How to Calculate and Simplify Ratios (With Examples)

Ratios are everywhere: the rice-to-water line on a bag of rice, the scale on a map, the 16:9 shape of your TV, the way a bill gets split between roommates. They look simple, but small mistakes, like mixing up the order or forgetting to match units, can throw the whole answer off.

This guide walks through everything you need: what a ratio means, how to simplify one, how to find a missing value, how to split an amount fairly, and how aspect ratios work. Every example is worked out step by step.

What is a ratio?

A ratio compares two or more quantities. If a class has 12 girls and 18 boys, the ratio of girls to boys is 12:18, read as "12 to 18."

There are three common ways to write the same ratio:

• With a colon: 12:18
• With the word "to": 12 to 18
• As a fraction: 12/18

Part-to-part vs. part-to-whole

This is where many people slip up.

• Part-to-part compares one group to another. Girls to boys = 12:18, which simplifies to 2:3.
• Part-to-whole compares one group to the total. Girls to all students = 12:30, which simplifies to 2:5.

Both are correct. They just answer different questions, so always check which one you need.

How to simplify a ratio

A simplified ratio keeps the same proportions but uses the smallest whole numbers possible.

1. Find the greatest common factor (GCF) of all the numbers: the biggest number that divides into each of them evenly.
2. Divide every part of the ratio by the GCF.
3. Check that no number other than 1 divides into all parts. If one does, divide again.

Example: 12:18

• The GCF of 12 and 18 is 6.
• 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
• Simplified ratio: 2:3

Example with three numbers: 24:36:60

• The GCF of 24, 36 and 60 is 12.
• 24 ÷ 12 = 2, 36 ÷ 12 = 3, 60 ÷ 12 = 5.
• Simplified ratio: 2:3:5

INSERT IMAGE HERE: how-to-simplify-a-ratio.png

Simplifying ratios with decimals

Multiply every part by 10, 100 or another number until all parts are whole numbers, then simplify as usual.

• 1.5 : 2.5 → multiply by 10 → 15 : 25 → divide by 5 → 3 : 5
• 0.75 : 2 → multiply by 4 → 3 : 8 → already simplified → 3 : 8

Simplifying ratios with fractions

Multiply every part by the lowest common denominator to clear the fractions.

• 1/2 : 3/4 → multiply both by 4 → 2 : 3 → 2 : 3

Need help with the fractions themselves? Our fraction calculator handles them step by step.

Simplifying ratios with different units

The units must match before you simplify.

• 2 feet : 8 inches → convert feet to inches: 24 inches : 8 inches → divide by 8 → 3 : 1

If you skip the conversion, you'd get 2:8 = 1:4, which is completely wrong. A length converter makes the first step quick.

How to find a missing value in a ratio

When two ratios are equal, it's called a proportion: for example, 2:3 = 4:6. If one number in a proportion is unknown, you can find it with cross-multiplication.

For a : b = c : x, the missing value is x = (b × c) ÷ a

Example: 3 : 4 = 10 : x

1. Write it as fractions: 3/4 = 10/x
2. Cross-multiply: 3 × x = 4 × 10, so 3x = 40
3. Divide: x = 40 ÷ 3 ≈ 13.33

INSERT IMAGE HERE: find-missing-value-proportion.png

Real-world example: scaling a recipe

A pasta recipe uses 300 g of pasta for 4 servings. How much do you need for 6 servings?

• 4 : 300 = 6 : x
• x = (300 × 6) ÷ 4 = 450 g

For quick unit swaps while you cook, try the recipe converter.

Real-world example: map scale

A map has a scale of 1:50,000. Two towns are 4 cm apart on the map. How far apart are they in real life?

• 1 : 50,000 = 4 : x
• x = 4 × 50,000 = 200,000 cm = 2 km

How to split an amount in a given ratio

This is useful for sharing costs, profits or ingredients.

1. Add up all the parts of the ratio.
2. Divide the total by that sum to get the value of one part.
3. Multiply each part of the ratio by that value.

Example: split $1,200 in the ratio 2 : 3 : 5

• Total parts: 2 + 3 + 5 = 10
• One part: $1,200 ÷ 10 = $120
• Shares: 2 × $120 = $240, 3 × $120 = $360, 5 × $120 = $600
• Check: $240 + $360 + $600 = $1,200 ✓

INSERT IMAGE HERE: split-amount-in-ratio.png

How to convert a ratio to a percentage or fraction

For a two-part ratio a : b:

• Fraction of the total: a ÷ (a + b)
• Percentage: (a ÷ (a + b)) × 100

Example: 2 : 3

• Total parts = 5
• First part = 2/5 = 40%
• Second part = 3/5 = 60%

A percentage calculator is handy when the numbers get messy.

Aspect ratios: ratios for screens, photos and video

An aspect ratio is the ratio of an image's or screen's width to its height. You find it the same way you simplify any ratio.

Example: 1920 × 1080

• The GCF of 1920 and 1080 is 120.
• 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9.
• Aspect ratio: 16:9

Common aspect ratios:

Aspect ratio	Example size (pixels)	Common use
16:9	1920 × 1080, 2560 × 1440	HD video, TVs, most monitors
4:3	1024 × 768	Older screens, some tablets and cameras
1:1	1080 × 1080	Square social posts
4:5	1080 × 1350	Portrait social posts
9:16	1080 × 1920	Reels, Stories, Shorts

INSERT IMAGE HERE: common-aspect-ratios.png

Keep the ratio the same:

New height = new width × (original height ÷ original width)

Example: a 16:9 image resized to 1280 pixels wide → 1280 × 9 ÷ 16 = 720 pixels tall.

Everyday ratios you'll come across

• Cooking: many recipes use simple ratios, such as about 1 part rice to 2 parts water for long-grain white rice. Check the package, because different rice types need different amounts.
• Coffee: many pour-over recipes start around 1:15 to 1:17 coffee to water by weight. At 1:16, 20 g of coffee needs 320 g of water.
• Money: splitting rent, bills or profit in proportion to what each person uses or invests.
• Construction: a general-purpose concrete mix is often given as 1:2:4 (cement : sand : aggregate). For structural work, always follow the mix your engineer or local building code specifies. See our concrete calculator for quantities.
• Maps and models: scales like 1:50,000 or 1:24 tell you how much smaller the drawing is than the real thing.

Common mistakes to avoid

1. Switching the order. 2:3 is not the same as 3:2. Keep the order the question asks for.
2. Mixing units. Convert everything to the same unit before you simplify.

3. Confusing part-to-part with part-to-whole. Girls to boys is not the same as girls to all students.
4. Not simplifying fully. 12:18 → 6:9 isn't finished. Keep going to 2:3.
5. Rounding too early. In proportions, keep full precision until the final answer.

Simplify any ratio in seconds

Working through the steps by hand helps you understand ratios, but a calculator is faster when you have several to do. The free Numrexo Ratio Calculator has three modes:

1. Simplify: enter two or three numbers (decimals work too) to get the simplest form.
2. Find Missing: enter a, b and c for a : b = c : x, and it solves for x.
3. Aspect Ratio: enter a width and height to get the simplified aspect ratio.

You can also download your result as a PDF or email it to yourself, and the calculation runs in your browser.

The bottom line

Every ratio problem comes back to a few moves: match the units, keep the order, divide by the greatest common factor, and cross-multiply when a value is missing. Once those click, recipes, budgets, maps and screen sizes all become simple arithmetic.

Ready to try it? Open the ratio calculator and test it with the examples above.