Ratio Calculator & Solver
Simplify any ratio to lowest terms, solve for a missing term, scale a ratio up or down, split an amount in a given ratio, or turn a ratio into a fraction and percentage. Every answer comes with step-by-step working.
Fill in three terms and leave the unknown empty (or type x).
Step-by-step working
How to use the Ratio Calculator & Solver
- Choose a tab: Simplify, Solve, Scale or Fraction & %.
- Enter your ratio with colons between the terms, for example 12 : 18 or 1.5 : 2.25 : 3.
- To solve a proportion, fill three of the four boxes and leave the unknown empty.
- To scale, pick multiply, divide, split a total, or set one term to a new value, then enter the number.
- Read the answer and the step-by-step working, and press Copy result to reuse it.
Ratio methods at a glance
| Task | Method | Example |
|---|---|---|
| Simplify | Divide all terms by their GCD | 18 : 24 → GCD 6 → 3 : 4 |
| Remove decimals | Multiply all terms by a power of 10 | 0.4 : 1.2 → 4 : 12 → 1 : 3 |
| Remove fractions | Multiply by the LCM of the denominators | 1/2 : 3/4 → × 4 → 2 : 3 |
| Solve for x | Cross-multiply: A × D = B × C | 2 : 5 = x : 35 → 5x = 70 → x = 14 |
| Split a total | Total ÷ sum of parts × each part | $90 in 1 : 2 → $30 and $60 |
| Ratio to percent | First ÷ second × 100, or part ÷ total × 100 | 3 : 5 → 60%, or 3 of 8 = 37.5% |
How the Euclidean algorithm finds the GCD
The greatest common divisor of two whole numbers can be found by repeated division. Divide the larger number by the smaller one, keep the remainder, then divide the previous divisor by that remainder. When the remainder is 0, the last divisor is the GCD.
Example for 150 : 225: 225 = 1 × 150 + 75, then 150 = 2 × 75 + 0, so the GCD is 75 and the ratio simplifies to 150 ÷ 75 : 225 ÷ 75 = 2 : 3. For three or more terms, find the GCD of the first two, then the GCD of that result with the next term, and so on.
Common ratios and aspect ratios
| Ratio | As n : 1 | Where you see it |
|---|---|---|
| 16 : 9 | 1.78 : 1 | HD and 4K video (1920 × 1080, 3840 × 2160), most TVs and monitors |
| 4 : 3 | 1.33 : 1 | Older TVs, many tablets and compact cameras (1024 × 768) |
| 3 : 2 | 1.5 : 1 | 35 mm film and many DSLR photos (6000 × 4000), 4 × 6 in prints |
| 21 : 9 | 2.33 : 1 | Ultrawide monitors (2560 × 1080 is about 2.37 : 1) |
| 9 : 16 | 0.5625 : 1 | Vertical phone video, Stories, Reels and TikTok (1080 × 1920) |
| 1 : 1.414 | √2 | A-series paper (A4 is 210 × 297 mm) |
| 1 : 1.618 | φ | The golden ratio used in design and layout |
To check an aspect ratio, enter the width and height in the Simplify tab: 1920 : 1080 simplifies to 16 : 9 because their GCD is 120.
Frequently asked questions
How do I simplify a ratio?
Divide every term by their greatest common divisor (GCD). For 24 : 36 the GCD is 12, so the ratio simplifies to 2 : 3. If the ratio has decimals or fractions, first multiply every term by the same number to make them whole numbers.
How do I simplify a ratio with decimals?
Multiply all terms by 10, 100 or 1,000 so that no decimals remain, then divide by the GCD. For 1.5 : 2.25, multiply by 100 to get 150 : 225, then divide by 75 to get 2 : 3.
How do I solve a ratio for x?
Write both ratios as fractions and cross-multiply. For 3 : 4 = 15 : x, cross-multiplying gives 3x = 4 × 15 = 60, so x = 20.
How do I divide an amount in a ratio?
Add the parts of the ratio, divide the amount by that sum to get the value of one part, then multiply by each term. Splitting $500 in the ratio 2 : 3 : 5 gives one part = 500 ÷ 10 = 50, so the shares are $100, $150 and $250.
What is the difference between a ratio and a fraction?
A ratio compares parts to each other (3 boys : 5 girls), while a fraction usually compares a part to the whole (3 out of 8 children are boys). The ratio 3 : 5 equals the fraction 3/5 when you compare the first term with the second.
Can a ratio have more than two terms?
Yes. Ratios such as 2 : 3 : 5 are common in recipes, mixtures and budgets. You simplify and scale them the same way, using the GCD of all the terms.