- 1Enter Value A and Value B to define the primary ratio A : B.
- 2The calculator instantly simplifies ratio A : B into lowest integer terms.
- 3To solve a proportion equation (A : B = C : D), enter Value C to automatically compute the missing term D.
A ratio compares two quantities showing how much of one term exists relative to another (e.g. 4 : 3). A proportion is an equation stating that two ratios are equal (A : B = C : D), widely used in recipe scaling, map distances, and financial modeling.
Divide both terms by their Greatest Common Divisor (GCD).
Simplified Ratio = (A / GCD) : (B / GCD) | Example: 12 : 16 = (12/4) : (16/4) = 3 : 4In proportion A : B = C : D, product of extremes equals product of means (A · D = B · C).
D = (B × C) / A | Example: 4 : 3 = 12 : D → D = (3 × 12) / 4 = 94 : 3 = 12 : D → D = (3 × 12) / 4 = 916 : 9 = 1920 : Height → Height = (9 × 1920) / 16 = 1080D = (B × C) / A = (4 × 9) / 3 = 36 / 3- Order Matters: The ratio A : B is not equal to B : A (e.g. 4 : 1 is four times larger than 1 : 4).
- Cross-Multiplication Rule: In any proportion A/B = C/D, multiplying diagonally gives A · D = B · C.
- Division by Zero: Value A cannot be zero in proportion equation A : B = C : D because division by zero is undefined.
What is the difference between a ratio and a fraction?
A ratio compares two separate quantities to each other (e.g. 3 red to 2 blue = 3:2). A fraction compares a part to the total whole (e.g. 3 red out of 5 total = 3/5).
How do I solve for D in a proportion A : B = C : D?
Multiply B by C, then divide the product by A: D = (B × C) / A.
Can ratio terms contain decimals?
Yes. The calculator automatically converts decimal ratio terms into whole-number integers before finding their simplified integer ratio.
What happens if the first term A is zero?
Solving the proportion divides by A, so an A of 0 is mathematically undefined and the calculator returns no result.