Data Capacity & Calculating Capacity Requirements

Calculating Image Capacity

• Formula: $\text{Size} = \text{Width} \times \text{Height} \times \text{Color Depth (in bits)}$. This calculates the total bits, which must then be divided by 8 to convert to Bytes.
• Application: If an image is $1000 \times 1000$ pixels with 24-bit color, the raw size is $24,000,000$ bits or $3,000,000$ Bytes (3 MB).

Calculating Audio Capacity

• Formula: $\text{Size} = \text{Sample Rate} \times \text{Bit Depth} \times \text{Number of Channels} \times \text{Duration (seconds)}$.
• Application: High-fidelity audio requires higher sample rates and bit depths, significantly increasing the storage footprint per second of playback.

Calculating Video Capacity

• Formula: $\text{Size} = \text{Frame Size (W} \times \text{H)} \times \text{Color Depth} \times \text{Frame Rate} \times \text{Duration}$.
• Note: This formula calculates uncompressed video; in practice, compression algorithms (codecs) are used to reduce these massive requirements by removing redundant data.

• It is critical to distinguish between the Binary (IEC) and Decimal (SI) systems of measurement, as they lead to different capacity expectations.

• Bits vs. Bytes: Always check the casing of the abbreviation; 'b' stands for bits (used for speeds), while 'B' stands for Bytes (used for storage capacity).

• Unit Consistency: Always convert all variables to the same base unit (usually seconds for time and bits for depth) before performing the final multiplication. Mixing minutes and seconds is a frequent source of calculation errors.

• The 'Divide by 8' Rule: Most raw calculations result in bits. Examiners often provide options in Bytes, so remember that the final step in almost every capacity problem is dividing the total bits by 8.

• Sanity Checks: If calculating a small image results in several Gigabytes, re-check your decimal places and unit conversions. A standard uncompressed photo should typically be in the Megabyte range, not Gigabytes.

• Buffer for Growth: In practical capacity planning questions, always add a percentage (often 10-20%) for future growth and system overhead if the question asks for 'required storage' rather than 'file size'.