Ratio Calculator
Simplify ratios and solve proportions to find a missing value.
Inputs
Simplified Ratio (A:B)
3 : 4
Missing Value (D in A:B = C:D)
12.0000
A ÷ B
0.7500
Step by step
Find the GCD of A and B
GCD(3, 4)
= 1
Divide both parts by the GCD to simplify
3 ÷ 1 : 4 ÷ 1
= 3 : 4
GCD is 1 — the ratio is already in simplest form.
Compute A ÷ B as a decimal
3.0000 ÷ 4.0000
= 0.7500
Solve for D in A:B = C:D
D = (4.0000 × 9.0000) ÷ 3.0000
= 12.0000
How it works
A ratio compares two quantities. Simplifying divides both parts by their greatest common divisor. To solve a proportion A:B = C:D for D, cross-multiply: D = (B × C) ÷ A.
Formulas
Simplified ratio
Simplified A:B = (A ÷ GCD) : (B ÷ GCD)
- A
- First part of the ratio
- B
- Second part of the ratio
- GCD(A,B)
- Greatest common divisor of A and B
Proportion — solve for D
A:B = C:D → D = (B × C) ÷ A
- A
- First known ratio term
- B
- Second known ratio term
- C
- New first term
- D
- Missing value to find
Frequently Asked Questions
How do I scale a recipe with ratios?
Set the known ratio as A:B, put your new amount as C, and the calculator solves for the matching quantity D that keeps the proportion identical.
What does a simplified ratio mean?
It expresses the same relationship using the smallest whole numbers. For example, 6:8 simplifies to 3:4.