Metric prefixes are words placed in front of a unit to multiply it by a power of ten: kilo means 1,000, mega a million, milli one-thousandth and micro one-millionth. So 4.7 kilometers is 4,700 meters, and 350 milligrams is 0.35 grams. To convert between prefixes, subtract their exponents and move the decimal point that many places.
The system is the same for every unit, which is its great strength. Once you know that milli means 10⁻³, you know what a millimeter, milliliter, milligram, millisecond and milliamp are.
The SI prefix chart
| Prefix | Symbol | Factor | US name |
|---|---|---|---|
| quetta | Q | 10³⁰ | nonillion |
| ronna | R | 10²⁷ | octillion |
| yotta | Y | 10²⁴ | septillion |
| zetta | Z | 10²¹ | sextillion |
| exa | E | 10¹⁸ | quintillion |
| peta | P | 10¹⁵ | quadrillion |
| tera | T | 10¹² | trillion |
| giga | G | 10⁹ | billion |
| mega | M | 10⁶ | million |
| kilo | k | 10³ | thousand |
| hecto | h | 10² | hundred |
| deca | da | 10¹ | ten |
| (base unit) | 10⁰ | one | |
| deci | d | 10⁻¹ | tenth |
| centi | c | 10⁻² | hundredth |
| milli | m | 10⁻³ | thousandth |
| micro | µ | 10⁻⁶ | millionth |
| nano | n | 10⁻⁹ | billionth |
| pico | p | 10⁻¹² | trillionth |
| femto | f | 10⁻¹⁵ | quadrillionth |
| atto | a | 10⁻¹⁸ | quintillionth |
| zepto | z | 10⁻²¹ | sextillionth |
| yocto | y | 10⁻²⁴ | septillionth |
| ronto | r | 10⁻²⁷ | octillionth |
| quecto | q | 10⁻³⁰ | nonillionth |
The four outermost prefixes, ronna, quetta, ronto and quecto, were added by the General Conference on Weights and Measures (CGPM) in 2022. The official definitions are published by the International Bureau of Weights and Measures (BIPM) and, for the US, by NIST.
The US names use the short scale, where a billion is 10⁹. Several European languages use the long scale, in which “billion” means 10¹² and 10⁹ is “a thousand million.” Prefixes avoid that ambiguity entirely: giga is 10⁹ in every language, which is one reason scientists prefer them to number words.
Away from the middle of the table, prefixes step by a factor of 1,000. Only hecto, deca, deci and centi break that pattern, and of those, only centi is common (centimeter, centiliter).
How to convert between prefixes
Here p is the prefix’s exponent (3 for kilo, −3 for milli, 0 for no prefix).
- Look up the exponents of the starting and ending prefixes.
- Subtract: old exponent minus new exponent.
- Move the decimal point that many places: right if the result is positive, left if negative.
4.7 km to m: 3 − 0 = 3 → move right 3 → 4,700 m
350 mg to g: −3 − 0 = −3 → move left 3 → 0.35 g
2.5 µF to nF: −6 − (−9) = 3 → move right 3 → 2,500 nF
2,500,000 mm to km: −3 − 3 = −6 → move left 6 → 2.5 km
A sanity check: converting to a smaller unit always gives a bigger number, and vice versa. There are more millimeters than meters in any length.
The staircase method
Many students learn the prefixes from kilo down to milli as a staircase: kilo, hecto, deca, base, deci, centi, milli. Each step down multiplies by 10, and each step up divides by 10. A classroom mnemonic helps with the order: “King Henry Died By Drinking Chocolate Milk.” The staircase works for these seven prefixes; beyond them, remember that the steps become jumps of 1,000.
The metric prefix converter does the exponent arithmetic for any pair of prefixes.
Squared and cubed units
This is where most conversion errors happen. When a unit is squared or cubed, the prefix factor is squared or cubed too.
| Conversion | Linear factor | Area factor | Volume factor |
|---|---|---|---|
| m ↔ cm | 100 | 10,000 | 1,000,000 |
| m ↔ mm | 1,000 | 1,000,000 | 1,000,000,000 |
| km ↔ m | 1,000 | 1,000,000 | 1,000,000,000 |
So a 3 m × 4 m room is 12 m², which is 120,000 cm², not 1,200 cm². Useful volume equivalences follow from this:
- 1 cm³ = 1 mL
- 1 dm³ = 1 L
- 1 m³ = 1,000 L
For area, the hectare (10,000 m², a square 100 m on each side) is the standard land unit, and 1 km² = 100 hectares. The area converter and volume converter apply the squared and cubed factors automatically.
Rules for writing prefixes
- Case matters. M (mega) and m (milli) differ by 10⁹. Kilo is lowercase k; K is the symbol for kelvin.
- Micro is µ. When that symbol is unavailable, “u” is a common substitute (uF for µF), and “mc” is used in medicine to avoid confusion with “m.”
- No double prefixes. Write ns, not mµs.
- Mass prefixes attach to the gram. The kilogram is the SI base unit, but a thousandth of a kilogram is a gram and a millionth is a milligram.
- Leave a space between number and unit, as in 5 km, per SI style.
Everyday examples
| Quantity | Value | In base units |
|---|---|---|
| Processor clock | 3.2 GHz | 3,200,000,000 Hz |
| Power plant output | 1.2 GW | 1,200,000,000 W |
| Phone charger | 2 A at 5 V | 10 W |
| Capacitor | 0.47 µF | 0.000 000 47 F |
| Human hair width | about 70 µm | 0.000 07 m |
| Visible light wavelength | 400 to 700 nm | 0.000 000 4 to 0.000 000 7 m |
| Vitamin dose | 600 µg | 0.000 6 g |
Engineering work often keeps exponents in multiples of three so they line up with prefixes, as explained in how to write scientific notation; the scientific notation converter switches between the forms.
Binary prefixes for computer memory
Computing borrowed the decimal prefixes but sometimes uses them for powers of 2, so a “kilobyte” may mean 1,000 or 1,024 bytes. The IEC defined separate binary prefixes (kibi, mebi, gibi, tebi) to remove the ambiguity. The difference grows with each step, reaching about 10% at the tera level, which is why a 1 TB drive shows up as about 931 GB on some computers. The full explanation is in data storage units explained, and the data storage converter handles both systems.
For converting between metric and US units rather than between prefixes, use the length converter or see how to convert cm to feet and inches.
Frequently asked questions
What are the metric prefixes in order?
From largest to smallest, the common ones are tera (10¹²), giga (10⁹), mega (10⁶), kilo (10³), hecto (10²), deca (10¹), then the base unit, deci (10⁻¹), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹) and pico (10⁻¹²). The full SI list runs from quecto (10⁻³⁰) to quetta (10³⁰).
How do you convert between metric prefixes?
Subtract the exponents of the two prefixes and move the decimal point that many places. Going to a smaller prefix makes the number larger. For example, kilo (10³) to milli (10⁻³) is a difference of 6, so 4.7 km = 4,700,000 mm.
What is the newest metric prefix?
Ronna (10²⁷), quetta (10³⁰), ronto (10⁻²⁷) and quecto (10⁻³⁰) were adopted by the General Conference on Weights and Measures in November 2022, the first additions since 1991.
Why is the kilogram the base unit if it has a prefix?
For historical reasons, the SI base unit of mass is the kilogram, but prefixes are always attached to the gram. So a millionth of a kilogram is a milligram, not a microkilogram.
Does capitalization matter in metric prefixes?
Yes. M is mega (a million) and m is milli (a thousandth), so MW and mW differ by a factor of a billion. Kilo is always a lowercase k.