Metric Prefix Converter
Convert a value between metric prefixes, from nano to tera. Enter the value, then choose its current prefix and the prefix you want to convert to.
Metric Unit Scale Converter
Metric Prefix Formula
Where:
- \(V_{\mathrm{from}}\) — the value entered in the starting prefix.
- \(V_{\mathrm{to}}\) — the converted value in the target prefix.
- \(e_{\mathrm{from}}\) and \(e_{\mathrm{to}}\) — the powers of ten represented by the starting and target prefixes; the unprefixed base unit has exponent zero.
Each prefix scales the same underlying unit by a power of ten. The formula converts the entered value to the unprefixed unit, then expresses it using the target prefix.
Metric Prefix – Calculation Example
Example: with the default settings, convert 1 base unit to kilo-units. The base unit has exponent 0, and kilo has exponent 3.
\[1\times\frac{10^0}{10^3}=0.001\]
Result: 1 base unit equals 0.001 kilo-units. For example, 1 meter equals 0.001 kilometers.
How to use the calculator
- Enter a nonnegative number in Value.
- Choose its current scale under From prefix. Select Base Unit if the unit has no prefix.
- Choose the desired scale under To prefix. The Converted Value shows how many units with that prefix equal the amount you entered.
Keep the underlying unit the same in both selections. For example, choose milli and kilo to convert millimeters to kilometers, or milliwatts to kilowatts. The calculator does not ask which unit you are using because the prefix calculation is identical in both cases.
What metric prefixes mean
A metric prefix changes the size of a unit by a stated power of ten. Kilo means 1,000 times the unprefixed unit, while milli means one-thousandth of it. Thus, 1 kilometer is 1,000 meters, and 1 millimeter is 0.001 meters. Moving between prefixes changes the number used to describe an amount, not the amount itself.
The direction of conversion matters. If the target unit is larger, fewer of those units are needed, so the converted number becomes smaller. If the target unit is smaller, the converted number becomes larger. For instance, 2.5 kilograms equals 2,500 grams; going the other way, 2,500 grams equals 2.5 kilograms.
The calculator supports the prefixes in the table below. Prefix symbols are case-sensitive: lowercase m means milli, while uppercase M means mega. The symbol for micro is μ, and deca uses two letters, da.
Supported metric prefixes
| Prefix | Symbol | Multiplier |
|---|---|---|
| Nano | n | \(10^{-9}\) |
| Micro | μ | \(10^{-6}\) |
| Milli | m | \(10^{-3}\) |
| Centi | c | \(10^{-2}\) |
| Deci | d | \(10^{-1}\) |
| Base Unit | — | \(10^0\) |
| Deca | da | \(10^1\) |
| Hecto | h | \(10^2\) |
| Kilo | k | \(10^3\) |
| Mega | M | \(10^6\) |
| Giga | G | \(10^9\) |
| Tera | T | \(10^{12}\) |
Assumptions and practical limits
This is a prefix converter, not a general unit converter. It can convert centimeters to kilometers because both are lengths measured in meters. It cannot convert meters to feet, or watts to joules. For a conversion between different length units, use the Meters to Feet calculator.
The listed multipliers apply directly when the prefix is attached to a unit of the quantity being converted, such as meters, grams, or hertz. Squared and cubed units need additional care: 1 square kilometer is \((1{,}000\text{ meters})^2\), or 1,000,000 square meters—not 1,000 square meters. If you are converting area or volume, account for the exponent on the entire unit.
The displayed result is rounded to six decimal places. A very small nonzero result may therefore appear as zero; convert in the opposite direction or calculate from the formula when more precision is needed. The available range runs from nano through tera, so prefixes outside that range are not selectable.
Metric prefixes represent powers of ten. Digital storage can also use binary-based units, which follow different multipliers; use the Digital Storage converter when those distinctions matter. For conversions between units of frequency rather than just their prefixes, see the Frequency converter.
Frequently Asked Questions
How can I convert metric prefixes by hand?
Write each prefix as a power of ten, then subtract the target exponent from the starting exponent. Move the decimal point by that many places: right for a positive difference, left for a negative one. For example, micro is \(10^{-6}\) and milli is \(10^{-3}\), so 750 micro-units equal \(750\times10^{-3}=0.75\) milli-units.
How many micrograms are in a milligram?
One milligram equals 1,000 micrograms. Milli means \(10^{-3}\) of a gram, while micro means \(10^{-6}\) of a gram. The three-exponent difference gives a factor of \(10^3\). In the other direction, divide micrograms by 1,000 to get milligrams. For medication amounts, always check the unit on the label before converting.
Why is kilogram the SI base unit of mass if kilo is a prefix?
The kilogram is an unusual case: it is the SI base unit of mass even though its name contains a prefix. For ordinary prefix conversions, use grams as the unprefixed unit. Select kilo for kilograms and Base Unit for grams; selecting Base Unit for kilograms would give an incorrect result.
Is there a best metric prefix to use?
There is no universally best prefix; choose one that makes the number easy to read and suits the context. A distance of 0.000002 meters is often clearer as 2 micrometers, while 2,000 meters is often clearer as 2 kilometers. Scientific fields may have established conventions, so use the unit expected by your audience.
Can I use metric prefixes to convert milliseconds to minutes?
Not by prefix conversion alone. Milli scales seconds, but a minute is 60 seconds rather than a prefixed second. First convert milliseconds to seconds by dividing by 1,000, then divide by 60 to get minutes. For example, 120,000 milliseconds equal 120 seconds, or 2 minutes.
What happens if I confuse m (milli) with M (mega)?
The answer changes by a factor of one billion. Milli (m) means \(10^{-3}\), whereas mega (M) means \(10^6\); their exponents differ by nine. For example, 1 milliwatt is 0.001 watt, but 1 megawatt is 1,000,000 watts. Check capitalization carefully when copying unit symbols.
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