Text & Writing
Output length from input length
Each group of three input bytes becomes four output characters, and the final partial group is padded, so the length is always a multiple of four.
The Formula
Base64 characters = 4 x ceil(bytes / 3)
Each group of three input bytes becomes four output characters, and the final partial group is padded, so the length is always a multiple of four.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| n | Input bytes | bytes | The size of the data in bytes. |
| L | Output length | characters | How many Base64 characters the result contains. |
What Each Symbol Means
nbytes
Input bytes
The size of the data in bytes.
Lcharacters
Output length
How many Base64 characters the result contains.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to encode text to base64 page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Encode Text To Base64, filed under Everyday Life. Every number the guide produces comes from substituting into this one line.