Metric Prefix Converter

Shifts a numeric value between SI prefixes from yocto (10⁻²⁴) up to yotta (10²⁴). Internally the input is normalized to the unprefixed base, then scaled by the difference between source and target exponents.

The 2009-added prefixes ronna/ronto and quetta/quecto are included for completeness.

The full set of decimal SI prefixes spans 60 orders of magnitude (10⁻³⁰ to 10³⁰). Prefix symbols use single uppercase letters at and above 10⁶ (M, G, T, P, E, Z, Y, R, Q) and lowercase at and below 10³ (m, μ, n, p, f, a, z, y, r, q), with kilo (k) as the lone lowercase exception at 10³. The mixed-case rule is convention rather than physics, established by the CGPM to disambiguate unit symbols (mm = millimeter; Mm = megameter). The newest pair, ronna/quetta and ronto/quecto, were adopted at the 27th CGPM in November 2022 to give a name to the rapidly growing scale of global data storage and the diminishing scale of subatomic measurements.

A worked example: a 5 GHz processor clock equals 5×10⁹ Hz, which the converter restates as 5,000 MHz, 0.005 THz, or 5,000,000 kHz. A 2 TB hard drive holds 2×10¹² bytes (using SI convention), 2,000,000 MB, or 0.002 PB. The arithmetic is a single power-of-ten shift and is exact within double-precision representation up to about 10¹⁵; beyond that, scientific notation preserves precision while the integer form loses trailing digits.

Limitations are mostly about the binary/decimal distinction and units of information. The IEC binary prefixes (kibi, mebi, gibi, etc., based on powers of 1024) are not included here; this converter handles only decimal SI. A '2 GB' file in the SI sense is 2,000,000,000 bytes; in the binary sense it is 2,147,483,648 bytes. RAM advertising historically uses binary, storage uses decimal, and the discrepancy still confuses end users at every product launch. Very small or very large values can fall outside the supported prefix range or below the precision floor of IEEE 754 doubles.

The mu (μ) prefix for micro is technically the Greek letter, not the Latin u, though most ASCII contexts substitute u for compatibility. The converter accepts both as input and emits the Greek letter on output where the document encoding supports it.