Ratio Calculator
Online ratio calculator to simplify ratios and solve for missing values in proportions. Enter 2 values to simplify A:B, or 3 values to calculate the fourth in A:B=C:D. Instant results.
About Ratio Calculator
Ratio Calculator is a free online tool designed to solve for missing values in proportional relationships. Given a ratio in the form A : B = C : D, you can enter any three values and the calculator will automatically compute the fourth missing value. This tool is useful for solving proportion problems, scaling recipes, calculating missing dimensions, and various mathematical and practical applications where proportional relationships are involved.
Ratio Calculation Principles
1. What is a Ratio?
A ratio is a comparison between two numbers that shows how many times one value contains or is contained within the other. In the form A : B = C : D, it means that the ratio of A to B is equal to the ratio of C to D.
2. Cross Multiplication
To solve for a missing value in A : B = C : D, we use cross multiplication: A × D = B × C. This allows us to find any missing value when the other three are known.
3. Solving for Each Variable
- If A is missing: A = (B × C) / D
- If B is missing: B = (A × D) / C
- If C is missing: C = (A × D) / B
- If D is missing: D = (B × C) / A
4. Common Uses
- Solving proportion problems in mathematics
- Scaling recipes in cooking
- Calculating missing dimensions in similar shapes
- Mixing solutions in chemistry
- Converting between units using proportions
5. Mathematical Process
The fundamental principle is that in a proportion A : B = C : D, the cross products are equal: A × D = B × C. This relationship allows us to solve for any unknown value.
6. Important Notes
- All values must be positive numbers
- Zero cannot be used in a ratio
- Exactly three values must be provided
- The calculated value will maintain the proportional relationship
Understanding Ratios and Proportions
Ratio Notation:
Ratios are written as A : B = C : D, where the colon (:) represents 'to'. This means A is to B as C is to D, indicating that the two ratios are equivalent.
Proportional Relationships:
When A : B = C : D, the ratios are proportional. This means that if you multiply A and D, you get the same result as multiplying B and C. This cross-multiplication property is the key to solving for missing values.
Practical Applications:
Proportions are used extensively in real-world scenarios, from cooking (doubling or halving recipes) and construction (scaling blueprints) to finance (calculating interest) and science (diluting solutions). Understanding how to solve proportions is essential for many practical tasks.
