Ratio Calculator

Solve proportion equations (A:B = C:D), simplify ratios to lowest terms, and scale aspect dimensions. Detailed cross-multiplication step-by-step breakdowns.

Proportion Terms

Leave 1 field empty

Enter 3 known values to solve for the 4th missing term (A:B = C:D):

First Ratio (A : B)
Second Ratio (C : D)
Calculated Missing Value
15
Computational Solution

D = (B × C) ÷ A = (6 × 10) ÷ 4 = 15.00

Cross-Multiplication Verification
A × D60.00
B × C60.00
Cross products are equal: The proportion A/B = C/D is balanced.

What is a Ratio and Proportion?

A ratio is a quantitative relationship expressing how many times one number contains another (A:B or A/B). A proportion is a mathematical statement demonstrating that two ratios are exactly equivalent (A/B = C/D).

1. Fundamental Proportion & Cross-Multiplication Rule
AB
=
CD
⟹A × D = B × C
2. Solving for Any Missing Proportion Term
A =
B × CD
B =
A × DC
C =
A × DB
D =
B × CA
Step-by-Step Calculation Breakdown
Step 1: Setup Proportion Fraction Equivalence (4 : 6 = 10 : D)
46
=
10D
Step 2: Apply Cross-Multiplication
4 × D=6 × 10=60
Step 3: Solve for Missing Variable (D)
D=
604
=15.00

Standard Aspect Ratio Reference Table

Aspect RatioDecimal EquivalentStandard Industry Applications
16 : 91.78 : 1Global widescreen standard (1080p, 4K UHD, YouTube, modern computer monitors).
4 : 31.33 : 1Classic SD television, iPad displays, and medium format film photography.
1 : 11.00 : 1Square social media posts, profile avatars, album cover art.
21 : 92.33 : 1Cinematic anamorphic widescreen (CinemaScope) and ultra-wide gaming monitors.
1 : 1.6180.618 : 1The Golden Ratio (φ), utilized in graphic design, typography, and classical architecture.

Frequently Asked Questions

How does cross-multiplication solve proportions?
A mathematical proportion states that two fractions are equal: A/B = C/D. By multiplying both sides by (B × D), we obtain the cross-product equality: A × D = B × C. If one value is unknown, simply divide the product of the known diagonal by the remaining single value.
How do I simplify a ratio to its lowest terms?
Find the Greatest Common Divisor (GCD) of both parts of the ratio and divide each number by that GCD. For example, in 36:48, the GCD is 12. Dividing both by 12 gives the irreducible simplified ratio 3:4.
What is the Golden Ratio (φ)?
The Golden Ratio is an irrational mathematical constant approximately equal to 1.618033... Two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one ((A+B)/A = A/B = φ).
How are aspect ratios calculated in digital media?
An aspect ratio expresses the proportional relationship between display width and height. For example, Full HD (1920 × 1080) simplifies by dividing both dimensions by their GCD (120), resulting in the ubiquitous 16:9 widescreen standard.

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