在我看来，正确的公式应该是:

n64 = 4 * (n / 3) + (n % 3 != 0 ? 4 : 0)

当其他人都在讨论代数公式时，我宁愿用BASE64本身来告诉我:

$ echo "Including padding, a base64 string requires four bytes for every three-byte chunk of the original string, including any partial chunks. One or two bytes extra at the end of the string will still get converted to four bytes in the base64 string when padding is added. Unless you have a very specific use, it is best to add the padding, usually an equals character. I added an extra byte for a null character in C, because ASCII strings without this are a little dangerous and you'd need to carry the string length separately."| wc -c

525

$ echo "Including padding, a base64 string requires four bytes for every three-byte chunk of the original string, including any partial chunks. One or two bytes extra at the end of the string will still get converted to four bytes in the base64 string when padding is added. Unless you have a very specific use, it is best to add the padding, usually an equals character. I added an extra byte for a null character in C, because ASCII strings without this are a little dangerous and you'd need to carry the string length separately." | base64 | wc -c

710

因此，3个字节由4个base64字符表示的公式似乎是正确的。

在我看来，正确的公式应该是:

n64 = 4 * (n / 3) + (n % 3 != 0 ? 4 : 0)

我认为给出的答案忽略了原始问题的重点，即需要分配多少空间来适合长度为n字节的给定二进制字符串的base64编码。

答案是((n / 3) + 1) * 4 + 1

这包括填充和终止空字符。如果你在做整数运算，你可能不需要楼层调用。

Including padding, a base64 string requires four bytes for every three-byte chunk of the original string, including any partial chunks. One or two bytes extra at the end of the string will still get converted to four bytes in the base64 string when padding is added. Unless you have a very specific use, it is best to add the padding, usually an equals character. I added an extra byte for a null character in C, because ASCII strings without this are a little dangerous and you'd need to carry the string length separately.

4 * n / 3为无填充长度。

并四舍五入到最接近4的倍数进行填充，因为4是2的幂，可以使用逐位逻辑运算。

((4 * n / 3) + 3) & ~3

对于所有会说C语言的人，看看这两个宏:

// calculate the size of 'output' buffer required for a 'input' buffer of length x during Base64 encoding operation
#define B64ENCODE_OUT_SAFESIZE(x) ((((x) + 3 - 1)/3) * 4 + 1) 

// calculate the size of 'output' buffer required for a 'input' buffer of length x during Base64 decoding operation
#define B64DECODE_OUT_SAFESIZE(x) (((x)*3)/4) 

从这里拍的。