Convert between all 30 SI metric prefixes — from quecto (10⁻³⁰) to quetta (10³⁰) — including the four new 2022 BIPM additions: ronna, quetta, ronto, quecto. Includes real-time converter, unit examples (m/g/Hz/W), all-values panel, and a complete 2500+ word guide to the International System of Units.
30 Prefixes (quecto → quetta)2022 New: Ronna & QuettaReal-Time ConversionUnit Examples ExplorerEtymology of Every Prefix
⇄ SI Prefix Converter
1 kilo = 1,000 base
Formula: value × 10³ ÷ 10⁰ = value × 10³
Step: 1 × 10³ = 1,000 base units
📊 Value in All SI Prefixes (amber border = 2022 new prefix)
🔬 Prefix + Unit Examples Explorer
Select a Base Unit to See Common Prefix Combinations
📖 How to Use This SI Prefix Converter
1
Enter Your Value and Select the Source Prefix
Type your number in the "Value" field. Select the source prefix in "Convert From" — from quecto (10⁻³⁰) at the smallest to quetta (10³⁰) at the largest, including the 2022 BIPM additions. The converter includes the base unit (10⁰ = 1) as a separate option. All 30 prefixes are available simultaneously. Defaults to 1 kilo converting to base.
2
Select the Target Prefix and Read the Result
Choose "Convert To" — the result updates in real time. The result panel shows: the main conversion result, the conversion formula \(V_{target} = V_{source} \times 10^{(a-b)}\) where \(a\) and \(b\) are the exponents, a step-by-step calculation trace, and a scrollable panel of the value in ALL 30 prefixes simultaneously. Click ⇄ to swap direction. Click "Copy Result" to copy to clipboard.
3
Explore Prefix + Unit Combinations
The "Unit Examples Explorer" lets you select a base SI unit (meters, grams, seconds, hertz, watts, joules, pascals, amperes, volts, bytes) and instantly see every meaningful prefix combination — from nm and µm to km and Mm for meters; from mg and µg to kg and Mg for mass; from mHz and kHz to GHz and THz for frequency. This gives practical context for when each prefix is used in real-world science and engineering.
4
Read the Formula, Steps, and Reference Table
Every conversion shows the MathJax-rendered mathematical formula and a step-by-step calculation trace showing how the base-unit intermediate value was computed. Scroll down for the complete 30-prefix reference table including etymology, date of adoption, and usage examples. The MathJax formulas section shows the general conversion formula, the relationship between scientific notation and SI prefixes, and worked examples.
📐 SI Prefix Conversion Formulas — MathJax Rendered
\( \text{where: } V_A = \text{value in prefix A (exponent } a), \quad V_B = \text{value in base unit, } \quad V_C = \text{value in prefix C (exponent } b) \)
The universal formula converts any prefix combination in two steps: (1) multiply the source value by \(10^a\) to get the base (unprefixed) unit value; (2) divide by \(10^b\) (equivalently multiply by \(10^{-b}\)) to convert to the target prefix. Combined: multiply by \(10^{(a-b)}\). If \(a>b\): multiply (going to smaller prefix = more units needed). If \(a<b\): divide (going to larger prefix = fewer units needed). If \(a=b\): no conversion needed. Exponents are integers ranging from –30 (quecto) to +30 (quetta).
Scientific Notation and SI Prefix Equivalence
\( N = m \times 10^n \;,\quad 1 \leq m < 10 \;,\quad n \in \mathbb{Z} \)
\( \text{SI prefix equivalence: } m \times 10^n \equiv (m \times 10^{n-3k}) \;\text{[prefix at }3k\text{]}, \quad k=\text{0,±1,±2,...} \)
\( \text{Choose prefix so that coefficient } m' \text{ lies in } [1,\;1000): \)
The practical rule for choosing the best SI prefix: express the value in scientific notation, then select the prefix \(P\) where the exponent \(n\) satisfies \(3k \leq n < 3(k+1)\) for the main prefixes (k=...,−2,−1,0,1,2,...), giving a coefficient between 1 and 999. This ensures the number is readable without excessive digits. For the "step" prefixes (deci/centi/deka/hecto), the exponents are ±1 or ±2 — useful for everyday units like centimeters and hectoliters but less common in science. Note: for non-multiples-of-3 exponents, multiple valid representations exist; choose the one with the most familiar prefix for the application context.
The "main" SI prefixes (skipping hecto/deka/deci/centi) form a clean ladder where each step is exactly 1,000× (three decimal places, or one order of three zeros). This is why scientists prefer these multiples-of-three prefixes — they match the natural grouping of digits in decimal notation. Moving up one step (e.g., milli→base) multiplies the numerical coefficient by 1,000. Moving down one step (e.g., base→milli) divides by 1,000 (equivalently, multiplies by \(10^{-3}\)). The full chain from quecto to quetta spans 20 steps of ×1,000, covering a total range of \(10^{60}\) — from \(10^{-30}\) to \(10^{30}\).
📋 Complete SI Prefix Reference Table (2026 — 30 Prefixes)
Symbol
Prefix
Power
Factor
Etymology
Adopted
Example Use
⚠️ New 2022 Prefixes — Ronna (R, 10²⁷), Quetta (Q, 10³⁰), Ronto (r, 10⁻²⁷), Quecto (q, 10⁻³⁰): Approved by the 27th General Conference on Weights and Measures (CGPM) on November 18, 2022. These were needed because global data storage is approaching yottabyte (10²⁴) scale, and the mass of Earth (~6 × 10²⁴ kg) caused awkward notation beyond yotta. The symbols R/r and Q/q were chosen because they were not previously used as SI prefix symbols. The names derive from roundo, ronnda, quecture, quecto — informal proposals circulated before BIPM standardization.
💡 Complete Guide to SI Metric Prefixes and the International System of Units
The International System of Units (SI) is the bedrock of modern science, engineering, medicine, and commerce. It is the most universally accepted measurement system in human history — used by 197 countries and nearly every scientific institution, publication, and regulatory body on Earth. At the heart of its power lies a set of standardized prefixes that allow any measurement to be expressed concisely across scales ranging from the subatomic to the cosmological. Understanding SI prefixes is not merely a matter of scientific literacy; it is a practical life skill for anyone who reads a nutrition label (milligrams), chooses a hard drive (terabytes), programs a microcontroller (microseconds), or fills a car with fuel (liters, kilometers).
The metric system — and with it the prefix concept — was born from the chaos of the French Revolution. Before 1793, France alone had over 800 different local units of measurement, making trade, taxation, and scientific communication a nightmare. In 1790, the French National Assembly commissioned the Académie des Sciences to develop a rational, universal measurement system. The result was the metric system, formally introduced in 1795. The key innovation was the decimal structure: every unit differed from adjacent units by a factor of 10 or a power of 10, with systematic Latin and Greek prefixes to denote the scale. The meter was defined as one ten-millionth of the distance from the equator to the North Pole (along the meridian through Paris). The gram was defined as the mass of 1 cubic centimeter of water at 4°C.
The modern SI system (Système International d'Unités) was formally established in 1960 at the 11th General Conference on Weights and Measures (CGPM) in Sèvres, France — the same city where the Bureau International des Poids et Mesures (BIPM) is headquartered. The BIPM, established by the Metre Convention in 1875, is the international authority on measurement standards. The 2019 redefinition of SI units — adopted on World Metrology Day, May 20, 2019 — was the most radical update in the system's history: all seven SI base units (second, metre, kilogram, ampere, kelvin, mole, candela) are now defined by fixing the numerical values of fundamental physical constants (speed of light, Planck's constant, elementary charge, Boltzmann constant, Avogadro's number, luminous efficacy of a specific radiation) rather than physical artifacts. The last physical artifact — the International Prototype Kilogram (IPK), a platinum-iridium cylinder in a triple-locked vault in Sèvres — was retired after 130 years of service.
🔬
SI Prefixes in Modern Physics
Attosecond lasers (10⁻¹⁸ s) probe electron dynamics. Femtosecond pulses (10⁻¹⁵ s) study chemical reactions. Nanometer (10⁻⁹ m) transistors — TSMC's 2 nm node is ~10 silicon atom widths. Picotesla (10⁻¹² T) sensors detect brain magnetic fields (MEG). Megaparsec (3.086×10²² m) describes galaxies. Gigahertz (10⁹ Hz) CPU clocks. Terawatt (10¹² W) is Earth's total human power consumption. Petaflops (10¹⁵ FLOP/s) describe supercomputers. Exajoule (10¹⁸ J) quantifies global annual energy consumption (~580 EJ in 2024).
🏥
SI Prefixes in Medicine & Pharmacy
Microgram (µg, 10⁻⁶ g) — vitamin D supplement dosing (400–2000 IU = ~10–50 µg). Milligram (mg, 10⁻³ g) — most drug dosages (aspirin 325 mg; ibuprofen 200 mg). Nanomolar (nM, 10⁻⁹ mol/L) — receptor binding affinity. Femtogram (fg) — viral load quantification (HIV RNA: <20 copies/mL ≈ 34 fg/mL). Milliliter (mL) — liquid medicine dosing. Centimeter (cm) — wound measurement, organ size. Millimetre of mercury (mmHg) — blood pressure (a non-SI unit still widely used). The FDA and EMA mandate SI units in all drug labeling.
💻
SI vs Binary Prefixes in Computing
SI kilo (k) = 10³ = 1,000. Binary "kilo" (kibi, Ki) = 2¹⁰ = 1,024 — a 2.4% difference. At terabyte scale: SI TB = 10¹² bytes; binary TiB = 2⁴⁰ = 1.0995 × 10¹² bytes (+9.95%). Hard drive makers use SI (1 TB = 10¹² bytes); Windows reports binary GiB. IEC 80000-13 (1998) introduced KiB/MiB/GiB/TiB to eliminate ambiguity. Network speeds use SI: 1 Gbps = 10⁹ bits/sec. RAM uses binary: 16 "GB" DDR5 = 16 × 2³⁰ bytes. CPU frequencies use SI: 4 GHz = 4 × 10⁹ Hz exactly.
🇫🇷
Why the Kilogram Has a Prefix
The kilogram is the only SI base unit whose name contains a prefix — a historical quirk. When the original metric system was defined in 1799, the "grave" (= 1 kg) and "gravet" (= 1 g) were proposed as base units. The grave was renamed kilogram to align with the physical standard (the IPK was a kilogram, not a gram). When SI was formalized in 1960, changing the kilogram to gram would have disrupted all established tables. Consequently, while we say "milligram" and "microgram" (not "microkilogram"), we do NOT say "kilogram" as a prefixed gram in the mathematical sense — it IS the base unit. Prefixes are applied to grams: mg, µg, ng (not mkg, µkg, nkg).
💡 The Right Prefix Matters — Scientific Rule of Thumb: When reporting a measurement, choose the prefix that places the numerical value between 1 and 999 (ideally between 1 and 100). Using 0.000025 meters (25 micrometers) instead of 25 µm is technically correct but scientifically poor practice. Similarly, 1,500,000 Hz is written as 1.5 MHz. This convention reduces transcription errors, aids quick comparison, and is mandated by scientific journals (Nature, Science, Physical Review). The formula: express in scientific notation \(m \times 10^n\), then round \(n\) to the nearest multiple of 3 — the corresponding prefix is your best choice.
📌 Case Sensitivity Rules — Critical for Avoiding Errors: SI prefix symbols are case-sensitive: lowercase 'm' = milli (10⁻³) but uppercase 'M' = mega (10⁶). Writing "5 Mg" means 5 megagrams; "5 mg" means 5 milligrams — a factor of 10⁹ difference. Similarly: 'k' (kilo) vs 'K' (kelvin — a unit, not a prefix); 'G' (giga) vs 'g' (gram — a unit); 'T' (tera) vs 't' (metric ton/tonne — non-SI); 'P' (peta) vs 'p' (pico); 'E' (exa) vs 'e' (not an SI symbol). In medical/pharmaceutical contexts, case errors can cause dosing errors — the reason FDA guidance documents explicitly warn about "mg" vs "Mg" confusion.
N
Written & Reviewed by
Num8ers Editorial Team — Metrology, Physics & International Standards Researchers
Last updated: April 2026 · Sources: Bureau International des Poids et Mesures (BIPM), "The International System of Units (SI)" 9th edition (2019) — brochure.bipm.org/en/publications/si-brochure · BIPM 27th CGPM Resolution 3 (November 18, 2022) — adoption of new SI prefixes ronna (R, 10²⁷), quetta (Q, 10³⁰), ronto (r, 10⁻²⁷), quecto (q, 10⁻³⁰) · IEC 80000-13:2008 — binary prefix standard (KiB, MiB, GiB, TiB) · NIST Special Publication 811 (2008 edition) — "Guide for the Use of the International System of Units" — nist.gov/pml/special-publication-811 · CGPM Resolution, 11th meeting (1960) — establishment of the SI · Law 28 June 1799 ("Loi du 19 frimaire an VIII") — French metric system adoption · Wilkins, J., "An Essay towards a Real Character and a Philosophical Language" (1668) — early metric prefix concept · Mouton, Gabriel, "Observationes diametrorum solis et lunae apparentium" (1670) — first systematic decimal measurement proposal · BIPM 26th CGPM — SI redefinition effective May 20, 2019 (fixing h, e, k, NA, c, ΔνCs, Kcd) · IEEE/ASTM SI 10-2016 — American National Standard for SI usage in technical writing · World Metrology Day, May 20 — anniversary of the Metre Convention (1875). This converter uses IEEE 754 double-precision floating-point arithmetic — sufficient precision for all practical SI prefix conversions within the yocto-to-yotta range.
❓ Frequently Asked Questions — SI Prefixes
What are SI prefixes and why do we need them?
SI (Système International d'Unités) prefixes are standardized multipliers — from quecto (10⁻³⁰) to quetta (10³⁰) — that allow expression of very large or very small quantities without writing out all zeros. The formula: value with prefix = value × 10^(exponent). Without prefixes, the wavelength of green light (5.5 × 10⁻⁷ m = 550 nm) would require awkward scientific notation or long decimal strings. With prefixes: 550 nanometers (nm) is immediately intuitive. The SI prefix system is defined by the BIPM (Bureau International des Poids et Mesures) under the authority of the Metre Convention treaty, signed by 62 nations as of 2024.
How do I convert between SI prefixes?
Universal formula: \(V_{target} = V_{source} \times 10^{(a-b)}\) where \(a\) = source prefix exponent and \(b\) = target prefix exponent. If \(a > b\): multiply (going to a smaller prefix). If \(a < b\): divide (going to a larger prefix).
Examples:
5 km → m: 5 × 10^(3-0) = 5 × 1,000 = 5,000 m.
300 µA → mA: 300 × 10^(-6-(-3)) = 300 × 10⁻³ = 0.3 mA.
2.5 GHz → MHz: 2.5 × 10^(9-6) = 2.5 × 1,000 = 2,500 MHz.
750 nm → µm: 750 × 10^(-9-(-6)) = 750 × 10⁻³ = 0.75 µm.
Mental shortcut: moving up one step (e.g., micro→milli) divides by 1,000; moving down one step multiplies by 1,000.
What do kilo, mega, giga, and tera mean?
kilo (k) = 10³ = 1,000 — from Greek "khilioi" (thousand). 1 kilometer = 1,000 meters. 1 kilogram = 1,000 grams. 1 kilohertz = 1,000 Hz (AM radio uses kHz).
mega (M) = 10⁶ = 1,000,000 — from Greek "megas" (great/large). 1 megawatt = 1,000,000 watts. 1 megahertz = 10⁶ Hz (FM radio uses MHz).
giga (G) = 10⁹ = 1,000,000,000 — from Greek "gigas" (giant). 1 gigahertz = 10⁹ Hz (CPU speed). 1 gigabyte (SI) = 10⁹ bytes.
tera (T) = 10¹² = 1,000,000,000,000 — from Greek "teras" (monster/enormous). 1 terabyte (SI) = 10¹² bytes. Global power generation ≈ 25 terawatts.
What do milli, micro, nano, and pico mean?
milli (m) = 10⁻³ = 0.001 — Latin "mille" (thousand = 1/1000th). 1 millimeter = 0.001 m. 1 milligram = 0.001 g. Common in everyday measurement.
micro (µ) = 10⁻⁶ = 0.000001 — Greek "mikros" (small). Symbol is Greek letter mu (µ). 1 micrometer (µm) = 10⁻⁶ m. Human hair width ≈ 60–100 µm.
nano (n) = 10⁻⁹ = 0.000000001 — Greek "nanos" (dwarf). 1 nanometer = 10⁻⁹ m ≈ 10 hydrogen atoms end-to-end. Modern transistors: 2–5 nm nodes.
pico (p) = 10⁻¹² = 10⁻¹² — Spanish "pico" (tiny amount/beak). 1 picofarad (pF) = 10⁻¹² F. Common in electronic circuit capacitors. 1 picosecond = 10⁻¹² s (ultrafast laser pulses).
What are the four new 2022 SI prefixes?
The 27th General Conference on Weights and Measures (CGPM) approved four new SI prefixes on November 18, 2022:
ronna (R) = 10²⁷ — approximately the mass of Earth in grams (Earth mass ≈ 5.972 × 10²⁴ kg = 5.972 × 10²⁷ g).
quetta (Q) = 10³⁰.
ronto (r) = 10⁻²⁷.
quecto (q) = 10⁻³⁰.
Motivation: global data storage was approaching yottabyte (10²⁴) scale, necessitating larger prefixes. Additionally, the mass of Earth in grams (~6 × 10²⁷ g) required expressions beyond yotta (10²⁴). Symbols R, r, Q, q were chosen because these letters were not previously assigned as SI prefix symbols. These four raise the total count of BIPM-approved prefixes to 28 (30 including base unit steps deka and hecto, and deci and centi).
What is the difference between kilo (SI) and kibi (binary)?
SI kilo (k) = 10³ = 1,000 exactly. Used in physics, chemistry, engineering, network speeds.
Binary kibi (Ki) = 2¹⁰ = 1,024. Defined by IEC 80000-13 (1998). Used for RAM, CPU cache, and computer memory that is naturally addressed in powers of 2.
Difference: 2.4% at kilo scale; 7.4% at giga scale; 9.95% at tera scale; 12.6% at peta scale.
Practical application: A "1 TB" hard drive (decimal SI) = 10¹² bytes. Windows reports in binary: 10¹² / 2³⁰ ≈ 931.32 GiB. A "32 GB" RAM module (binary) = 32 × 2³⁰ = 34,359,738,368 bytes = 34.36 GB (SI). Network speeds ALWAYS use SI: 1 Gbps = exactly 10⁹ bits per second.
Why is the kilogram named with a prefix?
The kilogram is the only SI base unit whose name contains a metric prefix (kilo-) — a historical accident. When the original metric system was designed in 1799, the fundamental mass unit was called the "grave" (later "kilogram") — defined as the mass of 1 liter of water at 4°C. When the gram was introduced as the practical unit, "kilogram" became the official name for the primary standard rather than "gram." When SI was established in 1960, the kilogram was retained as the base unit (not the gram) because the International Prototype Kilogram (IPK) was already the world's mass reference standard. Consequently, all mass prefixes attach to "gram," not "kilogram": milligram (mg), microgram (µg), nanogram (ng), megagram (Mg = 1 tonne). You would never say "microkilogram" — use "microgram."
Can SI prefixes be combined or stacked?
No — SI prefixes may NEVER be combined (stacked). "Millikilogram" is incorrect; the correct term is "gram" (since 1 mg = 0.001 g and 1 kg = 1,000 g, so 1 millikilogram would equal 1 gram). Similarly, "megakilometer" is incorrect; use "gigameter" (Gm). The SI rules (BIPM SI Brochure, 9th ed., Section 3.2) explicitly state: "SI prefix symbols are attached directly to SI unit symbols, without any multiplication sign or space. Multiple prefixes are not allowed." This rule prevents ambiguity — if stacking were allowed, "megamicro" could be interpreted as (10⁶)(10⁻⁶) = 1 (no prefix) or as a new combined unit. The rule is absolute: one prefix, one unit symbol.
How do femto and atto relate to quantum physics?
femto (f) = 10⁻¹⁵ and atto (a) = 10⁻¹⁸ are central to modern quantum physics and ultrafast science:
1 femtometer (fm) = 1 fermi = size of a proton (≈0.87 fm radius). Nuclear physics operates at the femtometer scale.
1 femtosecond (fs) = 10⁻¹⁵ s — timescale of fast chemical bond breaking/forming. Nobel Prize 1999 (Ahmed Zewail) — femtochemistry.
1 attosecond (as) = 10⁻¹⁸ s — timescale of electron motion within atoms. Nobel Prize 2023 (Anne L'Huillier, Pierre Agostini, Ferenc Krausz) — for methods to generate attosecond pulses. "Attophysics" is now a recognized subfield. The shortest controlled laser pulses as of 2024: ~43 attoseconds. An attosecond is to a second what 1 second is to approximately 32 billion years.
What are zepto, yocto, ronto, and quecto used for?
zepto (z) = 10⁻²¹: Mass of a single atom. A carbon-12 atom = 1.993 × 10⁻²⁶ kg = 19.93 zeptograms (zg). Electric charge of quarks: ±1/3 and ±2/3 of an elementary charge = hundreds of zeptocoulombs.
yocto (y) = 10⁻²⁴: Mass of a proton = 1.673 × 10⁻²⁷ kg = 1.673 × 10⁻²⁴ g = 1.673 yoctograms (yg). Also used for neutrino mass upper bound estimates.
ronto (r) = 10⁻²⁷ (NEW 2022): Mass of a neutron = 1.675 × 10⁻²⁷ kg — one of the first real-world applications of this prefix. 1 neutron mass ≈ 1.675 rontograms.
quecto (q) = 10⁻³⁰ (NEW 2022): Mass of an electron = 9.109 × 10⁻³¹ kg = 0.9109 quectograms (qg). This is the most practical application of the quecto prefix — expressing the electron mass without scientific notation.
How do SI prefixes work with watts, joules, and volts?
SI prefixes attach to any SI unit. For power (watts, W):
Milliwatt (mW): LED indicator light, Bluetooth power. Watt (W): smartphone charging, LED bulb. Kilowatt (kW): electric car motor power, household electricity billing (kWh). Megawatt (MW): large power plant output unit. Gigawatt (GW): national grid scale (US generates ≈1,200 GW peak capacity). Terawatt (TW): global human power consumption ≈25 TW. Petawatt (PW): NIF laser peak power ~540 TW; some ultrashort laser pulses reach petawatts for nanoseconds.
For energy (joules, J): millijoule (mJ) surgery lasers; kilojoule (kJ) food energy (1 Calorie = 4.184 kJ); megajoule (MJ) car collision energy; exajoule (EJ) national energy budgets.
