Explanation
What a ratio tells you
A ratio compares two quantities in a specified order. The quotient first ÷ second describes how much of the first quantity corresponds to one unit of the second. Scaling preserves the same relative amounts while changing the size.
Choose the question
Choose simplify to one to find A ÷ B, the value of the ratio, so 16 : 9 becomes 1.78 : 1. Choose scale to keep the same proportion at a new size: enter the original pair and a new first amount, and the calculator finds the matching second amount, so 16 : 9 at a width of 1,920 needs a height of 1,080. Keep the order and units consistent.
q = A ÷ B
| q | value of the ratio (A per one B) |
|---|---|
| A | first amount |
| B | second amount |
B′ = A′ × B ÷ A
| B′ | matching new second amount |
|---|---|
| A′ | new first amount |
| A | first amount |
| B | second amount |
2 compared with 4
| First amount (A) | 2 |
|---|---|
| Second amount (B) | 4 |
| Result | 0.5 |
2 ÷ 4 = 0.5, so 2 : 4 = 0.5 : 1
Scale a 2:3 mixture
| First amount (A) | 2 |
|---|---|
| Second amount (B) | 3 |
| New first amount | 10 |
| Result | 15 |
10 × 3 ÷ 2 = 15
A zero first quantity
| First amount (A) | 0 |
|---|---|
| Second amount (B) | 5 |
| Result | 0 |
0 ÷ 5 = 0, so 0 : 5 = 0 : 1
Diagram of this result
The ratio you entered beside the equivalent ratio the calculator found.
Two ratios are written side by side with an equals sign: the one entered and its equivalent, either reduced to a value per one or scaled to a new first amount. The exact numbers are stated in the answer and the steps.
Common mistakes
Swapping the two quantities reciprocates a ratio and changes the meaning. Ratios between amounts with different units are rates, so retain their units. In a two to three mixture, the first share is two fifths of the combined total, not two thirds.
Assumptions and limits
Amounts cannot be negative. The second amount must be above zero, and scaling also needs a first amount above zero. Repeating decimals are evaluated at 50 significant digits and rounded only for display. The calculator does not reduce whole-number pairs such as 4 : 6 to 2 : 3 or infer units.
Sources
OpenStax Prealgebra 2e, ratios and proportions: https://openstax.org/details/books/prealgebra-2e
Can a quantity be zero?
A zero first quantity is valid for comparison and gives zero. Scaling from a zero first quantity is undefined because it would require division by zero.