➗ Ratio Calculator, Simplify, Divide & Solve Ratios Instantly

A ratio compares two or more numbers. This ratio calculator handles four types of problems in one place: simplifying, solving for a missing value, scaling, and comparing. Pick the tab that matches your problem. Enter your numbers. The result shows up instantly.

You get the simplified ratio, the GCD, the decimal form, the fraction, and the visual proportion bar. No switching between tools.

How the Ratio Calculator Works

The tool has four tabs. Each one solves a different ratio problem.

Simplify reduces any ratio to its lowest terms. Enter A and B. You can also enter C and D for a four-term ratio.

Solve Missing finds the unknown value in A:B = C:D. Leave one field blank. The calculator uses cross multiplication to solve it.

Scale Ratio multiplies or divides both terms by a scale factor. There are eight aspect ratio presets so you can jump straight to 16:9 or 4:3 without typing.

Compare checks if two ratios are equivalent. It simplifies both, computes the decimal value of each, and gives a clear verdict.

What a Ratio Actually Is

A ratio is a way of expressing how two quantities relate to each other. The ratio 3:2 means for every 3 units of the first thing, there are 2 units of the second.

Ratios appear in three common formats. The colon form is 3:2. The fraction form is 3/2. The word form is “3 to 2.” They all mean the same thing.

A ratio is not the same as a fraction, even though they look alike. A fraction represents a part of a whole. A ratio compares two separate quantities. The ratio 3:2 does not mean 3 out of 2. It means 3 of one thing for every 2 of another.

The Ratio Formula

The formula for calculating a ratio is straightforward. Knowing it helps you understand exactly what the ratio calculator computes behind the scenes.

Ratio = A : B

To simplify, divide both A and B by their Greatest Common Divisor.

Simplified ratio = A/GCD : B/GCD

Example: Simplify 12:8. GCD of 12 and 8 is 4. 12 ÷ 4 = 3. 8 ÷ 4 = 2. Simplified ratio: 3:2

To convert to a decimal, divide A by B. 3 ÷ 2 = 1.5. To convert to a percentage split, A/(A+B) × 100 = 3/5 × 100 = 60%. So 3:2 is a 60/40 split.

How to Simplify a Ratio

Simplifying a ratio means reducing both terms to the smallest whole numbers that keep the same relationship.

The GCD does the work. Find the largest number that divides evenly into both terms. Then divide both by it.

Example: Simplify 36:24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. GCD = 12. 36 ÷ 12 = 3. 24 ÷ 12 = 2. Answer: 3:2

You can simplify ratios with decimals too. The ratio calculator scales both terms up to whole numbers first, then applies the GCD. So 1.5:1 becomes 3:2 after scaling.

Solving for a Missing Value

The proportion formula is A:B = C:D. If you know any three values, you can find the fourth using cross multiplication.

To find A: A = (B × C) / D To find B: B = (A × D) / C To find C: C = (A × D) / B To find D: D = (B × C) / A

Example: You know the ratio is 3:4. You want to scale it so the second number becomes 20. What is the first number? A:B = C:D becomes 3:4 = C:20. C = (3 × 20) / 4 = 15

The ratio calculator shows the formula it used and cross-checks the result. You can verify every answer.

Practical use case: A recipe uses a 1:3 ratio of concentrate to water. You need 12 cups of water. How much concentrate do you need? 1:3 = X:12. X = (1 × 12) / 3 = 4 cups.

Scaling a Ratio Up or Down

Scaling keeps the same proportion while changing the actual numbers.

Multiply both terms by the scale factor to scale up. Divide both terms by the scale factor to scale down.

Scale up example: 3:4 scaled by 5 becomes 15:20. That still simplifies to 3:4.

Scale down example: 48:36 divided by 6 becomes 8:6, which simplifies to 4:3.

The ratio calculator shows the scaled result and the simplified version. This matters when you need specific numbers for a project but want to confirm the ratio holds.

Aspect Ratios

An aspect ratio describes the relationship between width and height. Screen dimensions, video formats, and image crops all rely on it.

16:9 is the most common widescreen format. Most monitors, TVs, and YouTube videos use it.

4:3 is the older standard. You see it on older monitors and some educational software.

1:1 is a square. Instagram originally enforced this format.

9:16 is portrait orientation. Used in Instagram Stories, TikTok, and YouTube Shorts.

21:9 is ultra-wide. Used for cinema-style monitors and some film formats.

The Scale tab has preset buttons for all eight common aspect ratios. Enter a scale factor to calculate the ratio for any target resolution instantly.

Example: You need a 16:9 image at a width of 1920 pixels. Scale factor: 120. 16 × 120 = 1920 wide. 9 × 120 = 1080 high.

Gear Ratios

A gear ratio compares the number of teeth on the driven gear to the number of teeth on the driving gear.

Gear ratio = driven gear teeth / driving gear teeth

Example: Driving gear has 10 teeth. Driven gear has 30 teeth. Ratio = 30:10 = 3:1

That means the driving gear completes three rotations for every one rotation of the driven gear. This is a reduction ratio. It increases torque but reduces speed.

Bicycle gears: A 44-tooth chainring with a 16-tooth sprocket gives a ratio of 44:16 = 2.75:1. For every crank revolution, the rear wheel turns 2.75 times.

For RPM calculations: If the input shaft spins at 1800 RPM and the gear ratio is 3:1, the output shaft spins at 1800 / 3 = 600 RPM.

Equivalent Ratios

Two ratios are equivalent if they simplify to the same lowest terms.

4:6 and 6:9 are equivalent because both simplify to 2:3.

The Compare tab checks this automatically. It simplifies both ratios and computes their decimal values. If the decimals match, the ratios are equivalent. Use this ratio calculator any time you need to verify whether two proportions are truly equal.

This is useful for checking whether a scaled image kept the right proportions, or whether two recipes are using the same ingredient balance.

Common Mistakes When Working with Ratios

Forgetting to simplify. A ratio of 100:75 means the same as 4:3. But most people leave it unsimplified and then compare wrong.

Confusing ratio with fraction. The ratio 1:4 does not mean 1/4 of the total. It means 1 part to 4 parts. The total is 5 parts. The fraction of the total is 1/5.

Mixing up the order. 3:1 and 1:3 are different ratios. The order always matters. The first number refers to the first quantity mentioned.

Using different units without converting. A ratio of 500 grams to 1 kilogram is not 500:1. Convert first: 500g to 1000g = 1:2. The ratio calculator handles any units as long as you convert before entering values.

Scaling only one side. When you scale a ratio, both terms must change by the same factor. Changing 3:4 to 6:4 breaks the proportion. The correct scale-up is 6:8.

Frequently Asked Questions

Final Thoughts

Most ratio problems fall into four categories: simplify, solve, scale, or compare. This ratio calculator handles all four without switching tools or reloading pages. Each result shows the GCD, the fraction, the decimal, the percentage split, and the visual bar.

For aspect ratios, use the preset buttons. For gear ratios, use the Scale tab with the right scale factor. For proportion problems like recipes or map scales, use Solve Missing.