Ratio Calculator
Simplify any ratio, solve a : b = c : d, scale a ratio up or down, split a total or compare two ratios. You get exact answers, the 1 : n form, percents and every step, free and with no signup.
Choose a Ratio Tool
Pick what you need: simplify a ratio, solve a : b = c : d, scale it, split a total, or compare two ratios. Every answer shows the steps.
Simplest form
2 : 3
12 : 18 = 2 : 3
1 : n form
1 : 1.5
Every term divided by the first
n : 1 form
0.6667 : 1
Every term divided by the last
As a fraction
2/3
First term over second
Decimal and percent
0.6667 · 66.67%
First term ÷ second term
Step by step
- Start with the ratio 12 : 18.
- Find the greatest common factor (GCF) of 12, 18. It is 6.
- Divide every term by 6: 12 ÷ 6, 18 ÷ 6 gives 2 : 3.
- Check: 12 : 18 and 2 : 3 describe the same comparison, because each term was scaled by the same amount.
Equivalent ratios
| Scale | A | B |
|---|---|---|
| Simplest | 2 | 3 |
| ×2 | 4 | 6 |
| ×3 | 6 | 9 |
| ×4 | 8 | 12 |
| ×5 | 10 | 15 |
| ×10 | 20 | 30 |
Multiply every term by the same number to get a ratio that means the same thing.
Part to whole
| Part | Fraction of total | Percent |
|---|---|---|
| Part 1 | 2/5 | 40% |
| Part 2 | 3/5 | 60% |
Each part divided by the total of all parts, 5.
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Table of Contents
- What Is a Ratio Calculator?
- How to Use the Ratio Calculator
- What Is a Ratio?
- How to Simplify a Ratio
- How to Solve a Ratio Problem (a : b = c : d)
- How to Split an Amount in a Ratio
- How to Compare Two Ratios
- Ratio to Fraction, Decimal and Percent
- Common Ratios You See Every Day
- Ratio vs Proportion
- Features of Our Ratio Calculator
- Why Choose This Ratio Calculator Over Others?
- Who Should Use This Calculator?
- Common Ratio Mistakes to Avoid
- How We Make Sure Every Answer Is Right
- What Users Say
- Frequently Asked Questions
- Start Solving
What Is a Ratio Calculator?
A ratio calculator is a free online tool that does the math behind a ratio for you. You type the numbers you are comparing, pick what you need, and the calculator returns the answer along with the working.
Most ratio calculators only reduce a ratio to its simplest form. Ours handles the five jobs people actually bring to a ratio:
- Simplify a ratio with 2 to 6 terms, even when the terms are decimals, fractions, mixed numbers or percents.
- Solve a ratio problem in the form a : b = c : d, or check whether two ratios are equal.
- Scale a ratio by a factor, or make one term hit a target value.
- Split a total, such as rent, profit or time, in a given ratio.
- Compare two ratios to see which one is larger and by how much.
Every answer also shows the ratio as a fraction, a decimal and a percent, plus the 1 : n and n : 1 forms, a part to whole table and a proportional bar. So one tool covers simplifying, converting and word problems in a single place.
How to Use the Ratio Calculator
Pick a tab at the top of the calculator, fill in the boxes and press Calculate. The page then scrolls to your answer. Here is what each tab does.
Simplify a ratio
- Open the Simplify tab.
- Type each part of the ratio in its own box, such as 12 and 18. Press Add term for ratios like 2 : 3 : 5.
- Press Calculate. You get the simplest form, here 2 : 3, plus the fraction, decimal, percent and part to whole shares.
Solve a : b = c : d
- Open the Solve tab.
- Fill three of the four boxes and leave the missing one empty.
- Press Calculate to find the missing term. Fill all four boxes instead to check whether the two ratios are equal.
Scale a ratio
- Open the Scale tab and type the ratio.
- Choose Multiply by, Divide by or Make one term equal.
- Enter the number and press Calculate. For example, 3 : 4 with term B set to 20 becomes 15 : 20.
Split a total in a ratio
- Open the Split a total tab and type the total, such as 2400.
- Add a unit or currency symbol if you like, such as $ or kg, then type the ratio.
- Choose exact values, cents or whole units. The cents and whole unit options always add up to the exact total.
Compare two ratios
- Open the Compare tab.
- Type the first ratio on top and the second ratio below.
- Press Calculate to see whether they are equal, which one is larger and the percent difference.
Each answer has three buttons. Copy answer copies the result, Copy steps copies the full working for homework or notes, and Share link copies a link that opens the calculator with your numbers already filled in.
What Is a Ratio?
A ratio compares two or more quantities by division. It tells you how much of one thing there is for each amount of another. If a class has 3 boys for every 2 girls, the ratio of boys to girls is 3 to 2.
You can write the same ratio in three ways:
| Form | Example | How you read it |
|---|---|---|
| With a colon | 3 : 2 | 3 to 2 |
| With the word to | 3 to 2 | 3 to 2 |
| As a fraction | 3/2 | 3 over 2 |
Each number in a ratio is called a term. In a two term ratio a : b, the first term is the antecedent and the second is the consequent. Order matters: 3 : 2 (boys to girls) is not the same as 2 : 3 (girls to boys).
Part to part and part to whole ratios
A part to part ratio compares one group with another group, like 3 boys to 2 girls. A part to whole ratio compares one group with the total, like 3 boys out of 5 students. You turn a part to part ratio into part to whole by adding the terms to get the whole.
So 3 : 2 means boys make up 3/5 of the class, or 60%, and girls make up 2/5, or 40%. The calculator builds this part to whole table for you every time you simplify.
Ratio vs rate
A ratio usually compares amounts in the same unit, such as cups of flour to cups of sugar. A rate compares amounts in different units, such as 150 miles in 3 hours. A rate with 1 in the second term is a unit rate, here 50 miles per hour. The OpenStax Prealgebra chapter on ratios and rate explains both ideas with extra practice problems.
How to Simplify a Ratio
A ratio is in simplest form when its terms are whole numbers that share no common factor other than 1. To get there, divide every term by the greatest common factor (GCF).
- List the terms, for example 36 : 48.
- Find the GCF of 36 and 48. It is 12.
- Divide each term by 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4.
- Write the result: 36 : 48 = 3 : 4.
Ratios with decimals or fractions
First turn the terms into whole numbers. Multiply every term by the same number, then simplify as usual. Multiplying every term by the same amount never changes the ratio.
- Decimals: 1.5 : 2 becomes 15 : 20 after multiplying by 10, then 3 : 4 after dividing by 5.
- Fractions: 1/2 : 3/4 becomes 2 : 3 after multiplying both terms by 4, the common denominator.
- Three decimal terms: 2.5 : 1.25 : 0.75 becomes 10 : 5 : 3 after multiplying by 4. These terms share no other factor, so 10 : 5 : 3 is the simplest form.
Ratios with three or more terms
The method stays the same. Find one GCF that divides every term. For 15 : 25 : 40, the GCF is 5, so the ratio simplifies to 3 : 5 : 8.
The 1 : n and n : 1 forms
Sometimes a whole number ratio is not the most useful form. Map scales and concrete mixes often use 1 : n, where you divide every term by the first one. For 2 : 3, that gives 1 : 1.5. The n : 1 form divides by the last term, so 2 : 3 becomes 0.6667 : 1. The calculator shows both forms with every simplified ratio.
How to Solve a Ratio Problem (a : b = c : d)
When two ratios are equal, they form a proportion. If you know three of the four terms, you can find the fourth with cross multiplication, because a × d always equals b × c in a true proportion.
Take a map with a scale of 1 : 50, where 1 inch stands for 50 miles. How far is 3.5 inches on the map?
- Set up the proportion: 1 : 50 = 3.5 : x.
- Cross multiply: 1 × x = 50 × 3.5.
- Solve: x = 175, so 3.5 inches stands for 175 miles.
The same method finds a missing screen size. A 16 : 9 video that is 1280 pixels wide is 1280 × 9 ÷ 16 = 720 pixels tall. For inverse proportions, units in word problems, ratio tables and graphs, use our full proportion calculator.
How to Split an Amount in a Ratio
Splitting, or sharing, an amount in a ratio is one of the most common real world ratio problems. You use it to divide rent by room size, profit by investment or time by priority.
- Add the terms of the ratio to find the total number of parts.
- Divide the total amount by the number of parts to find the value of one part.
- Multiply each term by the value of one part.
Say two roommates split $2,400 rent in the ratio 2 : 3. That makes 2 + 3 = 5 parts, so one part is $2,400 ÷ 5 = $480. The first roommate pays 2 × $480 = $960 and the second pays 3 × $480 = $1,440. Check: $960 + $1,440 = $2,400.
What happens when the split does not divide evenly?
Split $100 three ways and each share is $33.333…, which you cannot pay in real money. Rounding every share to $33.33 loses a cent. Our calculator uses the largest remainder method instead: it rounds every share down, then hands the leftover cents, one at a time, to the shares that lost the most. You get $33.34, $33.33 and $33.33, which adds up to exactly $100.00.
How to Compare Two Ratios
To compare a : b with c : d, cross multiply. Compare a × d with b × c. If the products match, the ratios are equal. If a × d is larger, the first ratio is larger.
Which drink has more juice: 3 parts juice to 5 parts water, or 5 parts juice to 8 parts water? Cross multiply: 3 × 8 = 24 and 5 × 5 = 25. Since 24 is less than 25, the second mix is stronger. As decimals, 3 ÷ 5 = 0.6 and 5 ÷ 8 = 0.625.
Equal ratios work the same way. A team that wins 18 of 24 games and a team that wins 15 of 20 both have a 3 : 4 win ratio, because 18 × 20 = 24 × 15 = 360.
Ratio to Fraction, Decimal and Percent
A two term ratio a : b converts to the fraction a/b and the decimal a ÷ b. For the part to whole share, divide each term by the total of all terms. This table covers the ratios people look up most often.
| Ratio | Fraction (a/b) | Decimal | First term as a share of the whole |
|---|---|---|---|
| 1 : 1 | 1/1 | 1 | 1/2 = 50% |
| 1 : 2 | 1/2 | 0.5 | 1/3 ≈ 33.33% |
| 1 : 3 | 1/3 | 0.3333 | 1/4 = 25% |
| 1 : 4 | 1/4 | 0.25 | 1/5 = 20% |
| 2 : 3 | 2/3 | 0.6667 | 2/5 = 40% |
| 3 : 2 | 3/2 | 1.5 | 3/5 = 60% |
| 3 : 4 | 3/4 | 0.75 | 3/7 ≈ 42.86% |
| 3 : 5 | 3/5 | 0.6 | 3/8 = 37.5% |
| 4 : 3 | 4/3 | 1.3333 | 4/7 ≈ 57.14% |
| 16 : 9 | 16/9 | 1.7778 | 16/25 = 64% |
Notice the difference between the last two columns. The ratio 1 : 3 as a fraction is 1/3, but the first part is only 1/4 of the whole, because the whole has 1 + 3 = 4 parts. Mixing up these two ideas is one of the most common ratio mistakes.
Common Ratios You See Every Day
| Ratio | Where you see it |
|---|---|
| 16 : 9 | Widescreen TVs, monitors and YouTube videos, such as 1920 × 1080 pixels |
| 4 : 3 | Older TVs, iPad screens and many digital photos |
| 3 : 2 | DSLR camera sensors and 6 × 4 inch photo prints |
| 1 : 1 | Square social media posts and equal mixes |
| 1 : 2 : 3 | A common concrete mix of cement, sand and gravel |
| 1 : 2 | Rice to water for white rice cooked on the stove |
| 1 : 16 | Coffee to water for a typical pour over brew |
| 1.618 : 1 | The golden ratio used in design and photography |
Type any of these into the Simplify tab to see the fraction, percent and part to whole shares, or use the Scale tab to resize them.
Ratio vs Proportion
A ratio compares quantities, such as 2 : 3. A proportion is an equation that says two ratios are equal, such as 2 : 3 = 14 : 21. In short, a ratio is one comparison and a proportion links two of them.
That is why the Solve tab here and our proportion calculator use the same cross multiplication rule. Use this ratio calculator for simplifying, scaling, splitting and comparing. Use the proportion calculator when you need inverse proportions, units, ratio tables and graphs.
Features of Our Ratio Calculator
- Five tools in one: simplify, solve, scale, split and compare without switching sites.
- Up to 6 terms: work with ratios like 1 : 2 : 3 or 3 : 5 : 7 : 9.
- Any number format: whole numbers, decimals, fractions, mixed numbers, percents and decimal commas.
- Exact answers: results like 14/3 stay exact, with the decimal shown next to them.
- Fair rounding for splits: cents and whole units always add up to the total.
- Named parts: label the parts, such as Ana and Ben, and see names in the answer.
- 1 : n and n : 1 forms with every simplified ratio.
- Fraction, decimal and percent conversion, plus a part to whole table.
- Equivalent ratio table with ×2, ×3, ×4, ×5 and ×10 rows.
- Proportional bar chart so you can see the split at a glance.
- Step by step working that you can copy in one tap.
- Shareable links that reopen the calculator with your numbers.
- Recent calculations saved privately in your own browser.
- Accessible design with keyboard support, screen reader labels and clear focus states.
Why Choose This Ratio Calculator Over Others?
We studied the ratio calculators that rank on the first page of Google and listed what each one leaves out. Then we built those gaps into one tool.
| What you need | Typical ratio calculator | Our ratio calculator |
|---|---|---|
| Simplify ratios with decimals and fractions | Often whole numbers only | Yes, exact |
| Ratios with more than 3 terms | Rare | Up to 6 terms |
| Split a total in a ratio | Usually a separate tool | Built in |
| Rounded shares that still add up | Not offered | Largest remainder rounding |
| Compare ratios with a percent difference | Equal or not only | Yes |
| 1 : n form, part to whole and percents | One or two of these | All of them |
| Full steps you can copy | Short or missing | Every answer |
| Share a prefilled link | Rare | Yes |
On top of that, the page loads fast, works the same on phones and laptops, and never asks you to sign up.
Who Should Use This Calculator?
- Students in grades 6 to 8 learning ratios and rates, plus anyone reviewing for the SAT, ACT or GED.
- Parents checking homework and teaching the steps behind the answer.
- Teachers and tutors who want worked examples and shareable links for class.
- Home cooks and bakers scaling recipes and mixing ingredients by ratio.
- Roommates and business partners splitting rent, bills or profit fairly.
- Designers, photographers and video creators working with aspect ratios like 16 : 9 and 4 : 3.
- Builders and DIYers mixing concrete, mortar, paint or fertilizer by parts.
Common Ratio Mistakes to Avoid
- Swapping the order. Boys to girls is not girls to boys. Keep the terms in the order the question names them.
- Confusing part to part with part to whole. In a 1 : 3 ratio, the first part is 1/4 of the total, not 1/3.
- Dividing by a common factor that is not the greatest one. 24 : 36 divided by 2 gives 12 : 18, which still is not simplest. Divide by 12 to reach 2 : 3.
- Mixing units. Compare 30 minutes to 2 hours as 30 : 120, not 30 : 2.
- Rounding too early. Round only the final answer, or your shares may no longer add up to the total.
How We Make Sure Every Answer Is Right
A calculator should earn your trust, so we show our work and publish our methods.
- Exact arithmetic. The calculator works with exact fractions instead of rounded floating point numbers, so 1/3 stays 1/3 until the final display.
- Standard definitions. Our terms and methods follow the Common Core standards for ratios and proportional relationships.
- Tested before launch. We checked every mode against hand worked problems, including decimals, fractions, zeros and splits that do not divide evenly.
- Answers that check themselves. Each solution ends with a check step, such as reducing both ratios or adding the shares back to the total.
- Private by design. Everything runs in your browser. We never see or store the numbers you type.
Read How Our Calculators Work and our Editorial Policy for the full details, or learn who builds Proportion Calculator.
What Users Say
This ratio calculator is new, and we would rather show real feedback than invent it. So, instead of fake reviews, we are asking you directly.
Did it help with homework, a recipe or a rent split? Did anything confuse you? Tell us at proportioncalculator.marketing@gmail.com. With your permission, we will feature genuine comments from our first users right here.
Frequently Asked Questions
How do you calculate a ratio?
Write the two amounts in the order the question asks, with a colon between them, then simplify. For 24 boys and 16 girls, the ratio of boys to girls is 24 : 16. Divide both terms by their greatest common factor, 8, to get 3 : 2.
How do you simplify a ratio?
Divide every term by the greatest common factor. For 36 : 48 the GCF is 12, so 36 : 48 simplifies to 3 : 4. If the terms are decimals or fractions, multiply every term by the same number first to make them whole.
What does a ratio of 3 to 5 mean?
It means that for every 3 units of the first quantity, there are 5 units of the second. As a fraction it is 3/5, or 0.6. As part of a whole, the first quantity is 3 out of 8 parts, or 37.5%.
How do you simplify a ratio with decimals?
Multiply every term by 10, 100 or 1000 until all the terms are whole numbers, then divide by the GCF. For example, 0.4 : 1.2 becomes 4 : 12 after multiplying by 10, then 1 : 3 after dividing by 4.
How do you split an amount in a ratio?
Add the ratio terms to get the number of parts, divide the total by that number, then multiply each term by the result. To split 350 in the ratio 3 : 4, there are 7 parts worth 50 each, so the shares are 150 and 200.
How do you convert a ratio to a percentage?
For a part to whole percent, divide one term by the sum of all terms and multiply by 100. In 3 : 2, the first part is 3 ÷ 5 × 100 = 60%. To express the ratio itself as a percent, divide the first term by the second: 3 ÷ 2 × 100 = 150%.
How do you tell if two ratios form a proportion?
Cross multiply. Two ratios a : b and c : d form a proportion when a × d equals b × c. For 5 : 15 and 3 : 9, both products are 45, so the ratios are equal and form a proportion.
What is the difference between a ratio and a rate?
A ratio compares quantities in the same unit, like 2 cups of flour to 1 cup of sugar. A rate compares quantities in different units, like 150 miles in 3 hours. A rate per one unit, such as 50 miles per hour, is called a unit rate.
What is a part to part ratio and a part to whole ratio?
A part to part ratio compares two groups, such as 3 boys to 2 girls. A part to whole ratio compares one group with the total, such as 3 boys out of 5 students. Add the terms of a part to part ratio to find the whole.
Does the order of numbers in a ratio matter?
Yes. The ratio 3 : 2 says the first quantity is larger, while 2 : 3 says it is smaller. Always write the terms in the same order as the words in the question, such as boys to girls.
Can a ratio have more than two numbers?
Yes. A ratio can compare three or more quantities, like a 1 : 2 : 3 concrete mix of cement, sand and gravel. You simplify, scale and split it the same way. This calculator accepts up to 6 terms.
What is a 1 : n ratio?
A 1 : n ratio, also called a unit ratio, rewrites a ratio so the first term is 1. Divide every term by the first term. For example, 4 : 10 becomes 1 : 2.5. Map scales often use this form, such as 1 : 50,000.
How do you scale a ratio up or down?
Multiply or divide every term by the same number. To scale 3 : 2 up by 4, multiply both terms to get 12 : 8. To make a specific term reach a target, divide the target by that term to find the scale factor first.
Can a ratio have a zero in it?
A term can be zero, such as 0 : 5, which simplifies to 0 : 1 and means none of the first quantity. However, a ratio written as a fraction cannot have zero as the second term, because you cannot divide by zero.
Is this ratio calculator free and private?
Yes. The ratio calculator is free with no signup and no usage limits. It runs entirely in your browser, so the numbers you type never leave your device.
Start Solving
Ratios show up in recipes, rent, screens, sports and school, and now you have one tool for all of them. Scroll back up, pick a tab and type your numbers. Then try an example and watch the bar chart and steps update. For two equal ratios with a missing value, the proportion calculator is one click away.
Go deeper with our guides
Ratios are the building blocks of proportions. These guides take the next step, with worked examples and practice problems.