Simplified ratios and proportional shares
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. In decimal mode, the GCD belongs to the scaled whole-number parts, not the original decimal inputs. Integer ratio reduction is exact; displayed continuous shares may be rounded.
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
Normalized 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. Decimal mode uses the larger fractional-place count to multiply both parts by the same power of ten. BigInt arithmetic reduces the resulting integers exactly before proportional shares are calculated.
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
- Choose Whole numbers or Decimals; each mode retains independent parts. At least one part must be positive.
- Decimal parts allow up to six places and require a digit before the decimal point. Enter the total to divide.
- Review the live reduced ratio, shares and percentages. Expand the normalization and common-divisor steps.
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.
Decimal ratios can be entered directly in Decimals mode. Both parts are multiplied by the same power of ten before reduction: 0.25:0.75 becomes 25:75, then 1:3. This scaling changes neither the proportion nor the split of a total.
Keep decimal proportions exact during reduction
For parts 0.1 and 0.3, the integer normalization is 1:3. A total of 80 splits into 20 and 60. The input digits determine the exact ratio; no binary approximation is used to choose the common divisor.
Trailing decimal zeros can increase the normalization factor and displayed GCD without changing the final simplest ratio. Parts 0.250 and 0.750 normalize to 250:750 with GCD 250; both still reduce to 1:3. Share values are continuous and do not allocate indivisible objects.
Assumptions & limitations
What this calculation assumes
- There are exactly two parts to the allocation.
- Ratio inputs are nonnegative whole numbers or finite decimals 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.
Can I enter decimal ratio parts directly?
Yes. Choose Decimals and enter nonnegative plain decimals with at most six fractional places. For 0.25:0.75, the calculator scales to 25:75 and reduces to 1:3.
Sources & further reading
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