Understanding your result
The simplified ratio divides both parts by their greatest common divisor. Shares divide the entered total in those same proportions. A ratio of 2:3 means the first part receives two of five total parts, not two thirds of the whole.
To add, subtract, multiply, or divide fractions after working out the shares, use the Fraction Calculator rather than treating a part-to-part ratio as a fraction of the whole.
The formula
Ratio parts are nonnegative whole numbers and cannot both be zero. The greatest common divisor is found using repeated remainders. The second share is computed from the total minus the first to preserve the entered total before display rounding.
Dividing 150 in the ratio 12:18
The greatest common divisor of 12 and 18 is 6, so the ratio reduces to 2:3. There are five combined parts. Each part represents 30 of the total 150, producing shares of 60 and 90, or 40% and 60%.
How to use this calculator
- Enter the two whole-number parts of the ratio.
- Enter a total to split, or zero if you only want the simplified relationship.
- Read the simplified ratio, proportional quantities, and percentages of the whole.
Part-to-part and part-to-whole relationships
The notation A:B compares one part with another. To turn it into a share of the whole, the denominator becomes A+B. Confusing these denominators can produce an allocation larger than the amount available. Both the amount outputs and percentage outputs here use the combined total.
For decimal ratios, multiply both terms by the same power of ten before entering whole numbers. For example, 1.5:2.5 can be entered as 15:25. Convert unlike units first: a ratio between metres and centimetres is misleading until both measurements use the same unit.
Assumptions & limitations
What this calculation assumes
- There are exactly two parts to the allocation.
- Ratio inputs are whole numbers on a consistent basis.
- The total can be divided continuously.
What to keep in mind
- Displayed decimal rounding can make visible shares differ slightly from a manually rounded total.
- Indivisible objects or currency-cent allocation may require a separate rounding decision.
Common questions
Can one ratio part be zero?
Yes. A zero part receives none of the total, and the other part receives all of it. The ratio 0:0 cannot specify an allocation.
Does simplifying change the shares?
No. Dividing both parts by the same nonzero factor preserves their relative sizes and therefore their shares of any total.