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Ratio Calculator

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A ratio compares two or more quantities using the same unit. This free ratio calculator simplifies ratios to their lowest form, finds the missing value in a proportion, and converts between fractions, decimals, and percentages. Enter your numbers above and get your answer instantly.

Ratio Calculator Tool

The ratio calculator above handles the most common ratio tasks in one place. Type two or more values separated by a colon (like 4:6 or 10:25:50) and the tool returns the simplified result, equivalent ratios, and converted forms.

Use it to:

  • Simplify any ratio to its simplest form
  • Solve for a missing value in a proportion (A:B = C:?)
  • Convert a ratio to a fraction, decimal, or percentage
  • Scale ratios up or down for recipes, materials, or budgets
  • Compare two ratios to check whether they form a true proportion

All results are estimates or mathematical outputs for planning purposes. For decisions in finance, engineering, or health, confirm results with a qualified professional.

How to Simplify Ratios With This Calculator

Simplifying a ratio means reducing it so both sides share no common factor other than 1. The ratio 12:8, for example, simplifies to 3:2.

Enter a ratio and simplify to the lowest fraction

  1. Type each number into the input fields (or enter them separated by a colon).
  2. Click "Calculate."
  3. The calculator finds the greatest common divisor (GCD) of your values and divides both sides by it.

The GCD is the largest number that divides evenly into every term. For 12:8, the GCD is 4. Dividing gives 3:2, the simplest form.

How do you simplify a ratio? Divide each number in the ratio by their greatest common divisor. The result is the ratio in its lowest terms.

Calculator to simplify ratios with a decimal or equation

Ratios don't always start as clean whole numbers. You might have 2.5:7.5 or a fraction like 3/4:1/2.

For decimals, the calculator multiplies both sides by the power of 10 needed to clear the decimal point, then simplifies. So 2.5:7.5 becomes 25:75, which simplifies to 1:3.

For fractional inputs, it converts each fraction to a common denominator, compares the numerators, and reduces. 3/4:1/2 becomes 3:2.

Equivalent Ratio Formula

Two ratios are equivalent when you can multiply or divide both terms of one ratio by the same number to get the other. The core formula is:

A : B = (A × n) : (B × n)

where n is any nonzero number (the scaling factor).

Evaluate equivalent ratios by scaling

Scaling means multiplying or dividing every term in a ratio by the same factor.

  • 1:2 scaled by 5 gives 5:10.
  • 20:50 divided by 10 gives 2:5.

Both pairs are equivalent because the relationship between the quantities stays the same. The calculator scales ratios automatically and lists several common equivalents for quick reference.

What is an equivalent ratio? It's a ratio that expresses the same comparison in different numbers. 2:3 and 10:15 are equivalent because 2 × 5 = 10 and 3 × 5 = 15.

Solve for the missing value in a proportion

A proportion states that two ratios are equal: A:B = C:D. If one value is missing, cross multiplication finds it.

Formula: A × D = B × C

Example: 3:5 = 12:?

3 × ? = 5 × 12 ? = 60 ÷ 3 ? = 20

So 3:5 = 12:20. Enter three known values into the calculator and it solves for the missing value instantly.

How do you solve a proportion? Cross multiply the two ratios and solve the resulting equation for the unknown term.

Convert a Ratio to a Fraction, Decimal, or Percentage

Ratios, fractions, decimals, and percentages are different representations of the same comparison. Converting between them makes it easier to use the number in spreadsheets, reports, or everyday math.

Ratio to fraction converter

A ratio like 3:5 converts to a fraction by placing the first term as the numerator and the second as the denominator: 3/5.

If you need each part as a fraction of the whole (the sum of the terms), divide each term by the total. For 3:5, the total is 8. The parts are 3/8 and 5/8.

The calculator returns both representations and their decimal and percentage equivalents.

How do I calculate a ratio by percentage? Convert the ratio to a fraction of the total, then multiply by 100. For 1:4, the total is 5. The first part is (1/5) × 100 = 20%. The second part is 80%.

Compare two ratios as a proportion

To check whether two ratios are equal, enter both pairs. The calculator cross multiplies and tells you if they form a true proportion.

For example, are 4:6 and 10:15 equal?

4 × 15 = 60 6 × 10 = 60

Yes, they are equivalent. If the cross products differ, the ratios are not proportional.

Can the calculator compare two ratios? Yes. Input both ratios and it checks whether the cross products match. If they do, the two ratios form a valid proportion.

Equivalent Ratio and Scaling in Recipe Math

Scaling ratios shows up constantly in cooking, baking, and mixing. If a recipe serves 4 and you need to serve 12, every ingredient quantity must be multiplied by the same factor.

Divide or multiply a recipe quantity

You're having a party and want to make 3 times as much as one recipe normally yields. Multiply every ingredient by 3.

  • Original: 2 cups flour, 1 cup sugar, 0.5 cup butter
  • Scaled (×3): 6 cups flour, 3 cups sugar, 1.5 cups butter

The ratio between ingredients stays the same. The calculator handles this by letting you enter your original quantities and a target scaling factor.

To halve a recipe, divide every quantity by 2. The proportions stay intact, and the result tastes right.

Ratio of sand to gravel: a scaling example

Construction mixes work the same way. A concrete recipe might call for sand to gravel in a ratio of 1:2. If you need 15 total buckets of material:

  1. Sum the ratio parts: 1 + 2 = 3
  2. Divide the total by the sum: 15 ÷ 3 = 5
  3. Multiply each ratio term by 5: sand = 5 buckets, gravel = 10 buckets

Can this calculator split a total by a ratio? Yes. Enter the ratio and the total quantity. The tool divides the total proportionally across each part.

Aspect Ratio Calculator

Aspect ratio describes the proportional relationship between width and height, most commonly for screens, images, and video. A 1920 × 1080 display has an aspect ratio of 16:9.

To find an aspect ratio, divide both the width and height by their GCD. For 1920:1080, the GCD is 120. That gives 16:9.

The calculator also solves for a missing dimension. If you know the aspect ratio is 16:9 and the width is 1280, it computes the height:

1280 ÷ 16 = 80 80 × 9 = 720

So the resolution is 1280 × 720.

Common aspect ratios:

  • 16:9 (widescreen monitors, YouTube video)
  • 4:3 (older TV screens, presentations)
  • 1:1 (square, Instagram posts)
  • 21:9 (ultrawide monitors)

Enter your width and height above and the tool returns the simplified aspect ratio plus scaled equivalents.

Math Calculators for Ratio, Fraction, and Proportion

This ratio calculator is part of a larger set of free math calculators on ezcalcs. If your task involves related calculations, these tools may help:

  • Fraction calculator for adding, subtracting, multiplying, or dividing fractions
  • Percentage calculator for finding percentage change, difference, or portion
  • Proportion calculator for solving multi-step proportions

Each calculator handles a specific type of computation so you can move from one step to the next without manual conversion.

FAQs

What is a ratio? A ratio is a comparison of two or more quantities that shows their relative sizes. It is usually written separated by a colon, like 3:4, or as a fraction (3/4).

How do you calculate a ratio? Divide one quantity by the other. For two numbers like 750 and 6000, divide both by their GCD (750). The ratio of 750 to 6000 is 1:8.

What is the ratio of 3 to 5? It is simply 3:5. As a fraction, that is 3/5 (0.6 or 60%).

What is the ratio of 1 to 4? 1:4. The first quantity is one fourth of the second. As a percentage of the total (5), the parts are 20% and 80%.

What are 3 ways to find a ratio?

  1. Divide both values by their GCD to get the simplest form.
  2. Convert both values to the same unit, then compare directly.
  3. Use a ratio calculator for instant simplification and scaling.

Can a ratio contain more than 2 numbers? Yes. A ratio like 2:3:5 compares three quantities at once. The calculator can simplify and scale multi-part ratios.

Do I need to input ratios in a specific format? Enter numbers separated by a colon (e.g., 4:6) or place each number in its own input field. The calculator accepts whole numbers, decimals, and fractions.

How do I find the ratio of two numbers? Divide each number by the GCD of both. For 45 and 60, the GCD is 15. The ratio is 3:4.

What is the golden ratio? The golden ratio is approximately 1:1.618. It appears in geometry, art, and nature. It is often represented by the Greek letter phi (φ).

How do I check if two ratios are equal using the ratio solver calculator? Enter both ratios and cross multiply. If the products are equal, the ratios form a valid proportion. The tool does this comparison automatically.