Ratio Calculator

Use this Ratio Calculator to simplify ratios, solve proportions, generate equivalent ratios, build ratio tables, convert scale ratios, and calculate screen or aspect ratios. Enter your numbers, choose the calculator mode that matches your problem, and get clear results for simplified ratios, fraction and decimal forms, percentage relationships, equivalent ratios, scaling, and aspect ratio calculations.

This page also works as a Proportion Calculator. A ratio compares two quantities, such as 3:4, while a proportion states that two ratios are equal, such as 3/4 = 6/8. Use the Ratio Calculator for simplifying and comparing values, the Proportion Solver for finding a missing value, or switch to the equivalent-ratio, scale-ratio, and screen-ratio tools for more advanced ratio calculations.

How to Use the Ratio Calculator

Choose the calculator mode that matches the problem you are trying to solve. The main Ratio Calculator simplifies two values into their lowest-term ratio. The Proportion Solver finds one missing value in an equation such as A/B = C/D. Equivalent Ratios creates a ratio table. Scale Ratio keeps the same width-to-height proportion while changing size. Screen Ratio simplifies a pixel resolution or image size into an aspect ratio.

For a basic ratio, enter the first number and second number, then click Calculate. If you enter 12 and 18, the calculator reduces 12:18 to 2:3 because both values can be divided by 6. The result also shows the fraction form, decimal quotient, percentage relationship, and an equivalent ratio.

If you need to solve a proportion, switch to Proportion Solver. Enter three known numbers and leave exactly one field blank. For example, enter 3/4 = 6/x by using A = 3, B = 4, C = 6, and leaving D blank. The calculator uses cross multiplication to solve x = 8 and then checks that both ratios are equivalent.

When your ratio problem involves fractions rather than whole or decimal numbers, the Fraction Calculator is useful for simplifying or converting the individual fractions before comparing them as a ratio.

What Is a Ratio?

A ratio compares two quantities. If a class has 12 students wearing blue shirts and 18 students wearing other colors, the ratio of blue shirts to other shirts is 12:18. That ratio can be simplified to 2:3.

Ratios can be written in several equivalent forms. The ratio 2 to 3 can be written as 2:3, 2 to 3, or 2/3. The notation changes, but the comparison is the same. Order matters. A ratio of 2:3 is not the same as 3:2 because the quantities being compared have been reversed.

A ratio does not have to describe pieces of the same type. It can compare miles to gallons, dollars to hours, ingredients in a recipe, wins to losses, width to height, or almost any two measurable quantities. A rate is a special type of ratio that compares quantities with different units, such as 100 kilometres per hour.

What Is a Proportion?

A proportion is an equation stating that two ratios are equal. For example, 2/3 = 4/6 is a proportion because both fractions represent the same numerical relationship.

Proportions are useful when one value is unknown. If 3 notebooks cost $12 and you want to know the equivalent cost of 5 notebooks at the same rate, you can set up a proportion and solve for the missing amount.

A common proportion format is A/B = C/D. Cross multiplication gives A × D = B × C. When one of the four values is unknown, that equation can usually be rearranged to solve it directly.

Khan Academy describes ratios as comparisons of quantities and proportions as equalities between two ratios, which is the same distinction used by this calculator. Their ratios and rates learning unit is a useful additional resource for studying the topic.

Ratio vs. Proportion: What Is the Difference?

A ratio compares two values. A proportion compares two ratios and says that they are equal. That is the simplest distinction between a ratio calculator and a proportion calculator.

Because ratios and proportions are closely related, combining both tools on one page makes sense. You can simplify the original ratio first, then use the same relationship in a proportion or an equivalent-ratio table.

How to Calculate a Ratio

To calculate a ratio between two numbers, place the first quantity before the colon and the second quantity after it. Then reduce both values by their greatest common factor whenever possible.

Example: Calculate the Ratio of 20 to 30

Start with 20:30. The greatest common factor of 20 and 30 is 10. Divide each side by 10:

The simplified ratio is 2:3. This means that for every 2 units of the first quantity, there are 3 units of the second quantity.

You can use the Simple Math Calculator if you want to check multiplication and division while working through a ratio problem manually.

How to Find the Ratio Between Two Numbers

Suppose you have 24 red objects and 36 blue objects. The ratio of red to blue is 24:36. Both numbers are divisible by 12, so the ratio simplifies to 2:3. If you reverse the comparison and ask for blue to red, the ratio becomes 36:24, which simplifies to 3:2.

This is why wording matters. “Ratio of A to B” means A:B. “Ratio of B to A” means B:A. The order should match the order of the quantities in the question.

Ratio Formula

There is no single complicated ratio formula. A ratio A:B represents the comparison A divided by B. The quotient A/B tells you how many units of B correspond to one unit of A when interpreted as a decimal relationship.

For example, a 3:4 ratio can be written as 3/4. Its decimal value is 0.75. Expressed as a percentage, 3 is 75% of 4. That does not mean a 3:4 part-to-part ratio contains 75% of the total; part-to-total percentage is a different calculation.

How to Simplify Ratios

Simplifying a ratio means reducing both values by the same factor until they cannot be reduced further using whole-number division. The method is similar to simplifying a fraction.

• Write the ratio in the correct order.
• Find the greatest common factor of both numbers.
• Divide both sides by that factor.
• Check that the new ratio has the same quotient as the original.

For 45:60, the greatest common factor is 15. Dividing gives 3:4. The original quotient 45/60 equals 0.75, and the simplified quotient 3/4 also equals 0.75.

Ratios With Decimals

Ratios can contain decimal values. To simplify a decimal ratio, multiply both quantities by a power of 10 large enough to remove the decimal places, then simplify the resulting whole-number ratio.

For example, 1.5:2.5 can be multiplied by 10 to become 15:25. Divide both by 5 and the simplified ratio is 3:5. The calculator handles this conversion automatically for common decimal inputs.

A search such as 1/1.5 can also be understood as a ratio comparison. Converting 1:1.5 to whole numbers gives 10:15, which simplifies to 2:3.

How to Solve Proportions

The standard way to solve a proportion is cross multiplication. If A/B = C/D, multiply A by D and B by C. Equivalent ratios produce equal cross products.

Example: 3/4 = 6/x

Cross multiply 3 × x = 4 × 6. That gives 3x = 24. Divide both sides by 3 and x = 8. The completed proportion is 3/4 = 6/8.

You can verify the answer by dividing both sides. 3 ÷ 4 = 0.75, and 6 ÷ 8 = 0.75. Because the quotients match, the proportion is valid.

Proportion Formula

The formula used depends on which value is missing:

• If A is missing: A = (B × C) ÷ D
• If B is missing: B = (A × D) ÷ C
• If C is missing: C = (A × D) ÷ B
• If D is missing: D = (B × C) ÷ A

The Proportion Solver automatically detects the blank position and applies the correct form.

Solving Proportions Step by Step

When solving proportions by hand, first make sure the two ratios compare corresponding quantities in the same order. If the left ratio is miles per gallon, the right ratio should also be miles per gallon rather than gallons per mile.

Next, cross multiply. Then isolate the unknown by dividing. Finally, substitute the answer into the original proportion and check whether the two ratios are equal.

That last check is useful because many proportion errors come from reversing one ratio or dividing by the wrong number rather than from difficult arithmetic.

Equivalent Ratios

Equivalent ratios describe the same relationship using different numbers. The ratios 2:3, 4:6, 6:9, and 10:15 are all equivalent because each side was multiplied by the same factor.

To create an equivalent ratio, multiply both sides of the original ratio by the same nonzero number. You can also divide both sides by the same nonzero number when both values divide cleanly.

The Equivalent Ratios mode generates this kind of table automatically. It first simplifies the base ratio and then creates additional rows by multiplying both values by the same number.

Ratio Table

A ratio table organizes equivalent ratios into rows or columns. Ratio tables are common in school math because they make proportional relationships easy to see.

Suppose 2 tickets cost $6. If the price remains proportional, 4 tickets cost $12, 6 tickets cost $18, and 8 tickets cost $24. A ratio table shows that the same multiplier is being applied to both quantities.

Ratio tables are useful for recipes, prices, unit conversions, map scales, manufacturing mixes, fuel rates, and many other proportional situations.

Common Ratios: 2:1, 3:2, 4:3, 4:5, and 5:4

Some ratio searches involve a specific relationship rather than a calculation method. A 2:1 ratio means the first quantity is twice the second. A 3:2 ratio means there are 3 units of the first quantity for every 2 units of the second. A 4:3 ratio means 4 units correspond to 3 units.

A 4:5 ratio means the first value is four-fifths of the second, or 80% as large. A 5:4 ratio means the first value is 1.25 times the second. The calculator can simplify larger equivalent versions of all these ratios.

Ratio to Fraction

A two-part ratio A:B can be written as the fraction A/B. For example, 3:4 becomes 3/4 and 5:2 becomes 5/2. This fraction compares the first quantity directly with the second quantity.

Be careful when converting a part-to-part ratio into a fraction of the total. If the ratio of red to blue items is 3:4, there are 7 total parts. Red represents 3/7 of the total and blue represents 4/7. The fraction 3/4 compares red to blue, while 3/7 compares red to all items.

For more complex fraction operations, the Fraction Calculator can add, subtract, multiply, divide, simplify, and convert fractions.

Ratio to Percentage

To express the first side of a ratio as a percentage of the second side, divide A by B and multiply by 100. For 3:4, 3 ÷ 4 = 0.75, and 0.75 × 100 = 75%. Therefore the first value is 75% of the second value.

This is different from asking what percentage the first part represents of the combined total. For a 3:4 part-to-part ratio, the total is 7 parts, so the first part represents 3/7 of the whole, or about 42.86%.

When you need more percentage calculations, such as percent change or increasing a value by a percentage, use the Percentage Calculator.

Percent Proportion

A percent proportion is commonly written as part/whole = percent/100. It connects ratios, fractions, proportions, and percentages in one equation.

For example, if 18 out of 24 questions are correct, set up 18/24 = x/100. Cross multiplication gives 24x = 1800, so x = 75. The score is 75%.

Scale Ratio Conversion

A scale ratio keeps the same proportions while making dimensions larger or smaller. If a rectangle is 4 units wide and 3 units high, its width-to-height ratio is 4:3. Scaling the width to 12 requires multiplying both dimensions by 3, giving 12 by 9.

The Scale Ratio mode lets you enter the original width and height, then choose a new width, new height, or scale factor. The missing scaled dimension is calculated automatically.

Scaling is used in maps, drawings, blueprints, photographs, models, print layouts, and digital graphics. The important rule is that both dimensions must change by the same scale factor if the original proportions are to remain unchanged.

Screen Ratio Calculator

Screen ratio, often called aspect ratio, compares width with height. A 1920 × 1080 display simplifies to 16:9 because both numbers can be divided by 120. A 1024 × 768 display simplifies to 4:3.

The Screen Ratio mode accepts width and height in pixels and reduces them using their greatest common factor. It also identifies common formats such as 1:1, 4:3, 3:2, 16:10, 16:9, 21:9, and 32:9 when the dimensions closely match one of those standards.

Aspect ratio is independent of absolute resolution. 1920×1080, 1280×720, and 3840×2160 are all 16:9 even though they contain very different numbers of pixels.

How to Calculate Aspect Ratio

To calculate an aspect ratio, divide the width and height by their greatest common divisor. For 1920 and 1080, the greatest common divisor is 120. Dividing produces 16 and 9, so the aspect ratio is 16:9.

If the dimensions do not simplify to a familiar whole-number ratio, they may represent a custom aspect ratio. The decimal width-to-height quotient can still be useful for comparing shapes.

Ratios in Recipes and Mixing

Recipes are one of the easiest real-world examples of ratios and proportions. If a mix uses 2 cups of one ingredient for every 3 cups of another, the ingredient ratio is 2:3.

If you double the recipe, both quantities must double. The equivalent ratio becomes 4:6. If you triple it, the ratio becomes 6:9. The simplified relationship remains 2:3.

Proportions help when the scale factor is not obvious. If a recipe uses 3 cups of flour for 8 servings and you need 20 servings, you can set up 3/8 = x/20 and solve for the new amount of flour.

Ratios in Maps and Scale Drawings

Maps and scale drawings use ratios to represent large real distances on a smaller surface. A scale of 1:50,000 means one unit on the map corresponds to 50,000 of the same units in the real world.

If one centimetre on a map represents 50,000 centimetres in reality, that equals 500 metres. A proportion can convert any measured map length into its real-world equivalent as long as the units are handled consistently.

Ratios in Finance, Shopping, and Unit Prices

Unit prices are ratios. If 6 items cost $18, the cost-to-item ratio is $18:6, and dividing gives $3 per item. Comparing unit ratios is often more useful than comparing package prices directly.

Ratios also appear in debt-to-income measurements, investment allocations, profit margins, staffing levels, and many business performance metrics. The same mathematical idea applies: one quantity is being compared with another.

Ratios in School Math

Ratios and proportions are commonly introduced before algebra because they teach students how quantities change together. They connect fractions, decimals, percentages, rates, scale drawings, and equations.

Students often use ratio tables before moving to cross multiplication. Both methods are valid. Ratio tables make the scaling relationship visible, while algebraic proportions are faster for many problems with one unknown.

If you are using ratios to work through class assignments and want to estimate the effect on your course result, the Grade Calculator can calculate weighted grades, test percentages, final-exam requirements, and GPA-related results.

How to Check Whether Two Ratios Are Equivalent

There are two easy methods. First, simplify both ratios. If both reduce to the same lowest-term ratio, they are equivalent. Second, use cross multiplication.

For A:B and C:D, compare A × D with B × C. If the two products are equal and the denominators are valid, the ratios are equivalent.

For 5:2 and 15:6, 5 × 6 = 30 and 2 × 15 = 30, so the ratios are equivalent. Both also simplify to 5:2.

How to Work Out a Ratio of Two Numbers

When people ask how to work out a ratio of two numbers, they usually want the simplified whole-number relationship. Write the numbers in the required order, remove decimals if necessary by multiplying both by the same power of 10, then divide by the greatest common factor.

For 7.5 and 12.5, start with 7.5:12.5. Multiply both by 10 to get 75:125. Divide both by 25. The final ratio is 3:5.

Common Ratio Mistakes

• Reversing the order of the quantities.
• Dividing only one side when simplifying.
• Confusing a part-to-part ratio with a part-to-whole fraction.
• Using different units without converting them first.
• Cross multiplying values that do not represent corresponding quantities.
• Allowing a denominator in a proportion to equal zero.
• Changing width and height by different scale factors when preserving aspect ratio.

Units deserve special attention. A ratio of 2 metres to 50 centimetres should not be simplified as 2:50 until both quantities use the same unit. Convert 2 metres to 200 centimetres first. Then 200:50 simplifies to 4:1.

Why Use a Ratio Calculator?

A ratio calculator is useful because ratio problems can involve several different tasks. Sometimes you only need to simplify two numbers. Other times you need to solve a proportion, create equivalent ratios, convert a scale, or calculate an aspect ratio.

• Simplify ratios into lowest terms.
• Calculate a ratio between two numbers.
• Convert a ratio to a fraction or decimal.
• Express the first value as a percentage of the second.
• Solve proportions with one unknown.
• Generate equivalent ratios.
• Create a ratio table.
• Scale dimensions proportionally.
• Calculate screen and image aspect ratios.
• Check whether two ratios are equivalent.

For calculations involving powers, roots, logarithms, or other advanced operations alongside ratios, the Scientific Calculator provides a broader set of mathematical functions.

Part-to-Part Ratio vs. Part-to-Whole Ratio

One of the most common sources of confusion is the difference between a part-to-part ratio and a part-to-whole ratio. Suppose a basket contains 3 red apples and 5 green apples. The ratio of red apples to green apples is 3:5. That compares one part with another part.

The total number of apples is 8, so the ratio of red apples to all apples is 3:8. The ratio of green apples to all apples is 5:8. These are part-to-whole ratios. They answer a different question from the original 3:5 comparison.

This distinction also matters when converting ratios to percentages. In a 3:5 part-to-part ratio, the first quantity is 60% as large as the second because 3 ÷ 5 = 0.6. But the first quantity represents 37.5% of the combined total because 3 ÷ 8 = 0.375.

Ratio Finder: Finding a Missing Ratio Value

A ratio finder often refers to calculating the missing number that keeps two ratios equivalent. This is really a proportion problem. If 4:7 is equivalent to 12:x, set up 4/7 = 12/x and solve for x.

Cross multiplication gives 4x = 84, so x = 21. The equivalent ratios are therefore 4:7 and 12:21. You can check the relationship by noticing that 4 was multiplied by 3 to become 12, so 7 must also be multiplied by 3 to become 21.

The Proportion Solver mode is useful for this type of ratio finder because you can leave any one of the four positions blank. It does not matter whether the missing number appears in the first ratio or second ratio.

Unit Ratios and Unit Rates

A unit ratio or unit rate rewrites a comparison so one side equals 1. For example, 300 kilometres in 4 hours can be written as the rate 300:4. Dividing both sides by 4 gives 75:1, meaning an average of 75 kilometres per hour.

Unit rates are useful for comparing prices, speeds, wages, fuel use, and production. If one package costs $18 for 6 items and another costs $20 for 8 items, the unit prices are $3 per item and $2.50 per item. The second package has the lower cost per unit even though its total price is higher.

When the units are different, a rate may be more descriptive than a plain ratio. Miles per gallon, dollars per hour, kilometres per litre, and dollars per kilogram are all ratios with units attached.

Compound Ratios

A compound ratio combines relationships involving three or more quantities. For example, if A:B = 2:3 and B:C = 4:5, the two ratios must first be scaled so the shared B value matches.

Multiply 2:3 by 4 to get A:B = 8:12. Multiply 4:5 by 3 to get B:C = 12:15. The combined ratio is A:B:C = 8:12:15.

The main calculator on this page focuses on two-number ratios because that is the most common ratio-calculator search. Compound ratios can still be worked out by matching the shared quantity and then combining the resulting values.

Ratios in Geometry

Ratios are used throughout geometry. Similar figures have corresponding side lengths in the same ratio. If one triangle has sides that are twice as long as another triangle, the linear scale factor is 2:1.

Area does not scale by the same factor as length. If all side lengths are doubled, area increases by a factor of 4 because 2² = 4. Volume increases by a factor of 8 because 2³ = 8. The Scale Ratio mode displays the area factor so you can see this relationship when resizing width and height.

This is important when resizing plans, images, rectangles, signs, and other two-dimensional objects. A 50% increase in both width and height produces an area that is 2.25 times the original because 1.5² = 2.25.

Ratio Math With Negative Numbers

In many everyday ratio problems, quantities are positive. However, mathematical ratios can include negative values. A ratio of -6:9 simplifies to -2:3. A ratio of 6:-9 can also be written -2:3 by moving the negative sign to the first value.

Negative ratios are less common in recipes, scale drawings, and physical measurements, but they can appear in algebra, coordinate geometry, rates of change, and financial comparisons. The calculator can simplify negative numeric inputs, although interpretation depends on the problem.

How to Use Ratios for Scaling Up and Down

Scaling up means multiplying all related quantities by the same factor. Scaling down means dividing them by the same factor. If a recipe uses a 2:5 ratio and you multiply both quantities by 4, the new ratio is 8:20. The quantities are larger, but the proportional relationship is unchanged.

To scale a ratio to a specific first value, divide the target first value by the original first value to find the multiplier. Then multiply the second value by that same multiplier. If 3:7 must be scaled so the first value becomes 15, the scale factor is 15 ÷ 3 = 5. The second value becomes 7 × 5 = 35, giving 15:35.

This same logic is what the Scale Ratio mode uses for width and height. It finds one scale factor and applies it consistently so the original proportion is preserved.

Ratios, Fractions, Decimals, and Percentages

Ratios, fractions, decimals, and percentages are different ways to describe numerical relationships. A ratio of 1:4 can be written as the fraction 1/4. Dividing gives the decimal 0.25, which becomes 25% when multiplied by 100.

However, context still matters. In a part-to-part ratio of 1:4, the first part is 25% as large as the second part, but it represents 1 out of 5 total parts, or 20% of the combined whole. Always identify what the denominator represents before interpreting a percentage.

Understanding these connections makes ratio math much easier because the same relationship can be viewed in whichever form best fits the problem.

Ratio Calculator Frequently Asked Questions

Final Thoughts

Ratios compare quantities, while proportions show that two ratios are equal. Once that distinction is clear, many ratio and proportion problems become much easier. Simplifying ratios uses common factors, equivalent ratios use the same multiplier on both sides, and solving proportions uses cross multiplication.

Use the main Ratio Calculator for basic ratio math, Proportion Solver for missing values, Equivalent Ratios for ratio tables, Scale Ratio for proportional resizing, and Screen Ratio for image or display dimensions. Together, the modes cover the most common ratio, proportion, scaling, and aspect-ratio calculations in one page.