Ratio Calculator
Simplify a ratio, solve for a missing value, and see the split as percentages.
Results
| Item | Value |
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Steps
| Step | Working |
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Quick Answer
To simplify a ratio, divide both numbers by their greatest common factor. For 15:40, the factor is 5, so the ratio is 3:8. To scale it, multiply by the new value and divide by the old one: 6 : B means B = 6 × 40 ÷ 15 = 16.
Embed this calculator
Adjust the size if needed, then copy the code below into your page or blog. The calculator will load in an iframe and stay updated automatically.
Table of Contents
- Ratio Calculator
- Quick Answer
- Related Calculators
- How This Ratio Calculator Works
- How to Use the Ratio Calculator
- Core Formulas
- Key Terms
- Worked Example
- Real-Life Examples
- Ratio vs Fraction vs Percentage
- Common Ratios as Percentages
- Where Ratios Are Used
- Common Mistakes to Avoid
- Frequently Asked Questions
- References & Sources
How This Ratio Calculator Works
A ratio compares two amounts. This calculator simplifies your ratio, shows it as a fraction and as percentages, and scales it to a new size if you enter a new value for A.
Quick explanation: divide both numbers by their greatest common factor.
- A and B: the two amounts you are comparing.
- Shares: how much of the total each amount is.
- New value: optional, to find the matching B.
How to Use the Ratio Calculator
- Enter the two parts of your ratio as A and B, such as 15 and 40.
- To scale the ratio, enter a new value for A.
- Press Calculate.
- Read the simplified ratio, the fraction, the percentages and the scaled value for B.
- Check the steps table to see how it was simplified.
Core Formulas
- Simplify: A ÷ GCF : B ÷ GCF
- Missing value: new B = new A × B ÷ A
- Share of A: A ÷ (A + B) × 100
Key Terms
- Ratio: a comparison of two amounts, written A:B.
- Simplest form: a ratio with no common factor other than 1, such as 3:8.
- Greatest common factor: the largest number that divides both parts exactly.
- Proportion: a statement that two ratios are equal, such as 2:3 = 4:6.
- Scale factor: the number you multiply both parts by to scale a ratio.
- Part-to-whole: one part compared with the total of all parts, as a fraction or percentage.
Worked Example
A recipe uses 300 g of flour and 200 g of sugar. You want to use 450 g of flour.
- Simplified ratio = 3 : 2
- New sugar = 450 × 200 ÷ 300 = 300 g
- Shares = 60% flour and 40% sugar
Real-Life Examples
- Screen sizes: a 16:9 video that is 1,080 pixels tall is 1,080 × 16 ÷ 9 = 1,920 pixels wide.
- Mixing liquids: a cleaner mixed 1:4 with water needs 4 cups of water for each cup of cleaner. For 500 ml of cleaner, use 2,000 ml of water.
- Sharing money: splitting $900 in the ratio 2:3 gives $360 and $540, because 2 ÷ 5 = 40% and 3 ÷ 5 = 60%.
- Map scale: on a 1:50,000 map, 4 cm on the map is 200,000 cm, or 2 km, on the ground.
Ratio vs Fraction vs Percentage
- Ratio: compares parts to each other, such as 2:3.
- Fraction: compares a part to the whole, such as 2/5.
- Percentage: a fraction out of 100, such as 40%.
- Converting: for 2:3, the whole is 2 + 3 = 5, so the first part is 2/5, or 40%.
Common Ratios as Percentages
| Ratio | First part | Second part |
|---|---|---|
| 1:1 | 50.00% | 50.00% |
| 1:2 | 33.33% | 66.67% |
| 1:3 | 25.00% | 75.00% |
| 1:4 | 20.00% | 80.00% |
| 2:3 | 40.00% | 60.00% |
| 3:4 | 42.86% | 57.14% |
| 3:5 | 37.50% | 62.50% |
| 4:5 | 44.44% | 55.56% |
| 16:9 | 64.00% | 36.00% |
Where Ratios Are Used
- Cooking: scaling a recipe up or down.
- Screens and images: keeping the same shape, such as 16:9.
- Maps and models: working with scale.
- Sharing: dividing an amount in a set proportion.
Common Mistakes to Avoid
- Mixing up the order. 2:3 is not the same as 3:2.
- Using different units. Convert both parts to the same unit first, such as grams.
- Treating a ratio as a fraction of the whole. In 2:3, the first part is 2/5 of the total, not 2/3.
- Adding to scale. To scale 3:2 to 9:?, multiply by 3. Adding 6 to both parts gives the wrong ratio.
- Rounding too early. Keep full numbers until the last step.
Frequently Asked Questions
Find the greatest common factor of both numbers and divide each by it. For example, 15:40 becomes 3:8.
Cross-multiply. If A:B = C:X, then X = C × B ÷ A.
Divide one part by the total of both parts, then multiply by 100.
Yes. The calculator scales decimals to whole numbers before simplifying.
It means 16 units of width for every 9 units of height, a common screen shape.
Add the parts, divide the amount by that total, then multiply by each part. $900 in 2:3 is $360 and $540.
Cross-multiply and divide. If 3:5 = 12:x, then x = 12 × 5 ÷ 3 = 20.
It is about 1.618 to 1. It appears in art, design and nature, and is often written as the Greek letter φ (phi).
Turn each into a fraction or decimal. For 3:4 and 5:7, 3 ÷ 4 = 0.75 and 5 ÷ 7 ≈ 0.714, so 3:4 is larger.
Yes, such as 1:2:3. This calculator handles two parts, so work through them in pairs.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Wikipedia, Ratio | Definition and use of ratios. | https://en.wikipedia.org/wiki/Ratio |
| Wikipedia, Greatest common divisor | How to find the common factor. | https://en.wikipedia.org/wiki/Greatest_common_divisor |