Aspect Ratio & Resolution Workbench
Calculate proportional dimensions, simplify exact ratios using Euclidean GCD algorithms, resize digital video, and optimize canvas resolutions for YouTube, TikTok, Instagram, and widescreen cinema.
Original Dimensions & Target Resize
Aspect Ratio & Pixel Ratios
Geometric Aspect Canvas Visualizer
Live geometric canvas rendering the true rectangular proportions, diagonal sightline, and dimension calipers based on current input parameters.
Aspect Ratio Geometry & Euclidean GCD Reduction
An aspect ratio represents the proportional relationship between width $W$ and height $H$. To express this ratio in standard lowest integer terms (e.g. 16:9 rather than 1920:1080), the dimensions are reduced by their Greatest Common Divisor using Euclid's algorithm:
\gcd(a, b) = \begin{cases} a & \text{if } b = 0 \\ \gcd(b, a \bmod b) & \text{if } b > 0 \end{cases}
\text{Example: For } 1920 \times 1080: \quad \gcd(1920, 1080) = \gcd(1080, 840) = \gcd(840, 240) = \gcd(240, 120) = 120.
2. Simplified Integer Ratio:
R_w = \frac{W}{\gcd(W, H)} = \frac{1920}{120} = 16, \qquad R_h = \frac{H}{\gcd(W, H)} = \frac{1080}{120} = 9 \implies 16:9
3. Proportional Dimension Scaling (Cross-Multiplication):
\frac{W_1}{H_1} = \frac{W_2}{H_2} \implies W_2 = \frac{W_1 \times H_2}{H_1}, \qquad H_2 = \frac{H_1 \times W_2}{W_1}
4. Video Compression Macroblock Divisibility (Mod 16):
\text{H.264 / H.265 encoding assigns pixels into } 16 \times 16 \text{ macroblocks.}\
\text{Enforce: } W \bmod 16 = 0 \quad \text{and} \quad H \bmod 16 = 0 \text{ to avoid padding artifacts.}
5 Critical Video Encoding & Aspect Ratio Pitfalls
1. Non-Divisible Macroblock Dimensions (Mod 2 / Mod 16)
Video codecs (H.264, HEVC, ProRes) compress frames in blocks of $8 \times 8$ or $16 \times 16$ pixels. If your scaled height or width is an odd number (e.g. 721px) or not divisible by 2, video encoders will either throw a rendering error or pad the edge with an ugly 1-pixel green or black glitch bar. Always round scaled dimensions to even numbers.
2. Pillarboxing vs Center Cropping in Vertical Video
Converting 16:9 horizontal footage to 9:16 vertical for TikTok or Instagram Reels by center cropping cuts off 67% of the original visual canvas. Important speaker gestures, logos, and lower-third graphics disappear. Use dynamic pan-and-scan or reframe with blurred letterbox margins rather than hard center cropping.
3. Instagram 4:5 Feed Compression vs 9:16 Story Crop
Instagram Stories and Reels support full 9:16 vertical video ($1080 \times 1920$). However, standard in-feed posts restrict maximum vertical aspect ratio to 4:5 ($1080 \times 1350$). Posting a 9:16 video directly to the main profile grid forces automatic top-and-bottom cropping that amputates text captions.
4. Storage Aspect Ratio (SAR) vs Display Aspect Ratio (DAR)
Standard DVD and broadcast media often store video in $720 \times 480$ pixels (a 3:2 storage ratio), but display it at 16:9 widescreen using non-square anamorphic pixels (Pixel Aspect Ratio = 1.185). Treating anamorphic footage as square pixels causes actors to look squished and circles to appear as ovals.
5. Sub-Pixel Blur from Non-Integer Downscaling
Arbitrarily scaling 4K video ($3840 \times 2160$) down to custom non-standard resolutions (e.g. $1400 \times 788$) causes bilinear interpolation algorithms to blend neighboring pixels, softening crisp text and rendering UI icons blurry. Stick to standard fractional steps (e.g. 50% scale to $1920 \times 1080$).