➗ Ratio Calculator
By ToolNimba Editorial Team · Updated 2026-06-19
Reduce a ratio to its lowest whole-number terms.
This ratio calculator does two jobs. In simplify mode it reduces a ratio like 18:24 to its lowest whole-number terms (3:4) using the greatest common divisor. In proportion mode it solves an equation of the form A:B = C:D for whichever value you leave blank, so you can scale a recipe, a map distance, or a mix to any size. Type your numbers and the answer, along with the steps, appears straight away.
What is the Ratio Calculator?
A ratio compares two quantities by division, telling you how much of one thing there is for a given amount of another. Written as A:B (read "A to B"), it carries the same information as the fraction A/B. The ratio 3:4 says that for every 3 units of the first quantity there are 4 of the second, exactly as 3/4 = 0.75 says the first is three quarters of the second. Because a ratio is really a fraction in disguise, you can shrink or grow it the same way you shrink or grow a fraction: multiply or divide both terms by the same number and the comparison stays true.
Simplifying a ratio means dividing both terms by their greatest common divisor (GCD), the largest whole number that divides both exactly. For 18:24 the GCD is 6, so dividing gives 3:4, the same ratio in its smallest whole-number form. A simplified ratio is easier to read and compare, which is why answers in textbooks and recipes are usually given in lowest terms. The calculator handles decimals too by first scaling them up to whole numbers, so 1.5:3 reduces cleanly to 1:2.
A proportion is a statement that two ratios are equal, written A:B = C:D. Cross-multiplication is the key tool: if A:B = C:D then A times D equals B times C. Rearranging that single equation lets you solve for any one of the four values when you know the other three. This is the everyday maths behind scaling a recipe up for more guests, reading a scale model or map, converting currencies at a fixed rate, or working out a tint when mixing paint. Leave one box empty in proportion mode and the calculator applies cross-multiplication for you.
When to use it
- Reducing a ratio such as screen pixels 1920:1080 down to the familiar 16:9 aspect ratio.
- Scaling a recipe: if 2 cups of flour serves 4 people, solving 2:4 = x:6 tells you how much for 6.
- Reading a map or scale model where 1 unit on paper equals a fixed number of real-world units.
- Mixing solutions, fuel, fertiliser, or paint where the parts must stay in a fixed proportion.
- Checking homework: confirming two ratios are equivalent by simplifying both to lowest terms.
How to use the Ratio Calculator
- Choose a mode: "Simplify a ratio" to reduce A:B, or "Solve a proportion" for A:B = C:D.
- In simplify mode, type the two terms (A and B). The lowest-terms ratio and the dividing factor appear instantly.
- In proportion mode, fill in three of the four boxes (A, B, C, D) and leave the unknown one empty.
- Read the solved value and the completed proportion shown below the inputs.
- Edit any number to recalculate; you do not need to press a button.
Formula & method
Worked examples
Simplify the ratio 18:24 to lowest terms.
- Find the greatest common divisor: gcd(18, 24) = 6.
- Divide the first term: 18 ÷ 6 = 3.
- Divide the second term: 24 ÷ 6 = 4.
Result: 18 : 24 simplifies to 3 : 4
Reduce a screen resolution of 1920:1080 to an aspect ratio.
- Find the greatest common divisor: gcd(1920, 1080) = 120.
- Divide the first term: 1920 ÷ 120 = 16.
- Divide the second term: 1080 ÷ 120 = 9.
Result: 1920 : 1080 is the 16 : 9 aspect ratio
Solve the proportion 3 : 4 = 9 : D for D.
- Cross-multiply: 3 × D = 4 × 9.
- So 3 × D = 36.
- Divide both sides by 3: D = 36 ÷ 3 = 12.
Result: D = 12, so 3 : 4 = 9 : 12
Scale a recipe: 2 cups of flour serves 4, how much serves 6? Solve 2 : 4 = C : 6.
- Cross-multiply: 2 × 6 = 4 × C.
- So 12 = 4 × C.
- Divide both sides by 4: C = 12 ÷ 4 = 3.
Result: C = 3 cups of flour for 6 people
Example ratios and their simplified (lowest-terms) form
| Ratio | GCD | Simplified |
|---|---|---|
| 6 : 9 | 3 | 2 : 3 |
| 18 : 24 | 6 | 3 : 4 |
| 50 : 100 | 50 | 1 : 2 |
| 16 : 40 | 8 | 2 : 5 |
| 21 : 28 | 7 | 3 : 4 |
| 1920 : 1080 | 120 | 16 : 9 |
Common aspect ratios as simplified pixel ratios
| Resolution | Aspect ratio |
|---|---|
| 1920 × 1080 | 16 : 9 |
| 1280 × 1024 | 5 : 4 |
| 1024 × 768 | 4 : 3 |
| 2560 × 1080 | 64 : 27 (ultrawide 21:9) |
| 3840 × 2160 | 16 : 9 (4K UHD) |
Common mistakes to avoid
- Adding the same number to both terms. Ratios stay equivalent only when you multiply or divide both terms by the same number, never when you add or subtract. 2:3 is not the same as 3:4, even though both gained 1.
- Stopping before the ratio is fully reduced. Dividing 18:24 by 2 gives 9:12, which is correct but not in lowest terms. Always divide by the greatest common divisor (6 here) so you reach 3:4 in one clean step.
- Mixing up the order of the terms. A ratio of boys to girls of 3:2 is not the same as 2:3. Keep the quantities in the same order on both sides of a proportion or the answer will be wrong.
- Setting up the proportion with crossed positions. In A:B = C:D, A and C are the "first" quantities and B and D the "second". If you swap one pair you change the relationship. Write the matching quantities in matching positions.
Glossary
- Ratio
- A comparison of two quantities by division, written A:B and read "A to B". It is equivalent to the fraction A/B.
- Proportion
- A statement that two ratios are equal, such as A:B = C:D. Solving a proportion finds an unknown term.
- Greatest common divisor (GCD)
- The largest whole number that divides two integers exactly. Dividing both terms of a ratio by it gives the simplest form.
- Equivalent ratios
- Ratios that represent the same comparison, like 1:2, 2:4 and 50:100. Each is obtained by multiplying or dividing both terms by the same number.
- Cross-multiplication
- A method for solving a proportion: from A:B = C:D you get A × D = B × C, which can be rearranged for any unknown.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor (GCD), the largest number that divides both exactly. For 18:24 the GCD is 6, so the simplified ratio is 3:4. This calculator finds the GCD and reduces the ratio for you.
What is an equivalent ratio?
An equivalent ratio is one that represents the same comparison after multiplying or dividing both terms by the same number. 1:2, 2:4 and 50:100 are all equivalent because each reduces to 1:2.
How do I solve a proportion for the missing value?
Write it as A:B = C:D and cross-multiply, so A × D = B × C. Rearrange to isolate the unknown. For example, in 3:4 = 9:D you get D = 4 × 9 ÷ 3 = 12. Leave one box empty in proportion mode and the tool does this automatically.
Can I simplify a ratio with decimals?
Yes. The calculator first scales both terms up to whole numbers, then divides by their GCD. For example 1.5:3 scales to 15:30 and simplifies to 1:2.
What does the ratio 16:9 mean?
16:9 is the aspect ratio of most modern screens. It means that for every 16 units of width there are 9 units of height. A 1920 by 1080 resolution simplifies to 16:9 because gcd(1920, 1080) is 120.
Is a ratio the same as a fraction?
They carry the same information but are written differently. The ratio 3:4 compares two parts and equals the fraction 3/4 (0.75). Both simplify using the same GCD method, which is why the rules look identical.