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 Kibibyte is a binary unit. It is defined as 1024^1 bytes, which equals 1024 bytes. Since 1 Byte = 8 bits, multiply the number of Bytes by 8 to express the value in bits.

$1\,\mathrm{KiB} = 1,024^{1} \,\mathrm{B} \times 8\, = 8,192\,\mathrm{bit}$

One Kilobit is equal to 1000 bits, while one Kibibyte equals 8192 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).

$\dfrac{ 1\,\mathrm{kb} }{ 1\,\mathrm{KiB} } = \dfrac{ 1,000\,\mathrm{bit} }{ 8,192\,\mathrm{bit} } = \dfrac{ 1,000 }{ 8,192 }$

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

$\dfrac{ 1,000 }{ 8,192 } = \dfrac{ 1,000\div 8 }{ 8,192\div 8 } = \dfrac{ 125 }{ 1,024 }$

The exact factor is 125/1024. The decimal result is shown to 30 places or fewer when the division terminates earlier.

$\dfrac{ 125 }{ 1,024 } \approx 0.1220703125$

The conversion factor from Kilobit (kb) to Kibibyte (KiB) is 0.1220703125. Therefore, any value in Kilobit can be converted to Kibibyte by multiplying it by this factor.

$\boxed{ x\,\mathrm{kb} = x\times 0.1220703125\,\mathrm{KiB} }$

Multiply the number of Kilobits by 0.1220703125 to obtain the equivalent value in Kibibytes.