Simplify ratios, solve proportions, scale equivalent ratios, or split a total into proportional shares.
Calculator
Ratio Results
Review the answer, equivalent form, proportional shares, and calculation steps.
Ratio Parts
Calculation Steps
| Step | Value | Explanation |
|---|
Ratio calculator for four common problems
Use this calculator to simplify a two- or three-part ratio, solve one missing value in a proportion, multiply every term by the same scale factor, or divide a total into proportional shares. Enter whole numbers, decimals, or simple fractions such as 3/4. The result panel shows the answer first and then the arithmetic used to check it.
How to simplify a ratio
A ratio stays equivalent when every term is divided by the same nonzero factor. For whole-number terms, the calculator finds their greatest common divisor and divides every term by it. Decimal and fraction inputs are first written with a common denominator, then reduced to the smallest whole-number terms.
simplified ratio = each whole-number term / greatest common divisor
Simplifying ratio example
For 12:18, the greatest common divisor is 6. Dividing both terms by 6 gives 2:3. The relationship has not changed: 12/18 and 2/3 are both approximately 0.6667. For 1.5:2.5, clearing the decimal places gives 15:25, which reduces to 3:5.
How to solve a proportion
A proportion states that two ratios are equal: a/b = c/d. Leave exactly one of the four boxes empty. The calculator uses equal cross products, a x d = b x c, and isolates the missing term. For example, 2:3 = 14:x gives x = 3 x 14 / 2 = 21.
a / b = c / d, so a x d = b x c
How to split a total by ratio
Add the ratio terms to find the total number of parts. Divide the total by that sum to find one part, then multiply by each ratio term. Splitting 100 in a 3:2 ratio gives five total parts. One part is 20, so the shares are 60 and 40. The displayed shares are calculated from the unrounded values so they add back to the entered total apart from display rounding.
share = total x ratio term / sum of all ratio terms
Scaling an equivalent ratio
Multiply every term by the same positive scale factor. A 2:3:5 ratio scaled by 4 becomes 8:12:20. Scaling changes the quantities but preserves their relative relationship. Multiplying only one term creates a different ratio.
Part-to-part and part-to-whole percentages
In a ratio A:B, A divided by B is the unit comparison, while A divided by A+B is A's share of the combined whole. For 2:3, A/B is 66.67%, but A represents 40% of the total five parts. The calculator labels these separately because they answer different questions.
| Question | Fraction | Percent |
|---|---|---|
| A compared with B | 2/3 | About 66.6667% |
| A's share of the whole | 2/(2+3) = 2/5 | 40% |
| B's share of the whole | 3/(2+3) = 3/5 | 60% |
For a three-part ratio such as 2:3:5, add all three terms first: A's share is 2/10 = 1/5 = 20%. Use the fraction calculator to reduce the resulting fraction, or the percentage calculator to express a part as a percentage of its whole. The denominator depends on the question; a part-to-part comparison is not automatically a share of the total.
Use matching units
Ratio terms should describe comparable quantities. Convert measurements to the same unit before simplifying. A ratio of 1 foot to 6 inches is not 1:6; after converting 1 foot to 12 inches, the ratio is 12:6, or 2:1. OpenStax's ratios and rates guide likewise explains that measurements should use the same unit before their ratio is simplified.
Equivalent ratios and cross products
Equivalent ratios represent the same quotient. You can multiply or divide every term by one common factor to generate another equivalent form. For a proportion, equality can be checked by comparing the cross products. OpenStax defines a proportion as an equation between two ratios and shows why their cross products are equal.
Input and rounding limits
The calculator accepts positive integers, decimals with up to six decimal places, and simple fractions. Decimal digits are converted to fractions before reduction, without first rounding the decimal through binary multiplication. Reduced numerators and denominators must fit JavaScript's safe-integer range; larger or more precise inputs may need a separate exact-arithmetic tool. Scaling, proportional shares, and solved proportion values use floating-point arithmetic and are rounded for display.
Very small ratio results
A nonzero result is not the same as zero. Scaling 0.000001:0.000002 by 0.000001 gives 1e-12:2e-12, or 0.000000000001:0.000000000002. The notation e-12 means multiply by ten to the power of -12. The simplified ratio is still 1:2. Very small outputs use scientific notation rather than being rounded to a misleading 0:0; inputs themselves use ordinary decimal or fraction notation.
Frequently asked questions
What is the simplest form of a ratio?
For whole-number terms, it is the equivalent ratio whose terms have no common divisor greater than 1.
Can a ratio have three parts?
Yes. Simplify, scale, and split modes accept an optional third term and apply the same common factor to all terms.
Is 2:3 the same as 3:2?
No. Order carries meaning. Reversing the terms reverses which quantity is being compared with the other.
Why must one proportion box be blank?
The other three values define the missing fourth value. More than one blank leaves too little information, while no blank leaves nothing to solve.