Calculate an uncompressed image size with stated assumptions

To find the size of an uncompressed image, multiply the number of pixels by the number of bits each pixel uses: size in bits = width × height × colour depth. This appears whenever a question gives you a resolution and a colour depth and asks how much storage the picture needs.

It builds directly on bit depth from the previous module and is the first lesson in images, sound and storage.

Why does the answer need assumptions?

A bitmap image is a grid of pixels, and each pixel stores one colour as a binary number. The number of bits per pixel is the colour depth. More bits per pixel allow more colours, but the image needs more storage.

The formula gives the size of the pixel data only. A real file also stores the width, height and other details, and may be compressed. So write the assumptions you are making, for example “assuming no compression and ignoring file metadata”.

How do you calculate it, step by step?

1. Find the pixel count: width × height.
2. Find the bits per pixel. If you are given a number of colours, work out the smallest bit depth that can hold them (2^bits ≥ colours).
3. Multiply: pixels × bits per pixel gives the size in bits.
4. Convert: divide by 8 for bytes, then use the stated convention for larger units (see converting storage units).
5. State the assumption and give the unit.

The same method as Cambridge-style pseudocode:

INPUT Width, Height, Depth
Bits ← Width * Height * Depth
Bytes ← Bits / 8
OUTPUT Bytes

Trace with Width = 800, Height = 600, Depth = 8: Bits = 800 × 600 × 8 = 3 840 000, so Bytes = 480 000.

Worked example

A photo is 1 024 pixels wide and 768 pixels high with a 24-bit colour depth. Give the uncompressed size in bytes and in KiB (1 KiB = 1 024 bytes).

Step 1, pixels: 1 024 × 768 = 786 432.

Step 2, bits: 786 432 × 24 = 18 874 368 bits.

Step 3, bytes: 18 874 368 ÷ 8 = 2 359 296 bytes.

Step 4, KiB: 2 359 296 ÷ 1 024 = 2 304 KiB (which is 2.25 MiB).

Check by another route: 24 bits is 3 bytes, so 786 432 × 3 = 2 359 296 bytes. Both routes agree.

Assumption: no compression and no metadata, so the real file would be slightly larger or, if compressed, much smaller.

The mistake to watch for

A common slip is to use the number of colours as the bit depth.

Mistaken answer: An image is 640 × 480 with 256 colours. Size = 640 × 480 × 256 = 78 643 200 bits.

The student used 256 where the number of bits was needed.

The correction: 256 colours need 8 bits, because 2⁸ = 256. So size = 640 × 480 × 8 = 2 457 600 bits = 307 200 bytes. The wrong answer was 32 times too large, which a quick reasonableness check would reveal.

Check yourself

Show every step, then open each answer.

1. An image is 100 pixels wide and 50 pixels high with a 4-bit colour depth. How many bytes does it need?

2. An image of 640 × 480 pixels uses 16 colours. Give its uncompressed size in KiB.

3. A black-and-white image is 8 × 8 pixels. How many bytes does it need, and what bit depth did you assume?

Where this leads next

Sound is stored by the same kind of reasoning, so continue with calculating a sampled audio size. When you can do both without hesitation, test them in the practice set. The Python reasoning sandbox is a good place to turn the formula into code and check your arithmetic.

Some students follow every step here but lose marks because they forget to state the assumption or divide by 8. That is the kind of pattern our teachers look for in online one-to-one Computer Science tuition.