Ratio Calculator

A ratio compares the relative sizes of two quantities in the form A : B, while a proportion states that two ratios are equal (A : B = C : D). This free online ratio calculator operates in three automatic modes depending on how many values you enter: enter 2 values to simplify a ratio to its lowest terms, enter 3 values to solve for any missing value in a proportion, or enter 4 values to test whether two ratios are equivalent—complete with step-by-step mathematical working.

What Is a Ratio?

In mathematics, a ratio expresses how many times one number contains another or how two quantities relate to each other. In the ratio A : B (read as "A to B"), the first term A is called the antecedent and the second term B is called the consequent.

Ratios can be written in three interchangeable notations:

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Colon notation: 8 : 12 (standard form for comparing two or more parts).
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Word notation: 8 to 12 (used in everyday speech and technical descriptions).
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Fraction (quotient) notation: 8 / 12 (used when setting up algebraic proportion equations).

How to Simplify a Ratio

Simplifying a ratio means reducing both terms to the smallest possible whole numbers (or simplest proportional terms) without changing their relative relationship—just like reducing a fraction. To use the calculator as a ratio simplifier, enter only two values into either the left pair (A and B) or the right pair (C and D) and leave the other two boxes empty.

                            Simplified Ratio: A : B = (A ÷ GCD(A, B)) : (B ÷ GCD(A, B))
                        

To simplify a ratio manually:

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Step 1: Find the Greatest Common Divisor (GCD). Identify the largest positive number that divides both A and B without a remainder. (You can also find all shared divisors with our Common Factors Calculator.)
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Step 2: Divide both terms by the GCD. Divide A by the GCD and B by the GCD. For example, for 8 : 12, the GCD of 8 and 12 is 4, so (8 ÷ 4) : (12 ÷ 4) = 2 : 3.

How to Calculate a Missing Value in a Proportion (A : B = C : D)

When two ratios are set equal to each other (A : B = C : D), they form a proportion. By the cross-multiplication property of proportions, the product of the outer terms (the extremes, A and D) always equals the product of the inner terms (the means, B and C):

                            A : B = C : D  ⇔  A / B = C / D  ⇔  A × D = B × C
                        

When you enter any three known values and leave one field blank, the calculator solves for the unknown variable using the corresponding cross-multiplication formula:

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Solve for missing A: A = (B × C) / D
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Solve for missing B: B = (A × D) / C
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Solve for missing C: C = (A × D) / B
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Solve for missing D: D = (B × C) / A

Equivalent Ratios and How to Check Equivalence

Equivalent ratios are ratios that represent the same relative relationship between numbers, even though the numbers themselves are scaled up or down. You can generate an equivalent ratio by multiplying or dividing both A and B by the same non-zero scale factor k: for example, multiplying 2 : 3 by 4 gives 8 : 12, and multiplying by 10 gives 20 : 30.

To check whether two ratios A : B and C : D are equivalent, enter all four values into the calculator. The tool computes both cross products (A × D and B × C) and tells you whether the proportion is True (Equivalent) or False (Not equivalent).

Ratio vs. Fraction: How to Convert a Ratio to a Fraction

Understanding whether a ratio is part-to-whole or part-to-part determines how you convert it into a fraction or percentage:

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Part-to-Part Ratio (e.g., 1 : 2): Compares one subgroup directly against another subgroup. To convert a part-to-part ratio into fractions of the whole, first add the parts together to find the total denominator (1 + 2 = 3), then place each part over that total: 1 : 2 represents 1/3 (33.33%) for the first part and 2/3 (66.67%) for the second part.
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Part-to-Whole Ratio (e.g., 1 : 3 of the total): Compares one part directly against the entire group, which translates directly to the fraction 1/3. You can perform further arithmetic on fractions with our Fraction Calculator or convert fractions into decimals with the Fraction to Decimal Calculator.

Worked Ratio & Proportion Examples

Example 1: Simplifying a Ratio to Lowest Terms

Simplify the screen resolution ratio 1920 : 1080 to its simplest whole-number form:

                                    Step 1: Find GCD
                                    GCD(1920, 1080) = 120
                                
                                    Step 2: Divide A
                                    1920 ÷ 120 = 16
                                
                                    Step 3: Divide B
                                    1080 ÷ 120 = 9
                                
                                    Answer
                                    16 : 9

Example 2: Finding a Missing Value in a Proportion

Find the unknown value A in the proportion: A : 400 = 6 : 25

                                    Step 1: Proportion
                                    A / 400 = 6 / 25
                                
                                    Step 2: Cross-multiply
                                    A = (400 × 6) ÷ 25
                                
                                    Step 3: Simplify
                                    A = 2400 ÷ 25
                                
                                    Answer
                                    A = 96

Example 3: Solving a Proportion with a Coefficient

Find the value of b given the ratio equation: 5b : 8 = 2 : 5

                                    Step 1: Fractions
                                    5b / 8 = 2 / 5
                                
                                    Step 2: Isolate 5b
                                    5b = (2 / 5) × 8 = 16 / 5
                                
                                    Step 3: Isolate b
                                    b = (16 / 5) ÷ 5
                                
                                    Answer
                                    b = 16 / 25 = 0.64

Example 4: Splitting a Total Amount by a Ratio

Split $240 into two shares according to the ratio 3 : 5

                                    Step 1: Total parts
                                    3 + 5 = 8 parts
                                
                                    Step 2: Value of 1 part
                                    $240 ÷ 8 = $30
                                
                                    Step 3: First share (3)
                                    3 × $30 = $90
                                
                                    Step 4: Second share (5)
                                    5 × $30 = $150
                                
                                    Answer
                                    $90 and $150

Practical Everyday Applications of Ratios

Ratios and proportions are used across science, design, finance, and daily life whenever quantities must be scaled while keeping their relative balance intact:

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Images, Video & Aspect Ratios: Resizing photos, monitors, and UI layouts (such as 16 : 9 widescreen, 4 : 3 standard, or 1 : 1 square) without stretching or distorting the image.
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Cooking & Recipe Scaling: Adjusting ingredient weights up or down when changing a recipe from 4 servings to 10 servings, or maintaining culinary ratios like a 3 : 1 oil-to-vinegar dressing.
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Maps, Blueprints & Scale Models: Converting drawing measurements into real-world distances using scale ratios such as 1 : 100 in architecture or 1 : 50,000 in cartography.
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Chemistry, Construction & Mixtures: Mixing concrete (such as a 1 : 2 : 4 cement-sand-aggregate ratio), diluting solutions, or blending two-stroke fuel ratios (50 : 1).

Frequently Asked Questions (FAQ)

What is a ratio and how is it written?

A ratio is a mathematical comparison showing the relative sizes of two or more quantities. Ratios are most commonly written with a colon (A : B), read aloud as 'A to B' (such as 3 to 4), or expressed as a quotient fraction (A / B).

How do you simplify a ratio to its lowest terms?

To simplify a ratio A : B, find the Greatest Common Divisor (GCD) of both numbers and divide each term by that GCD. For example, to simplify 8 : 12, divide both numbers by their GCD of 4 to get 2 : 3. In the calculator, enter two values (A and B, or C and D) to reduce the ratio step by step.

How do you calculate a missing value in a ratio proportion (A : B = C : D)?

Use cross-multiplication based on the proportion identity A × D = B × C. Multiply the two known diagonal terms and divide by the remaining known term: A = (B × C) / D, B = (A × D) / C, C = (A × D) / B, or D = (B × C) / A. Enter any three known values in the calculator and leave the unknown field blank.

What is an equivalent ratio and how do you check if two ratios are equal?

Equivalent ratios express the exact same proportional relationship even though their numbers differ (for example, 2 : 3 and 8 : 12). You can check whether A : B and C : D are equivalent by entering all four values—the calculator compares the cross products A × D and B × C to confirm whether they are equal.

Can a ratio be written as a fraction?

Yes, depending on what the ratio describes. A part-to-whole ratio maps directly to a fraction (for example, 1 : 4 of a total is 1/4). For a part-to-part ratio such as 1 : 2, add the parts together to find the whole (1 + 2 = 3) and place each part over that sum, yielding the fractions 1/3 and 2/3.

Can you use decimals in a ratio?

Yes. This ratio calculator accepts whole integers, decimal numbers, and scientific notation across all four input fields (A, B, C, and D), rounding decimal outputs cleanly to up to 4 decimal places.

How do you split a total amount into a given ratio?

First, add the ratio parts together (A + B) to find the total number of parts. Next, divide the total amount by the sum of the parts to find the value of one single part. Finally, multiply that single-part value by each term in the ratio.

Related Calculators and Tools

Common Factors Calculator – find shared divisors and the Greatest Common Factor (GCF) to simplify ratios
Fraction Calculator – add, subtract, multiply, divide, and reduce fractions step by step
Fraction to Decimal Calculator – convert fractional ratios into exact decimals and percentages
Mixed Numbers Calculator – solve operations with mixed numbers and improper fractions
Percentage Calculator – calculate percentages, proportional shares, and percentage changes
Mean Calculator – calculate the arithmetic mean (average) and sum of any dataset

Last Updated: November 2026

Ratio Calculator – Simplify Ratios, Find Missing Values & Solve Proportions