Ratio Calculator
A : B = C : D (leave one empty to solve)
Missing Value (D)6.0000
Simplified Ratio2 : 3
A ratio compares two quantities, and a proportion states that two ratios are equal: A:B = C:D. This calculator solves a proportion when exactly one of the four values is missing, using cross multiplication, and it also reduces the resulting A:B ratio to its simplest whole-number form. It is built for scaling recipes, mixing, map distances, and any equivalent-ratio problem.
Formula
A:B = C:D ⇒ A·D = B·C, so any one term solves from the other three
- A, B
- The first ratio (numerator and denominator)
- C, D
- The second, equivalent ratio
How it works
- Enter three of the four values in the proportion A:B = C:D and leave the one you want to find blank. Exactly one field must be empty.
- The calculator cross-multiplies to solve for the missing value, for example A = B × C / D. When A and B end up as positive whole numbers it also divides both by their greatest common divisor to show the simplified ratio.
Worked example
Solve the proportion A:3 = 4:6, finding the missing A.
- Cross-multiply: A = (B × C) / D = (3 × 4) / 6.
- Compute: 12 / 6 = 2.
- Simplify the ratio A:B = 2:3, which is already in lowest terms.
The missing value A = 2, and the ratio 2:3 is fully simplified.
Frequently asked questions
- How many values do I need to leave blank?
- Exactly one of the four values must be left empty. If you leave none or more than one blank, the calculator cannot determine a unique missing value and returns no result.
- How does the calculator simplify a ratio?
- When the first two values A and B are positive whole numbers, it divides both by their greatest common divisor. For instance 6:8 reduces to 3:4. Non-integer or non-positive values are left unsimplified.
- Why does it return no result for some inputs?
- It returns nothing if more than one value is blank, or if solving would require dividing by zero, such as when the denominator that should multiply across is zero.