Ratio CalculatorFree online math calculator — instant results, no sign-up
Solve A:B = C:D for the missing value (enter 0 for D).
About the Ratio Calculator
This calculator solves for the unknown fourth term D in an equivalent proportion of the form A:B = C:D. It also reduces the baseline ratio A:B to its simplest integer form. It is commonly used by students, designers, chefs, and builders scaling recipes, dimensions, or physical mixtures.
- A
- The first term (antecedent) of the reference ratio. Must not be zero.
- B
- The second term (consequent) of the reference ratio.
- C
- The first term of the target ratio to scale against A:B.
Formula and method
D = (B × C) / A Simplified A:B = (A / gcd(A, B)) : (B / gcd(A, B))
- ANumerator or first quantity in the reference ratio
- BDenominator or second quantity in the reference ratio
- CFirst quantity in the scaled ratio
- DCalculated fourth term satisfying the proportion A:B = C:D
- gcd(A, B)Greatest common divisor of integer values A and B
The calculator multiplies term B by term C and divides the product by term A using cross-multiplication, rounding the final value of D to 6 decimal places. Simultaneously, it divides A and B by their greatest common divisor to return the simplified ratio A:B.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- A3
- B4
- C9
Results
- D12
- Simplified A:B3:4
How to use the Ratio Calculator
- 1Enter the known ratio quantities into fields A and B.
- 2Enter the known scaling quantity into field C.
- 3Cross-multiply B and C, then divide by A to solve for unknown term D.
- 4Inspect D and the reduced ratio A:B formatted in lowest integer terms.
Reading your result
The result D represents the exact quantity needed to keep the relationship C:D identical to A:B. The 'Simplified A:B' output displays the most compact whole-number ratio representation of your baseline inputs.
Limitations
The calculation requires A to be non-zero; entering zero for A causes a division-by-zero error. It also assumes a direct linear relationship and solves specifically for D rather than allowing arbitrary selection of any missing variable without rearranging the inputs.
Common questions
What happens if A is zero?+
Because solving for D involves dividing by A, setting A to zero results in a mathematical division by zero, yielding infinity or an undefined result.
How do I solve for a missing A, B, or C instead of D?+
Rearrange your values so the unknown is in position D. For example, if you need to find C in A:B = C:D, swap positions such that the known ratio is B:A and the target becomes D:C, placing the unknown at the end.
Can I use negative numbers or decimals?+
Yes, decimal and negative values can be entered into the calculation of D, though ratio simplification works best when A and B are positive integers.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.