Metric Prefixes Converter
Convert between SI metric prefixes from yocto to yotta or Base Converter.
SI Prefix Reference Table
| Prefix | Symbol | Factor | Power |
|---|---|---|---|
| yotta | Y | 1000000000000000000000000 | 10^24 |
| zetta | Z | 1000000000000000000000 | 10^21 |
| exa | E | 1000000000000000000 | 10^18 |
| peta | P | 1000000000000000 | 10^15 |
| tera | T | 1000000000000 | 10^12 |
| giga | G | 1000000000 | 10^9 |
| mega | M | 1000000 | 10^6 |
| kilo | k | 1000 | 10^3 |
| hecto | h | 100 | 10^2 |
| deka | da | 10 | 10^1 |
| deci | d | 0.1 | 10^-1 |
| centi | c | 0.01 | 10^-2 |
| milli | m | 0.001 | 10^-3 |
| micro | µ | 0.000001 | 10^-6 |
| nano | n | 0.000000001 | 10^-9 |
| pico | p | 0.000000000001 | 10^-12 |
| femto | f | 0.000000000000001 | 10^-15 |
| atto | a | 0.000000000000000001 | 10^-18 |
| zepto | z | 0.000000000000000000001 | 10^-21 |
| yocto | y | 0.000000000000000000000001 | 10^-24 |
Related Converters:
How SI Metric Prefix Conversion Works
The International System of Units (SI) defines 20 metric prefixes that scale a base unit by powers of 10, ranging from yocto (10⁻²⁴) to yotta (10²⁴). To convert between prefixes, you calculate the difference in their powers of 10 and shift the value accordingly. For example, converting from kilo (10³) to milli (10⁻³) means shifting by 10⁶ — so 1 kilometer = 1,000,000 millimeters. These prefixes work with any SI unit: meters, grams, liters, watts, hertz, and more.
Metric Prefix Conversion Formula
Result = Value × 10^(source_power − target_power). Equivalently: convert the value to the base unit first (multiply by 10^source_power), then convert from the base unit to the target prefix (divide by 10^target_power). For example, to convert 5 kilometers to centimeters: 5 × 10^(3−(−2)) = 5 × 10⁵ = 500,000 centimeters.
Worked Example: Convert 2.5 Megabytes to Kilobytes
Mega = 10⁶, Kilo = 10³. Power difference = 6 − 3 = 3. Result = 2.5 × 10³ = 2,500 kilobytes. Another example: Convert 750 nanometers to micrometers. Nano = 10⁻⁹, Micro = 10⁻⁶. Power difference = −9 − (−6) = −3. Result = 750 × 10⁻³ = 0.75 micrometers. This is the wavelength of red light, commonly expressed as either 750 nm or 0.75 µm.
Practical Applications of Metric Prefixes
Everyday life: kilo (kg, km, kW), centi (cm), milli (mL, mm, mg). Computing: giga (GB, GHz), tera (TB), mega (MB, MHz), kilo (KB). Science: nano (nm for light wavelengths, nanoparticles), micro (µm for cells, µs for timing), pico (pF for capacitors, ps for laser pulses). Engineering: mega (MPa for pressure), giga (GW for power plants). Telecommunications: tera (Tbps for fiber optic bandwidth), giga (Gbps for network speeds). Medicine: micro (µg for drug dosages), nano (nm for imaging resolution).
Technical Details
The SI prefix system was established by the General Conference on Weights and Measures (CGPM). The most recent additions were ronna (10²⁷), quetta (10³⁰), ronto (10⁻²⁷), and quecto (10⁻³⁰) in 2022, though this tool covers the traditional 20 prefixes from yocto to yotta. Note that in computing, binary prefixes (kibi, mebi, gibi) defined by IEC 80000-13 use powers of 1024 instead of 1000 — 1 kibibyte (KiB) = 1024 bytes, while 1 kilobyte (kB) = 1000 bytes in strict SI usage. This converter uses strict SI (powers of 10) for all calculations.
Frequently Asked Questions
How many millimeters are in a kilometer? 1 km = 10⁶ mm = 1,000,000 mm. The power difference is 3 − (−3) = 6. What is the difference between mega and giga? Mega is 10⁶ (million) and giga is 10⁹ (billion). 1 gigabyte = 1,000 megabytes in SI terms. Why are there 20 SI prefixes? The prefixes cover a range of 10⁴⁸ (from 10⁻²⁴ to 10²⁴), which spans the scales needed in science — from subatomic particles to astronomical distances. Is "micro" the same as the µ symbol? Yes, the prefix micro is represented by the Greek letter mu (µ). In computing contexts where µ is unavailable, "u" is sometimes used as a substitute (e.g., "uF" for microfarads). What is the smallest SI prefix? Yocto (y) at 10⁻²⁴. One yoctogram is approximately the mass of a single proton.
Solved Examples
Example 1: A pharmaceutical label says a tablet contains 500 µg of vitamin B12. How many milligrams is that? Micro (µ) = 10⁻⁶, milli (m) = 10⁻³. Power difference = −6 − (−3) = −3. Result = 500 × 10⁻³ = 0.5 mg. Answer: 0.5 mg. Example 2: A hard drive is 2 TB. How many GB is that? Tera = 10¹², Giga = 10⁹. Power difference = 12 − 9 = 3. Result = 2 × 10³ = 2,000 GB. Answer: 2,000 GB. Example 3: Visible light has wavelength 550 nm. Express in meters. Nano = 10⁻⁹, base = 10⁰. Result = 550 × 10⁻⁹ = 5.5 × 10⁻⁷ m. Answer: 5.5 × 10⁻⁷ meters. Example 4: A radio station broadcasts at 101.5 MHz. Express in Hz and GHz. MHz to Hz: 101.5 × 10⁶ = 101,500,000 Hz. MHz to GHz: 101.5 × 10⁻³ = 0.1015 GHz. Answer: 101,500,000 Hz = 0.1015 GHz.
Practice Questions
1. Convert 3.5 kilometers to meters. (Answer: 3,500 m) 2. How many micrometers are in 1 millimeter? (Answer: 1,000 µm) 3. Convert 250 mL to liters. (Answer: 0.25 L) 4. Express 4.7 GHz in MHz. (Answer: 4,700 MHz) 5. How many nanograms are in 1 microgram? (Answer: 1,000 ng) 6. Convert 1 pico-farad to femto-farads. (Answer: 1,000 fF)
Common Mistakes to Avoid
The most common error is confusing the direction of multiplication. When converting from a LARGER prefix to a SMALLER prefix (e.g., kilo to milli), the number gets LARGER — multiply by the power difference. Conversely, from a smaller to larger prefix, the number gets smaller. Another frequent mistake is confusing SI prefixes with binary prefixes in computing — 1 kilobyte (SI) = 1000 bytes, but 1 kibibyte (IEC) = 1024 bytes. The difference compounds: 1 TB (SI) = 1,000,000,000,000 bytes, while 1 TiB (binary) = 1,099,511,627,776 bytes (about 10% more). Students often forget that the symbol for micro is the Greek mu (µ), not the letter "u," and that kilo uses lowercase "k" (not capital K, which is reserved for Kelvin). Finally, when chaining conversions, simply add or subtract the exponents rather than converting step-by-step.
Key Takeaways
All SI prefixes represent powers of 10, making conversion a matter of shifting the decimal point. The conversion formula is: Result = Value × 10^(source_power − target_power). Each step of 3 in the exponent represents a factor of 1000 (kilo → mega → giga → tera). Memorize the common ones: kilo=10³, mega=10⁶, giga=10⁹, tera=10¹², milli=10⁻³, micro=10⁻⁶, nano=10⁻⁹. In computing, be careful to distinguish SI prefixes (powers of 1000) from binary prefixes (powers of 1024). These prefixes are universal — they work with any SI base unit (meter, gram, second, ampere, etc.).
SI Prefix History — Origins of the Names
The SI prefix names have fascinating etymological origins spanning Greek, Latin, Italian, and Danish roots. Kilo (10³) comes from the Greek "chilioi" meaning thousand. Mega (10⁶) comes from Greek "megas" meaning great. Giga (10⁹) derives from Greek "gigas" meaning giant. Tera (10¹²) comes from Greek "teras" meaning monster. Peta (10¹⁵) comes from Greek "pente" (five), representing the fifth power of 1000. Exa (10¹⁸) comes from Greek "hexa" (six). On the small side: milli (10⁻³) comes from Latin "mille" meaning thousand (one-thousandth). Micro (10⁻⁶) comes from Greek "mikros" meaning small. Nano (10⁻⁹) comes from Greek "nanos" meaning dwarf. Pico (10⁻¹²) comes from Italian/Spanish "piccolo" meaning small. Femto (10⁻¹⁵) and atto (10⁻¹⁸) come from Danish/Norwegian "femten" (fifteen) and "atten" (eighteen). The original metric prefixes (kilo, hecto, deka, deci, centi, milli) were introduced in 1795 with the metric system in France. Larger and smaller prefixes were added over the following two centuries as science required them, with the most recent additions (ronna, quetta, ronto, quecto) approved in 2022.
Binary vs Decimal Prefixes — The Kibi vs Kilo Confusion
One of the most common sources of confusion in computing is the difference between SI (decimal) prefixes and IEC (binary) prefixes. SI prefixes use powers of 1000: 1 kilobyte (kB) = 1,000 bytes, 1 megabyte (MB) = 1,000,000 bytes, 1 gigabyte (GB) = 1,000,000,000 bytes. Binary prefixes use powers of 1024: 1 kibibyte (KiB) = 1,024 bytes, 1 mebibyte (MiB) = 1,048,576 bytes, 1 gibibyte (GiB) = 1,073,741,824 bytes. The difference compounds at larger scales: 1 TB (SI) = 1,000,000,000,000 bytes, while 1 TiB (binary) = 1,099,511,627,776 bytes — about 10% more. This is why a "1 TB" hard drive shows as ~931 GB in Windows (which historically used binary interpretation). The IEC introduced binary prefixes (kibi, mebi, gibi, tebi) in 1998 to eliminate ambiguity, but adoption has been slow. Storage manufacturers use SI (decimal) values, RAM is measured in binary, and operating systems vary. macOS uses SI since 2009; Windows still uses binary values with SI labels.
Prefix Multiplication Table
Here is every SI prefix with its power of 10, numeric multiplier, and a real-world example: yotta (Y, 10²⁴) — total data created globally per year is ~120 yottabytes. zetta (Z, 10²¹) — global internet traffic is a few zettabytes per year. exa (E, 10¹⁸) — about 5 exabytes would store all words ever spoken by humans. peta (P, 10¹⁵) — Google processes petabytes of data daily. tera (T, 10¹²) — a consumer hard drive holds 1-20 terabytes. giga (G, 10⁹) — smartphone RAM is typically 4-12 gigabytes. mega (M, 10⁶) — a high-resolution photo is 5-30 megabytes. kilo (k, 10³) — a novel is about 500 kilobytes of text. hecto (h, 10²) — rarely used; a hectometer is 100 m. deka (da, 10¹) — rarely used; a dekameter is 10 m. deci (d, 10⁻¹) — a decimeter is 10 cm (hand width). centi (c, 10⁻²) — a centimeter is about the width of a pencil. milli (m, 10⁻³) — a millimeter is the thickness of a credit card. micro (µ, 10⁻⁶) — a human hair is about 70 micrometers wide. nano (n, 10⁻⁹) — a DNA strand is about 2 nanometers wide. pico (p, 10⁻¹²) — a transistor switching time is ~10 picoseconds. femto (f, 10⁻¹⁵) — visible light oscillates every ~2 femtoseconds. atto (a, 10⁻¹⁸) — the time for light to cross an atom is ~100 attoseconds. zepto (z, 10⁻²¹) — used in particle physics experiments. yocto (y, 10⁻²⁴) — the mass of one proton is ~1.67 yoctograms.
Additional Practice Questions
7. Convert 8 gigabytes to megabytes. (Answer: 8,000 MB) 8. How many microliters are in 2.5 milliliters? (Answer: 2,500 µL) 9. Express 0.003 kilometers in millimeters. (Answer: 3,000 mm — kilo to milli is 10⁶) 10. A CPU runs at 3.6 GHz. Express in MHz and Hz. (Answer: 3,600 MHz = 3,600,000,000 Hz) 11. Convert 500 picograms to nanograms. (Answer: 0.5 ng — pico to nano is 10⁻³) 12. How many milliamps (mA) are in 2.2 amps? (Answer: 2,200 mA) 13. A fiber optic cable has 400 Tbps capacity. Express in Gbps. (Answer: 400,000 Gbps) 14. Convert 25 centimeters to micrometers. (Answer: 250,000 µm — centi to micro is 10⁴) 15. Express 1.2 megawatts in kilowatts and watts. (Answer: 1,200 kW = 1,200,000 W)
More Common Mistakes and How to Avoid Them
Confusing milli (m, 10⁻³) with micro (µ, 10⁻⁶): These are 1000× apart. A milligram (mg) is 1000× larger than a microgram (µg). In medicine, confusing the two can be dangerous — always double-check drug dosages. Confusing Mega (M) with milli (m): Capital M means mega (10⁶, one million), while lowercase m means milli (10⁻³, one thousandth). MW (megawatts) vs mW (milliwatts) differ by a factor of 10⁹! The case matters enormously. Confusing Giga with Mega in data plans: 1 GB = 1,000 MB. A "5 GB" data plan is 5,000 MB. If your phone uses 200 MB/day, that lasts 25 days (5000÷200). Forgetting that prefixes are relative to a base unit: You cannot directly convert "meters to grams" using prefixes alone — prefixes only scale within the same unit type. You CAN convert kilometers to millimeters (both length), but not kilograms to kilometers (mass vs. length). The "k" in kilo should be lowercase: Writing "Km" for kilometer is technically incorrect (K = Kelvin). The correct abbreviation is "km" with lowercase k. Similarly, "kg" not "Kg", "kW" not "KW".