Perform calculations to estimate the file size for a bitmap image

1.2 Multimedia – Estimating Bitmap Image File Size

Learning Objective

Perform calculations to estimate the file size for a bitmap (raster) image.

Key Concepts

• Resolution: Number of pixels in the horizontal and vertical directions (e.g., 1920 × 1080).
• Colour depth (bits per pixel): Number of bits used to represent the colour of a single pixel.
• Uncompressed bitmap size: Calculated directly from resolution and colour depth.
• Compression: Reduces file size but is not considered in the basic estimation.

Formula for Uncompressed Bitmap Size

The size \$S\$ (in bits) of an uncompressed bitmap image is given by:

\$S = \text{horizontal pixels} \times \text{vertical pixels} \times \text{bits per pixel}\$

To convert bits to more convenient units:

• 1 byte = 8 bits
• 1 kilobyte (KB) = 1024 bytes
• 1 megabyte (MB) = 1024 KB
• 1 gigabyte (GB) = 1024 MB

Step‑by‑Step Calculation

1. Determine the image resolution (width × height).
2. Identify the colour depth (bits per pixel). Common values:

   • 1‑bit (black & white)
   • 8‑bit (256 colours)
   • 24‑bit (true colour, 16.7 million colours)
   • 32‑bit (true colour + alpha channel)

3. Apply the formula \$S = w \times h \times b\$ to obtain the size in bits.
4. Convert bits to bytes, then to KB/MB/GB as required.

Worked Example

Estimate the file size of a 1280 × 720 pixel photograph stored as a 24‑bit true‑colour bitmap.

1. Resolution: \$w = 1280\$, \$h = 720\$.
2. Colour depth: \$b = 24\$ bits.
3. Calculate bits:

   \$S = 1280 \times 720 \times 24 = 22\,118\,400\ \text{bits}\$

4. Convert to bytes:

   \$\frac{22\,118\,400}{8} = 2\,764\,800\ \text{bytes}\$

5. Convert to megabytes:

   \$\frac{2\,764\,800}{1024 \times 1024} \approx 2.64\ \text{MB}\$

Therefore, the uncompressed bitmap would be roughly 2.64 MB.

Summary Table

Practice Questions

1. Calculate the uncompressed file size of a 1024 × 768 image using a 32‑bit colour depth. Express your answer in megabytes (MB) to two decimal places.
2. A digital camera saves photos as 24‑bit bitmaps with a resolution of 4000 × 3000 pixels. What is the file size in gigabytes (GB)? (Round to two decimal places.)
3. If you reduce the colour depth of a 640 × 480 image from 24‑bit to 8‑bit, by what factor does the file size decrease?

Answers (for teacher reference)

1. \$S = 1024 \times 768 \times 32 = 25\,165\,824\ \text{bits}\$

   \$\text{Bytes} = \frac{25\,165\,824}{8} = 3\,145\,728\$

   \$\text{MB} = \frac{3\,145\,728}{1024^2} \approx 3.00\ \text{MB}\$

2. \$S = 4000 \times 3000 \times 24 = 288\,000\,000\ \text{bits}\$

   \$\text{Bytes} = 36\,000\,000\$

   \$\text{GB} = \frac{36\,000\,000}{1024^3} \approx 0.03\ \text{GB}\$

3. Size ratio = \$\frac{24}{8} = 3\$. The file size becomes one‑third of the original (a reduction factor of 3).