Ratio Calculator
Simplify a ratio, scale its terms, divide a total into proportional shares, or solve a missing value. See how each part relates to the whole.
- Share 1
- 40%
- Share 2
- 60%
Percentages are shares of the sum of all terms. Displayed rounded shares or amounts may not add up exactly.
Show working
Sum of ratio terms = 5 Common factor = 1 Divide every term by the common factor: 2 : 3
How to simplify a ratio
A ratio compares quantities in a fixed order. In a ratio of 12:18, there are 12 units of the first quantity for every 18 units of the second. Divide both terms by their greatest common factor, 6, to get 2:3. The relationship stays the same even though the numbers are smaller.
Decimal ratios can also be simplified. For 1.5:3:4.5, multiply by 10 to get 15:30:45, then divide by 15. The simplest whole-number ratio is 1:2:3. The calculator uses exact fraction arithmetic for decimal input before displaying rounded percentage shares.
Ratio to percentage: decide what the whole is
A part-to-part ratio of 2:3 has five total parts. The first part is 2 / 5 x 100 = 40% of the whole; the second is 60%.
That is different from asking what percentage 2 is of 3. That question gives 66.6667% because the denominator is 3, not 2 + 3. Use percentage of total for an explicit part and whole, or fraction to percentage when the input is already a fraction.
| Ratio | First share | Second share |
|---|---|---|
| 1:1 | 50% | 50% |
| 1:2 | 33.3333% | 66.6667% |
| 2:3 | 40% | 60% |
| 3:7 | 30% | 70% |
Split a total in a ratio
Add the ratio terms, then allocate the total in proportion to each term.
Amount for a part = total x that ratio term / sum of ratio terms
To divide 600 in the ratio 2:3:5, the sum of the terms is 10. The allocations are 120, 180 and 300. They add back to 600, and their percentage shares are 20%, 30% and 50%.
If the total represents indivisible items or currency cents, the exact mathematical allocations may need a separate rounding policy. The calculator displays the proportional values and does not silently redistribute leftover units.
Find a missing ratio value
For A:B = C:D, the equivalent fractions A/B and C/D must match. With A greater than zero, solve D using the following expression:
D = C x B / A
For 2:3 = 10:D, the scale factor from 2 to 10 is 5. Multiply 3 by 5 to find D = 15. You can use the same relationship for recipe quantities, scale drawings and proportional allocations when the units are consistent.
Scaling multiplies every original term by the same positive factor. It does not simplify the displayed scaled numbers: scaling 2:3 by 4 produces 8:12, which still has the simplified ratio 2:3.
Common questions
Can a ratio have more than two terms?
Yes. Simplify, scale and split modes accept two to eight nonnegative decimal terms, separated by colons. At least one term must be positive.
Can one term be zero?
Yes: 0:5 simplifies to 0:1 and has shares of 0% and 100%. An all-zero ratio cannot define shares of a whole.
Is this an image aspect-ratio calculator?
You can use the missing-value mode for proportional width and height calculations, but this page does not resize or crop image files. Keep width and height in the same order.
Related calculators
Back to the Percent Calculator.