Information Theory July 13, 2026 · 12 min read

The Information Theory of Digital Video Compression: Bitrates, Codec Efficiency, and Storage Volume Mathematics

A technical deep-dive into digital video signal processing. Learn how resolution, frame rates, and bitrates determine file sizes and streaming bandwidth.

Every second of raw, uncompressed 4K video contains hundreds of megabytes of visual data—far too much for normal internet connections or hard drives to store. To distribute digital video efficiently, engineers rely on advanced mathematical algorithms called codecs to compress these massive signals. The key metric that determines both the final visual quality and the size of a video file is the Bitrate. Understanding the relationship between bitrate, resolution, and encoding efficiency is essential for modern streaming and media production.

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A common point of confusion is the units of measurement used in video. Bitrates are measured in **bits per second** (e.g., Mbps or kbps), while file storage capacity is measured in **Bytes** (e.g., GB or MB). Because one Byte contains exactly 8 bits, you must divide your calculated bitrate by 8 to determine actual file storage requirements.

1. The Mathematics of Video File Size

Calculating the exact file size ($S$) of a compressed video file is straightforward once you know the total continuous video bitrate ($B_v$), audio bitrate ($B_a$), and duration ($T$ in seconds).

The mathematical equation is structured as:

File Size (Megabytes) = [ (Video Bitrate + Audio Bitrate) · Duration (seconds) ] / 8,000

For example, let's calculate the file size of a 2-hour (7,200 seconds) feature film encoded with a high-quality video bitrate of 12 Mbps (12,000 kbps) and a stereo audio track of 320 kbps:

  • Combined Bitrate = 12,000 + 320 = 12,320 kbps.
  • Total Bits = 12,320 kbps · 7,200 seconds = 88,704,000 kilobits.
  • Converting to Gigabytes (GB): 88,704,000 / (8 · 1,000,000) = 11.08 GB.

2. Codec Generation and Compression Efficiency

A bitrate of 10 Mbps produced a highly blocky, pixelated image in the late 1990s using MPEG-2 compression. Today, that same 10 Mbps can deliver a pristine, high-dynamic-range (HDR) 4K stream thanks to modern compression standards.

Let's compare the three most common codec standards in digital video:

  • H.264 / AVC (Advanced Video Coding): Released in 2003, H.264 is the most widely compatible video codec in the world. It is highly reliable but requires relatively high bitrates to maintain detail in fast-moving scenes.
  • H.265 / HEVC (High Efficiency Video Coding): Released in 2013, HEVC is twice as efficient as H.264. It allows 4K video to be streamed at half the bandwidth required by H.264, making it the standard for UHD blu-rays and premium streaming services.
  • AV1 (AOMedia Video 1): An open-source, royalty-free codec developed by major tech companies. It is roughly 30% more efficient than HEVC, allowing high-quality streaming at extremely low bitrates, though it requires significant processing power to encode.

Selecting the right combination of bitrate and codec is essential for balancing visual quality, streaming bandwidth, and hardware compatibility.