Math · ratios
Ratios and proportions, solved.
Simplify a two-part ratio, list equivalent ratios, solve a proportion for the missing term, and split a total in the same ratio.
Simplify a ratio
Enter two positive terms; decimals are accepted.
Simplified ratio
16 : 9
Decimal value 1.7778
Equivalent ratios
First part
64
Second part
36
Solve a proportion
Fill any three boxes and leave one blank for a / b = c / d.
Second denominator (d)
8
3 / 4 = 6 / ?
Cross-multiplication
Two ratios are equal when a × d equals b × c. The solver rearranges that identity to isolate whichever term you left blank, so no rounding happens until the final display.
How it works
What simplifying a ratio actually changes
A ratio compares two quantities. Simplifying it divides both terms by the same number, which keeps the relationship identical while making the numbers smaller. This tool also uses that relationship to solve proportions and split totals.
Equivalent ratios
Multiplying or dividing both terms by the same non-zero number produces an equivalent ratio. That is why 1920 : 1080 and 16 : 9 describe the same screen shape. The equivalent list makes the scale explicit, which helps when resizing an image or scaling a recipe.
Proportions and cross-multiplication
A proportion says two ratios are equal: a / b = c / d. Multiplying diagonally gives a × d = b × c. If exactly one value is unknown, rearranging that identity solves for it. The solver requires one blank box and three valid numbers.
Part-to-part versus part-to-whole
A ratio such as 3 : 2 compares two parts, while a share of the total uses 3/5 and 2/5. The split section converts the ratio into parts of a total, so you do not accidentally treat 3 : 2 as 3/2 of the whole. Both terms must be positive for a meaningful split.
Good to know
The result is a guide, not a guarantee.
This calculator runs entirely in your browser. Check the assumptions, keep the inputs realistic, and use the result as a starting point for a decision.
Ratios describe relationships between quantities, not quantities themselves, so the simplified answer keeps the same scale.
What is the difference between a ratio and a fraction?
A ratio compares two parts, such as 3 : 4. A fraction compares one part with the whole, such as 3/7 when the whole is 3 + 4. The ratio 3 : 4 and the fraction 3/4 describe different things, even though they use the same numbers.
How does the simplifier handle decimals?
Each term is scaled by the same power of ten so both become whole numbers, then divided by their greatest common divisor. For example, 0.5 : 0.25 becomes 2 : 1. Terms with more than six decimal places are rounded first.
What does solving a proportion mean?
A proportion states that two ratios are equal: a / b = c / d. If you know any three values, the fourth can be found by cross-multiplication. Leave exactly one box blank in the solver to get that value.
Can I use this for an aspect ratio?
Yes. Enter a width and height, such as 1920 and 1080, to get 16 : 9. The equivalent-ratio list shows other sizes that keep the same shape, and the split section works the same way for any two-part total.
Why must the ratio terms be positive?
A ratio of two positive quantities describes a real comparison. Negative or zero terms behave differently under simplification and are rarely meaningful, so this calculator requires both terms to be numbers greater than zero.
Is the calculator free and private?
Yes. It needs no account, runs entirely in your browser, and the values you enter are not sent to simplytools.us or any third party.