Categories🧮 MathRatio Calculator

Ratio Calculator

Solve ratio proportions (A:B = C:D) and scale values effortlessly.

:
EQUALS (PROPORTION)
:
9
Simplified Ratio (A:B): 4:3
📐 Formula
D = (B × C) / A = (3 × 12) / 4 = 9
Guide & Educational Reference
How to Use the Ratio & Proportion Calculator
  1. 1Enter Value A and Value B to define the primary ratio A : B.
  2. 2The calculator instantly simplifies ratio A : B into lowest integer terms.
  3. 3To solve a proportion equation (A : B = C : D), enter Value C to automatically compute the missing term D.
Understanding Ratios and Proportions

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.

Ratio & Proportion Formulas
1. Ratio Simplification

Divide both terms by their Greatest Common Divisor (GCD).

Simplified Ratio = (A / GCD) : (B / GCD) | Example: 12 : 16 = (12/4) : (16/4) = 3 : 4
2. Solving Proportions (Cross-Multiplication)

In 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 = 9
Practical Real-World Examples
Scaling a Recipe (4 servings requires 3 eggs)
4 : 3 = 12 : D → D = (3 × 12) / 4 = 9
12 servings require 9 eggs
Aspect Ratio Image Resizing (16 : 9 screen)
16 : 9 = 1920 : Height → Height = (9 × 1920) / 16 = 1080
1920px width = 1080px height
Solving the proportion 3 : 4 = 9 : D
D = (B × C) / A = (4 × 9) / 3 = 36 / 3
D = 12
Key Tips & Considerations
  • 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.
Frequently Asked Questions

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.

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