Aspect Ratio Calculator

Calculator and formulas for aspect ratios with mathematical background

Aspect Ratio Calculator

What is calculated?

This function reduces an aspect ratio to smallest whole numbers and computes the decimal ratio. Ideal for screen resolutions, image ratios and geometric proportions.

Enter aspect ratio

:
Examples: 1920:1080, 16:9, 4:3

Result
Format: :
Decimal: : 1
The ratio is reduced to smallest whole numbers

Aspect Ratio Info

What is an aspect ratio?

An aspect ratio describes the relationship between width and height:

  • Format: Width : Height
  • Decimal form: Width ÷ Height
  • Independent of size
  • Describes the shape

Usage: Aspect ratios are important for screens, photos, videos and all rectangular objects.

Common formats
16:9 = 1.778
Full HD, 4K, Widescreen
4:3 = 1.333
Classic TV, older monitors
21:9 = 2.333
Ultrawide monitors
1:1 = 1.000
Square, social media
Mobile formats

9:16 (0.5625) for portrait videos
18:9 (2.0) for modern smartphones

Mathematical formulas for aspect ratios

Aspect ratio
\[\text{Ratio} = \frac{\text{Width}}{\text{Height}} = \frac{a}{b}\] Basic formula
Reduced form
\[\frac{a}{b} = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)}\] Using greatest common divisor
Euclidean algorithm
\[\gcd(a,b) = \gcd(b, a \bmod b)\] For a > b, until remainder = 0
Decimal ratio
\[\text{Decimal} = \frac{a}{b} : 1\] Normalized to 1
Scaling
\[a:b = (a \cdot k):(b \cdot k)\] Proportional scaling
Inverse
\[\text{Height} : \text{Width} = \frac{1}{\text{Ratio}}\] Swapping sides

Step-by-step example: Full HD

Example: reduce 1920×1080 resolution

1Find greatest common divisor

\[\gcd(1920, 1080)\]

Euclidean algorithm:

1920 ÷ 1080 = 1 R 840
1080 ÷ 840 = 1 R 240
840 ÷ 240 = 3 R 120
240 ÷ 120 = 2 R 0

gcd = 120

2Divide by gcd

\[\frac{1920 \div 120}{1080 \div 120} = \frac{16}{9}\]

Reduced form: 16:9

Decimal form: 16 ÷ 9 = 1.778

3Interpret result

1920×1080 = 16:9 = 1.778:1

This is the standard widescreen format

Resolutions and their aspect ratios

16:9 Widescreen formats
1920×1080 (Full HD) = 16:9 = 1.778
\[\frac{1920}{1080} = \frac{16}{9} \approx 1.778\]
3840×2160 (4K UHD) = 16:9 = 1.778
\[\frac{3840}{2160} = \frac{16}{9} \approx 1.778\]
1366×768 (HD) ≈ 16:9 = 1.778
\[\frac{1366}{768} \approx 1.778\]
4:3 Classic formats
1024×768 (XGA) = 4:3 = 1.333
\[\frac{1024}{768} = \frac{4}{3} \approx 1.333\]
800×600 (SVGA) = 4:3 = 1.333
\[\frac{800}{600} = \frac{4}{3} \approx 1.333\]
640×480 (VGA) = 4:3 = 1.333
\[\frac{640}{480} = \frac{4}{3} \approx 1.333\]

Special formats

Ultrawide 21:9
2560×1080
\[\frac{2560}{1080} = \frac{64}{27} \approx 2.37\]

Gaming and film

Square 1:1
1080×1080
\[\frac{1080}{1080} = 1\]

Instagram, profile pictures

Portrait 9:16
1080×1920
\[\frac{1080}{1920} = \frac{9}{16} = 0.5625\]

TikTok, Instagram Stories

Practical applications

Image editing

Maintain crop ratios

When cropping images, keep the original aspect ratio:

Original: 3000×2000 = 3:2
Cropped: 1500×1000 = 3:2 ✓
Web design

Responsive images

Use CSS aspect-ratio property:

aspect-ratio: 16 / 9;
aspect-ratio: 4 / 3;
Print preparation

DIN A4: 210×297 mm = 1:√2 ≈ 1:1.414
Poster: 70×100 cm = 7:10 = 0.7

Video production

YouTube: 16:9 recommended
TikTok/Reels: 9:16 for mobile devices

Mathematical background

The Euclidean algorithm

The Euclidean algorithm is an efficient procedure to compute the greatest common divisor (gcd) of two numbers. It is based on the identity:

\[\gcd(a,b) = \gcd(b, a \bmod b)\]
Proportionality

Aspect ratios describe proportions. Two rectangles have the same aspect ratio if they are similar (same shape, different size).

Key properties
  • Scale invariance: Ratio remains unchanged when scaled
  • Uniqueness: Every ratio has a unique reduced form
  • Invertibility: a:b corresponds to b:a reversed
  • Transitivity: Similar rectangles share the same ratios

More Ratio Functions

Aspect Ratio  •  Compare Ratios  •  Decimal to Ratio  •  Fraction to Ratio  •  Ratio-Calculator  •  Ratio Simplifier  •  Ratio to Decimal  •  Ratio to Fraction  •  Scale Ratio  •