Base64 Algorithm Explained

How Does the Base64 Encoding Algorithm Work?

The Base64 algorithm converts binary data to printable text in 4 steps: (1) read 3 input bytes (24 bits), (2) split the 24 bits into four 6-bit groups, (3) map each 6-bit value (0-63) to a character from the Base64 alphabet, (4) output 4 characters. The algorithm repeats this process for every 3-byte block in the input data.

The algorithm is defined in RFC 4648 Section 4. It uses an alphabet of 64 printable ASCII characters: A-Z (indices 0-25), a-z (indices 26-51), 0-9 (indices 52-61), + (index 62), and / (index 63). The equals sign (=) serves as the padding character when the input length is not a multiple of 3. For the complete character-to-index mapping, see the Base64 character table.

The algorithm is stateless: each 3-byte block is processed independently, with no information carried between blocks. This property makes the algorithm simple to implement and allows parallel processing of large inputs. Both encoding and decoding follow the same block-based structure, making the process fully reversible. Try encoding text with the Base64 text encoder to see the algorithm in action.

What Is the Step-by-Step Base64 Encoding Process?

The following example traces the encoding of the string "Man" through every step of the Base64 algorithm. The input consists of 3 ASCII characters, which is exactly one complete block.

Step 1: Determine the ASCII decimal value of each input character.

Step 2: Convert each decimal value to its 8-bit binary representation.

Step 3: Concatenate all binary values into a single 24-bit string.

Step 4: Split the 24-bit string into four 6-bit groups.

Step 5: Convert each 6-bit group to its decimal value (the Base64 index).

Step 6: Map each index to the corresponding Base64 character.

Binary concatenation: 01001101 + 01100001 + 01101110 = 010011 010110 000101 101110

Result: "Man" encodes to "TWFu". The 3 input bytes (24 bits) produce exactly 4 output characters (4 x 6 = 24 bits). No padding is needed because the input length divides evenly by 3. For more encoding examples, see the Base64 encoding guide.

How Does Base64 Padding Work?

Base64 padding handles input whose byte count is not divisible by 3. The algorithm adds zero-bits to complete the final 6-bit group, then appends = characters to make the output length a multiple of 4. The number of padding characters tells the decoder how many trailing bytes to discard.

Padding Case 1: Two Remaining Bytes

When 2 bytes remain after processing all complete 3-byte blocks, the algorithm pads the binary with 2 zero-bits, produces 3 Base64 characters, and appends one =.

Example: encoding "Ma"

Padding Case 2: One Remaining Byte

When 1 byte remains, the algorithm pads the binary with 4 zero-bits, produces 2 Base64 characters, and appends two = characters.

Example: encoding "M"

Padding Summary

Use the Base64 validator to check whether a string has correct padding and valid characters.

How Does Base64 Decoding Work?

Base64 decoding reverses the encoding process in 4 steps: (1) map each Base64 character to its 6-bit index value using the alphabet lookup table, (2) concatenate all 6-bit values into a continuous binary string, (3) split the binary string into 8-bit groups (bytes), (4) convert each byte to its original value. Padding characters (=) are ignored during decoding.

Example: decoding "TWFu" back to "Man"

The decoding process is deterministic and lossless. The same Base64 input always produces the same binary output. Decode any Base64 string using the Base64 text decoder.

What Is the Mathematical Formula for Base64 Output Length?

The encoded output length follows a formula based on the input byte count. The formula accounts for the 3-to-4 byte ratio and the padding requirement that output length must be a multiple of 4.

Encoded length = ceil(input_bytes / 3) * 4

As input size increases, the overhead ratio approaches the theoretical minimum of 33.3% (the 4/3 ratio). For small inputs (1-2 bytes), the overhead is disproportionately large due to the padding requirement. Calculate exact sizes for your data using the Base64 size calculator.

How Does the Base64 Algorithm Handle Different Data Types?

The Base64 algorithm operates on raw bytes and does not distinguish between data types. Text, images, audio, video, and any other file format are all treated as sequences of bytes. The algorithm reads bytes, splits bits, maps to characters, and outputs text regardless of what the bytes represent.

The difference between encoding text and encoding binary files lies in the pre-processing step. Text must first be converted to bytes using a character encoding such as UTF-8 or ASCII. Binary files (images, PDFs, executables) are already byte sequences and require no pre-processing. The Base64 algorithm receives the same type of input in both cases: an array of bytes.

Encode images using the Base64 image encoder or encode other file types with the Base64 file encoder. Both tools apply the same underlying algorithm to different input sources.

What Is the Time Complexity of Base64 Encoding?

The Base64 encoding and decoding algorithms run in O(n) time, where n is the number of input bytes. Each byte requires a constant number of operations: bit extraction via shifting, array lookup for character mapping, and character output. No comparisons, sorting, or recursive operations are involved.

The space complexity is also O(n). The output size is always ceil(n/3) * 4 characters, which is linearly proportional to the input size. Streaming implementations process fixed-size chunks (typically 3 bytes at a time) and require only O(1) additional memory beyond the input and output buffers.

The linear time complexity means doubling the input size doubles the processing time. A 1MB file encodes in approximately the same time as two sequential 500KB files. Modern hardware encodes Base64 at speeds exceeding 1GB per second using optimized SIMD instructions. For a broader understanding of Base64 and its properties, see What is Base64 Encoding.

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