After reading the base64 wiki … I’m trying to figure out how’s the formula

Question

Editorial Team

Asked: June 14, 20262026-06-14T08:36:01+00:00 2026-06-14T08:36:01+00:00

After reading the base64 wiki …

I’m trying to figure out how’s the formula working :

Given a string with length of n , the base64 length will be enter image description here

Which is : 4*Math.Ceiling(((double)s.Length/3)))

I already know that base64 length must be %4==0 to allow the decoder know what was the original text length.

The max number of padding for a sequence can be = or ==.

wiki :The number of output bytes per input byte is approximately 4 / 3 (33%
overhead)

Question:

How does the information above settle with the output length enter image description here ?

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Editorial Team · Answer 1 · 2026-06-14T08:36:03+00:00

Editorial Team

Each character is used to represent 6 bits (log2(64) = 6).

Therefore 4 chars are used to represent 4 * 6 = 24 bits = 3 bytes.

So you need 4*(n/3) chars to represent n bytes, and this needs to be rounded up to a multiple of 4.

The number of unused padding chars resulting from the rounding up to a multiple of 4 will obviously be 0, 1, 2 or 3.

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