Learning Objectives
  • Calculate the uncompressed size of a bitmap image.
  • Calculate the uncompressed size of a digital sound recording.
  • Convert calculated values between bits, bytes and binary storage units.
  • Use only the data supplied in a question.
  • Show clear working and give the final answer in the requested unit.
Key Terms
Raw file size
The amount of data before compression and usually before extra header information.
Image resolution
Width in pixels multiplied by height in pixels.
Colour depth
Bits stored for each image pixel.
Duration
Length of a sound recording in seconds.
Channel
A separate stream of sound samples, such as left or right; use a channel factor only when supplied or clearly stated.
Summary diagram for 1.11 Image And Sound File Size Calculations
Summary Of The Main Ideas In This Lesson
Image File-Size Formula

An uncompressed bitmap stores a colour code for every pixel. The total number of pixels is width x height. Multiplying by colour depth gives the raw size in bits.

After calculating bits, divide by eight for bytes. Then divide by 1024 for each step to KiB, MiB or larger units. Keep the full value during intermediate steps to avoid rounding errors.

Real image files can contain headers and metadata, but do not add them unless the question supplies their size. Do not apply compression unless the question states a compression ratio or asks about compressed data.

Image size in bits = width x height x colour depth
Image size in bytes = (width x height x colour depth) / 8
Sound File-Size Formula

An uncompressed digital sound recording stores a sample value repeatedly over time. The number of samples is sample rate x duration in seconds. Multiplying by sample resolution gives the raw size in bits for one channel.

If a question states stereo or gives a number of channels, multiply by the channel count. If no channel information is given, use only the values supplied rather than automatically assuming stereo.

Duration must be expressed in seconds. Convert minutes to seconds before multiplying. Then convert the bit result into the requested storage unit.

Sound size in bits = sample rate x sample resolution x duration in seconds x number of channels
For one channel, omit the final channel factor
A Structured Calculation Method

First, identify the correct formula and list the supplied values with units. Second, convert time to seconds where necessary. Third, calculate in bits. Fourth, convert to the required unit using 8 and 1024. Finally, state the answer with its unit and reasonable precision.

Writing a complete formula before substitution helps prevent missing a factor. For image calculations, the common missing factor is either height or colour depth. For sound, it is often duration or sample resolution.

Use exact arithmetic for as long as possible. If a decimal result is unavoidable, round only the final answer and follow any instruction in the question.

Comparing File Sizes

When only one factor changes, the raw file size changes in the same proportion. Doubling colour depth doubles image size. Doubling sample rate doubles sound size. Doubling sound duration doubles size.

Changing both image dimensions has a multiplied effect. Doubling width and height gives four times as many pixels. If colour depth also doubles, the raw size becomes eight times as large.

Ratios can sometimes answer a comparison without calculating both complete files. However, show enough explanation to identify which factors changed.

Checking Whether An Answer Is Reasonable

Check that higher resolution, colour depth, sample rate, sample resolution or duration did not produce a smaller raw file. Check that converting from bits to bytes reduced the numerical value by a factor of eight. Check that converting from bytes to MiB reduced it further.

Estimate the order of magnitude. A multi-megapixel image at 24 bits per pixel should occupy millions of bytes before compression, not a few bytes. A long high-rate recording should normally be larger than a short low-rate recording.

Raw File-Size Formulae
Data Type Formula In Bits
Bitmap image width x height x colour depth
Sound, one channel sample rate x sample resolution x duration
Sound, multiple channels sample rate x sample resolution x duration x channels
Common Conversion Chain
Starting Value Operation Result Unit
Bits Divide by 8 Bytes
Bytes Divide by 1024 KiB
KiB Divide by 1024 MiB
MiB Divide by 1024 GiB
Worked Examples
Bitmap In KiB

Question: Calculate the raw size of a 640 x 480 image with 8-bit colour.

  1. Pixels = 640 x 480 = 307200.
  2. Bits = 307200 x 8 = 2457600.
  3. Bytes = 2457600 / 8 = 307200.
  4. KiB = 307200 / 1024 = 300.

Answer: 300 KiB.

High-Resolution Image In MiB

Question: Calculate the raw size of a 1920 x 1080 image with 24-bit colour.

  1. Bits = 1920 x 1080 x 24 = 49766400.
  2. Bytes = 6220800.
  3. MiB = 6220800 / 1024 / 1024.

Answer: Approximately 5.93 MiB.

Mono Sound In MiB

Question: A mono recording uses 44100 Hz, 16-bit resolution and lasts 30 seconds. Calculate the raw size.

  1. Bits = 44100 x 16 x 30 = 21168000.
  2. Bytes = 2646000.
  3. MiB = 2646000 / 1024 / 1024.

Answer: Approximately 2.52 MiB.

Stereo Sound With Minutes

Question: A stereo recording uses 48000 Hz, 24-bit resolution and lasts 2 minutes. Calculate the raw size in MiB.

  1. Duration = 2 x 60 = 120 seconds.
  2. Bits = 48000 x 24 x 120 x 2 = 276480000.
  3. Bytes = 34560000.
  4. MiB = 34560000 / 1024 / 1024.

Answer: Approximately 32.96 MiB.

Ratio Comparison

Question: Image B has twice the width, twice the height and twice the colour depth of Image A. Compare raw sizes.

  1. Pixel count increases by 2 x 2 = 4.
  2. Bits per pixel increase by 2.
  3. Total factor = 4 x 2.

Answer: Image B has eight times the raw size.

Examination Guidance
  • Write the formula before inserting values.
  • Convert minutes to seconds before a sound calculation.
  • Use 1024, not 1000, for KiB and MiB.
  • Give the answer in the unit requested, even if an earlier unit is a whole number.
  • Do not assume a channel count that is not stated.
Common Mistakes
  • Adding width and height instead of multiplying them.
  • Forgetting to multiply by colour depth or sample resolution.
  • Dividing by 1024 before converting bits to bytes.
  • Using minutes directly with a sample rate measured per second.
  • Rounding each intermediate value and accumulating error.
Knowledge Check

1. Calculate the raw size in bytes of a 320 x 200 image with 4-bit colour.

Answer: 32000 bytes.

2. A mono sound uses 8000 Hz, 8-bit resolution and lasts 10 seconds. Find the size in bytes.

Answer: 80000 bytes.

3. What happens to image size if colour depth changes from 8 to 24 bits?

Answer: It becomes three times as large if resolution is unchanged.

4. What happens to sound size if duration is halved?

Answer: It is halved if all other factors are unchanged.

5. Why should a final answer include its unit?

Answer: The number alone does not show whether it represents bits, bytes, KiB or another quantity.
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