kb to Kib Converter

The Kilobit is a decimal unit. It is defined as 1000^1 bits, which equals 1000 bits.

$1\,\mathrm{kb} = 1,000^{1} \,\mathrm{bit} = 1,000\,\mathrm{bit}$

The Kibibit is a binary unit. It is defined as 1024^1 bits, which equals 1024 bits.

$1\,\mathrm{Kib} = 1,024^{1} \,\mathrm{bit} = 1,024\,\mathrm{bit}$

One Kilobit is equal to 1000 bits, while one Kibibit equals 1024 bits. The conversion factor is obtained by dividing the value of 1 source unit (in bits) by the value of 1 target unit (in bits).

$\dfrac{ 1\,\mathrm{kb} }{ 1\,\mathrm{Kib} } = \dfrac{ 1,000\,\mathrm{bit} }{ 1,024\,\mathrm{bit} } = \dfrac{ 1,000 }{ 1,024 }$

The fraction can be simplified by dividing both the numerator and denominator by 8, giving the exact conversion factor.

$\dfrac{ 1,000 }{ 1,024 } = \dfrac{ 1,000\div 8 }{ 1,024\div 8 } = \dfrac{ 125 }{ 128 }$

The exact factor is 125/128. The decimal result is shown to 30 places or fewer when the division terminates earlier.

$\dfrac{ 125 }{ 128 } \approx 0.9765625$

The conversion factor from Kilobit (kb) to Kibibit (Kib) is 0.9765625. Therefore, any value in Kilobit can be converted to Kibibit by multiplying it by this factor.

$\boxed{ x\,\mathrm{kb} = x\times 0.9765625\,\mathrm{Kib} }$

Multiply the number of Kilobits by 0.9765625 to obtain the equivalent value in Kibibits.