How do you solve a proportion for an unknown variable (Solve for X)?

Proportions follow the fundamental rule: if A / B = C / D, the cross products are equal (A * D = B * C). To solve for an unknown variable, isolate it by multiplying opposite diagonal values and dividing by the remaining known term, such as X = (B * C) / A.

What is the quickest way to simplify a ratio to lowest terms?

Calculate the Greatest Common Divisor (GCD) using the Euclidean algorithm between both terms, then divide both terms by that GCD. For example, for 120:80, the GCD is 40; dividing both terms by 40 yields the irreducible form 3:2.

How do you divide an amount proportionally among multiple parts?

First, compute the sum of all ratio parts (for example, for a 3:2 split, total parts equal 3 + 2 = 5). Divide the total amount by this sum to find the value of a single unit share. Finally, multiply this unit share by each individual ratio component.

How do you convert a two-part ratio into a percentage?

A ratio A:B describes part-to-part relationships. To get percentage shares, determine each part relative to the total sum: Percentage(A) = (A / (A + B)) * 100%, and Percentage(B) = (B / (A + B)) * 100%. The sum of both shares will always equal 100%.

What is the difference between a ratio and a fraction?

A ratio represents a comparison between two distinct quantities (Part-to-Part, like 3 red balls to 2 blue balls). A fraction represents a portion of a whole entity (Part-to-Whole, like 3 out of 5 total balls, or 3/5).

How do aspect ratios work for digital screens and video?

An aspect ratio defines the proportional relationship between display width and height. For example, 16:9 widescreen means 16 horizontal pixels for every 9 vertical pixels (1920x1080). Vertical formats like 9:16 flip this relation (1080x1920) for mobile feeds.

Can ratios contain negative numbers or zero?

In standard physical, geometric, and scale modeling, ratio terms must be strictly non-zero positive numbers. A denominator or ratio antecedent of zero is mathematically undefined because division by zero is impossible.

Does this calculator save or transmit any input numbers to a server?

No. All calculations run strictly on your local device inside your web browser. No numbers, formulas, or outputs are ever transmitted across the network or stored in external databases.

The Ratio Calculator - Solve, Simplify & Scale Ratios Online

The Ratio Calculator

Solve, Simplify & Scale Ratios Online

Enter any 3 values. Leave 1 box empty to solve for X.

: = :

Proportion Solution

Enter ratio A and B to reduce to lowest integer terms.

Simplified Ratio

Divide a total amount (money, recipe, mix) by ratio A : B.

Calculated Distribution

Convert a ratio A : B into fraction & decimal forms.

Fraction Conversion

Convert ratio A : B into exact percentage values.

Percentage Equivalents

Convert Numerator / Denominator into a simplified ratio.

Ratio Output

Maintain original screen aspect ratio when resizing.

Aspect Ratio Dimensions

1. Solving Proportions for Unknown Variable X (A : B = C : D)

In mathematics, a proportion is a formal statement asserting that two distinct ratios are strictly equivalent. When expressed algebraically, a proportion is written as A / B = C / D or using classical colon notation as A : B = C : D. The terms A and D are historically defined as the extremes, while the inner terms B and C represent the means.

Fundamental Property of Proportions: A × D = B × C

To isolate and solve for any missing term (represented here as variable X), we employ algebraic cross-multiplication. Multiplying diagonally across the equals sign eliminates the rational denominators, yielding a simple linear relation. Depending on which position holds the unknown value, the solution is determined using one of four algebraic transformations:

• Finding Extremes (D): D = (B × C) / A
• Finding Extremes (A): A = (B × C) / D
• Finding Means (C): C = (A × D) / B
• Finding Means (B): B = (A × D) / C

Top 20 Solved Homework & Exam Proportions

Proportion Problem	Calculated Value (X)	Step-by-Step Formula Applied
1 : 2 = X : 10	5	(1 × 10) / 2 = 5
2 : 3 = 8 : X	12	(3 × 8) / 2 = 12
3 : 5 = 15 : X	25	(5 × 15) / 3 = 25
4 : 7 = X : 28	16	(4 × 28) / 7 = 16
5 : 8 = 20 : X	32	(8 × 20) / 5 = 32
2 : 9 = 6 : X	27	(9 × 6) / 2 = 27
3 : 10 = X : 50	15	(3 × 50) / 10 = 15
6 : 11 = 18 : X	33	(11 × 18) / 6 = 33
7 : 12 = X : 48	28	(7 × 48) / 12 = 28
9 : 4 = 36 : X	16	(4 × 36) / 9 = 16
1 : 3 = X : 21	7	(1 × 21) / 3 = 7
5 : 6 = 25 : X	30	(6 × 25) / 5 = 30
4 : 9 = X : 45	20	(4 × 45) / 9 = 20
7 : 8 = 35 : X	40	(8 × 35) / 7 = 40
3 : 7 = X : 49	21	(3 × 49) / 7 = 21
5 : 12 = 15 : X	36	(12 × 15) / 5 = 36
8 : 15 = X : 60	32	(8 × 60) / 15 = 32
2 : 15 = 8 : X	60	(15 × 8) / 2 = 60
11 : 20 = X : 100	55	(11 × 100) / 20 = 55
13 : 26 = 5 : X	10	(26 × 5) / 13 = 10

2. Ratio Simplifier: Reducing Quantities to Lowest Terms

A ratio reaches its irreducible or simplest form when its constituent terms (antecedent and consequent) are integers that are coprime—meaning their Greatest Common Divisor (GCD) or Highest Common Factor (HCF) equals 1. In academic curricula across the USA, UK, and Canada, writing answers in unreduced forms is penalized.

Simplification Rule: (A / GCD(A, B)) : (B / GCD(A, B))

The standard analytical method relies on the Euclidean algorithm: repeatedly dividing the larger integer by the smaller until the remainder is zero. Once the GCD is isolated, dividing both integers by this value preserves the fundamental relational balance while expressing it in minimal whole units.

Top 20 Simplified Integer Ratios Reference

Initial Ratio	Greatest Common Divisor (GCD)	Simplified Form
100 : 25	25	4 : 1
120 : 80	40	3 : 2
60 : 40	20	3 : 2
75 : 25	25	3 : 1
150 : 50	50	3 : 1
24 : 36	12	2 : 3
48 : 64	16	3 : 4
18 : 24	6	3 : 4
32 : 48	16	2 : 3
50 : 200	50	1 : 4
16 : 24	8	2 : 3
70 : 30	10	7 : 3
90 : 60	30	3 : 2
45 : 15	15	3 : 1
84 : 36	12	7 : 3
144 : 96	48	3 : 2
250 : 100	50	5 : 2
500 : 250	250	2 : 1
125 : 75	25	5 : 3
80 : 20	20	4 : 1

3. Scale & Divide: Proportional Sum Allocation

Dividing a gross sum according to a predefined ratio is an essential procedure in financial disbursements, corporate profit-sharing agreements, legal estate settlements, and commercial construction mixing. Rather than splitting amounts symmetrically, proportional distribution assigns weight corresponding to specific unit parts.

Step 1: Total Units = A + B | Step 2: Value Per Unit = Total / (A + B)

To compute individual shares, multiply the base unit value by each respective ratio component: Share A = A × Value Per Unit, and Share B = B × Value Per Unit. The sum of all calculated shares must always reconcile back to the original total amount.

Top 20 Common Proportional Allocations

Total Sum	Ratio (A : B)	Share A	Share B
100	1 : 1	50.00	50.00
100	1 : 3	25.00	75.00
100	2 : 3	40.00	60.00
100	1 : 4	20.00	80.00
500	1 : 4	100.00	400.00
500	2 : 3	200.00	300.00
500	3 : 7	150.00	350.00
1,000	1 : 1	500.00	500.00
1,000	2 : 3	400.00	600.00
1,000	3 : 5	375.00	625.00
1,000	1 : 9	100.00	900.00
1,000	7 : 3	700.00	300.00
10,000	60 : 40	6,000.00	4,000.00
10,000	70 : 30	7,000.00	3,000.00
10,000	50 : 50	5,000.00	5,000.00
10,000	1 : 3	2,500.00	7,500.00
50,000	2 : 3	20,000.00	30,000.00
50,000	1 : 4	10,000.00	40,000.00
100,000	75 : 25	75,000.00	25,000.00
100,000	80 : 20	80,000.00	20,000.00

4. Ratio to Fraction & Decimal Conversion

A ratio represents a comparative statement that can be evaluated in two distinct mathematical ways: Part-to-Part comparisons and Part-to-Whole comparisons. Confusing these two structures is one of the most common student errors in middle and high school math.

Part-to-Whole Fraction = A / (A + B) | Decimal = A / (A + B)

When converting a ratio into a standard fractional representation, the numerator represents the antecedent (A), while the denominator must encompass the totality of parts (A + B). Dividing the numerator by the denominator gives the precise decimal fraction required for scientific calculations.

Top 20 Academic Ratio to Fraction Conversions

Ratio (A : B)	Part-to-Whole Fraction	Exact Decimal Value
1 : 1	1/2	0.5000
1 : 2	1/3	0.3333
1 : 3	1/4	0.2500
1 : 4	1/5	0.2000
2 : 3	2/5	0.4000
2 : 5	2/7	0.2857
3 : 4	3/7	0.4286
3 : 5	3/8	0.3750
4 : 5	4/9	0.4444
5 : 6	5/11	0.4545
1 : 5	1/6	0.1667
3 : 7	3/10	0.3000
5 : 8	5/13	0.3846
7 : 9	7/16	0.4375
1 : 9	1/10	0.1000
4 : 7	4/11	0.3636
5 : 9	5/14	0.3571
3 : 8	3/11	0.2727
7 : 10	7/17	0.4118
9 : 10	9/19	0.4737

5. Ratio to Percentage (%) Equivalents

Percentages translate proportional statements into a normalized scale base of 100. Converting a ratio to its percentage values provides an immediate, universally understandable metric of how large each component is relative to the entirety.

Part A % = [A / (A + B)] × 100 | Part B % = [B / (A + B)] × 100

To verify the mathematical validity of any ratio-to-percentage conversion, add the resulting percentage shares together: Part A % + Part B % must always equal exactly 100.00%.

Top 20 Common Ratio to Percentage Standards

Ratio (A : B)	Part A Percentage (%)	Part B Percentage (%)
1 : 1	50.00%	50.00%
1 : 2	33.33%	66.67%
1 : 3	25.00%	75.00%
1 : 4	20.00%	80.00%
1 : 5	16.67%	83.33%
2 : 3	40.00%	60.00%
2 : 5	28.57%	71.43%
3 : 4	42.86%	57.14%
3 : 5	37.50%	62.50%
4 : 5	44.44%	55.56%
5 : 5	50.00%	50.00%
1 : 9	10.00%	90.00%
3 : 7	30.00%	70.00%
7 : 3	70.00%	30.00%
5 : 8	38.46%	61.54%
7 : 8	46.67%	53.33%
9 : 1	90.00%	10.00%
3 : 2	60.00%	40.00%
4 : 1	80.00%	20.00%
7 : 13	35.00%	65.00%

6. Fraction to Ratio: Structural Conversion Rules

A fraction represents division and sharing where the Numerator specifies designated quantities and the Denominator determines total partitioning. Translating a fraction into a standard two-term ratio requires treating the numerator as the first term (antecedent) and denominator as the second (consequent).

Fraction (N / D) → Antecedent (N / GCD) : Consequent (D / GCD)

If the original fraction is unreduced, compute the Greatest Common Divisor to express the resulting ratio in lowest integer terms, maintaining strict equivalence without fractional remainders.

Top 20 Fraction to Simplified Ratio Conversions

Input Fraction	Greatest Common Divisor (GCD)	Simplified Ratio
1/2	1	1 : 2
1/3	1	1 : 3
1/4	1	1 : 4
2/4	2	1 : 2
3/4	1	3 : 4
2/5	1	2 : 5
3/5	1	3 : 5
4/6	2	2 : 3
5/10	5	1 : 2
6/8	2	3 : 4
8/12	4	2 : 3
9/12	3	3 : 4
10/15	5	2 : 3
12/16	4	3 : 4
15/20	5	3 : 4
16/24	8	2 : 3
18/24	6	3 : 4
20/25	5	4 : 5
25/100	25	1 : 4
75/100	25	3 : 4

7. Aspect Ratio & Screen Resolutions Explained

Aspect ratio describes the proportional relationship between the width and height of an image, video display, or digital screen. Regardless of the absolute physical dimensions or pixel counts, an aspect ratio ensures that visual media retains its intended geometry without stretching, squeezing, or distortion.

Scaling Rule: New Height = (New Width × H1) / W1 | New Width = (New Height × W1) / H1

In modern digital video, 16:9 serves as the global standard for desktop monitors and widescreen TV broadcasting, while 9:16 represents the inverted mobile-first standard used across vertical formats like Instagram Reels, TikTok, and YouTube Shorts.

Top 20 Production Resolution Standards

Standard Name	Aspect Ratio	Resolution (W × H)
8K UHD	16 : 9	7680 × 4320
4K Ultra HD	16 : 9	3840 × 2160
2K Quad HD	16 : 9	2560 × 1440
Full HD 1080p	16 : 9	1920 × 1080
HD 720p	16 : 9	1280 × 720
SD 480p	16 : 9	854 × 480
Mobile 4K Vertical	9 : 16	2160 × 3840
Mobile Full HD	9 : 16	1080 × 1920
Mobile HD Vertical	9 : 16	720 × 1280
Square HD	1 : 1	1080 × 1080
Square High-Res	1 : 1	1200 × 1200
Classic TV/Monitor	4 : 3	1024 × 768
UXGA Monitor	4 : 3	1600 × 1200
QXGA Retina	4 : 3	2048 × 1536
VGA Classic	4 : 3	800 × 600
Ultrawide FHD	21 : 9	2560 × 1080
Ultrawide QHD	21 : 9	3440 × 1440
Ultrawide 5K	21 : 9	5120 × 2160
Photo Pro DSLR	3 : 2	3000 × 2000
Surface Laptop	3 : 2	2256 × 1504

Frequently Asked Questions (FAQ)

Clear, formula-backed mathematical explanations for common ratio, proportion, and scaling calculations.

Question	Mathematical Explanation & Method
How do you solve a proportion for an unknown variable (Solve for X)?	Proportions follow the fundamental rule: if `A / B = C / D`, the cross products are equal (`A : D = B : C`). To solve for an unknown, isolate the variable by multiplying the opposite diagonal values and dividing by the remaining known term (e.g., `X = (B : C) / A`).
What is the quickest way to simplify a ratio to lowest terms?	Calculate the Greatest Common Divisor (GCD) using the Euclidean algorithm between both terms, then divide both sides by that GCD. For example, for `120:80`, the GCD is `40`; dividing both by 40 yields the irreducible form `3:2`.
How do you divide an amount proportionally among multiple parts?	First, compute the sum of all ratio parts (e.g., for a `3:2` split, total parts = `3 + 2 = 5`). Divide the total amount by this sum to find the value of a single unit share. Finally, multiply this unit share by each individual ratio component.
How do you convert a two-part ratio into a percentage?	A ratio `A:B` describes part-to-part relationships. To get percentage shares, determine each part relative to the total sum: `Percentage(A) = (A / (A + B)) 100%`, and `Percentage(B) = (B / (A + B)) 100%`. The sum of both shares will always equal 100%.
What is the difference between a ratio and a fraction?	A ratio typically represents a comparison between two distinct quantities (Part-to-Part, like 3 red balls to 2 blue balls). A fraction represents a portion of a complete entity (Part-to-Whole, like 3 out of 5 total balls, or `3/5`).
How do aspect ratios work for digital screens and video?	An aspect ratio defines the proportional relationship between display width and height. For example, `16:9` widescreen means for every 16 horizontal pixels there are 9 vertical pixels (1920 : 1080). Vertical formats like `9:16` flip this relation (1080 * 1920) for mobile feeds.
Can ratios contain negative numbers or zero?	In standard physical, geometric, and scale modeling, ratio terms must be strictly non-zero positive numbers. A denominator or ratio antecedent of zero is mathematically undefined because division by zero is impossible.
Does this calculator save or transmit any input numbers to a server?	No. All calculations run strictly on your local device inside your web browser. No numbers, formulas, or outputs are ever transmitted across the network or stored in external databases.