# Ratio Calculator

> Solve proportions and scale ratios instantly.

**Category:** Math
**Keywords:** ratio, proportion, scale, math, percentage
**URL:** https://complete.tools/ratio-calc

## How it calculates

Calculating a ratio is straightforward with the formula: Ratio = A ÷ B, where A and B represent the two quantities you're comparing. To simplify the ratio, the tool finds the greatest common divisor (GCD) of A and B and divides both quantities by that number. For example, if A is 8 and B is 12, the GCD is 4. So, the simplified ratio becomes: Simplified Ratio = (A ÷ GCD) : (B ÷ GCD) = (8 ÷ 4) : (12 ÷ 4) = 2:3. This means for every 2 parts of A, there are 3 parts of B, clearly showing the relationship between the two quantities.

## Who should use this

Ratio Calc is perfect for a variety of users: 
- Chefs who need to adjust ingredient ratios for different serving sizes.
- Architects figuring out scale ratios for their building designs.
- Financial analysts comparing revenue ratios across fiscal years.
- Teachers explaining ratio concepts in math classes.
- Pharmacists calculating medication dosages based on patient weight ratios.

## Worked examples

Example 1: Imagine a chef adjusting a recipe that calls for 3 cups of flour and 2 cups of sugar. To find the ratio of flour to sugar, we apply the formula: Ratio = A ÷ B. Here, A is 3 (flour) and B is 2 (sugar). Thus, the ratio is 3 ÷ 2 = 1.5. The simplified ratio is 3:2, showing that for every 3 cups of flour, there are 2 cups of sugar.

Example 2: Picture an architect designing a model of a building that’s 50 feet tall while maintaining a height-to-width ratio of 4:3. If the height is 50 feet (A), we can find the width (B) using the ratio formula: B = (3/4) × A = (3/4) × 50 = 37.5 feet. So the model will stand 50 feet tall and 37.5 feet wide, keeping that desired ratio intact.

## Limitations

While Ratio Calc is handy, it does have some limitations: 
- It assumes inputs are always positive numbers; negative values can lead to undefined ratios.
- The tool may not handle ratios involving zero properly, since division by zero is undefined.
- Its simplification process relies on the GCD method, which could introduce inaccuracies if the GCD isn’t calculated correctly.
- It struggles with fractional quantities, which can complicate results for mixed numbers.
- Finally, precision may vary based on how many decimal points are allowed, potentially affecting accuracy for very small values.

## FAQs

**Q:** How does Ratio Calc handle mixed numbers in ratios?


**A:** The tool doesn’t directly support mixed numbers, so you'll need to convert them to improper fractions first.


**Q:** Can Ratio Calc convert between different units in ratios?


**A:** Yes, it can convert between certain compatible units, but make sure they’re suitable for accurate calculations.


**Q:** What if I input a negative ratio?


**A:** Negative values might lead to undefined ratios, as they’re usually expressed in positive terms.


**Q:** How does the tool find the greatest common divisor (GCD)?


**A:** It uses the Euclidean algorithm, which involves repeated division until you reach a remainder of zero.

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*Generated from [complete.tools/ratio-calc](https://complete.tools/ratio-calc)*