, which is why they suit recipes, paint mixes and scale models where the balance between parts matters more than the total.
Sample inputs and outputs
The table collects runs of the tool, including decimals.
| A, B | Simplified | Decimal A ÷ B | Share of A |
|---|---|---|---|
| 12, 8 | 3 : 2 | 1.5 | 60.0% |
| 1920, 1080 | 16 : 9 | 1.777778 | 64.0% |
| 1.5, 2.5 | 3 : 5 | 0.6 | 37.5% |
| 0.1, 0.3 | 1 : 3 | 0.333333 | 25.0% |
| 5, 2 | 5 : 2 | 2.5 | 71.4% |
Ratios, fractions and percentages
A : B compares two parts, whereas a fraction compares one part with a whole. A 3 : 2 ratio therefore splits a total into 3/5 and 2/5, which is the 60.0% and 40.0% the calculator prints. Keep the distinction in mind when a problem says "ratio of boys to girls" versus "fraction of the class who are boys". The first compares two groups with each other, the second compares one group with everybody.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →