What this calculator does
Engineering notation writes a number as a mantissa between 1 and 1,000 multiplied by 10 raised to a power that is always a multiple of 3, such as 45.6 × 10³ rather than 4.56 × 10⁴. That constraint is the whole point: because SI prefixes (kilo, mega, milli, micro and so on) step in multiples of a thousand, engineering notation lines up exactly with them, while ordinary scientific notation does not.
This differs from plain scientific notation, which only requires the mantissa to sit between 1 and 10 and allows any integer exponent. Scientific notation is more compact on paper, but engineering notation is what electrical, mechanical and other engineers actually work in day to day, because 45.6 × 10³ ohms reads directly as 45.6 kilohms, while 4.56 × 10⁴ ohms needs an extra mental step to get there.
The formula
Take the number, find its order of magnitude, and round the exponent down to the nearest multiple of 3. Dividing the original number by 10 raised to that exponent gives the mantissa, which always lands between 1 and 1,000 (or −1,000 and −1 for negative numbers). Because SI prefixes are also defined in steps of 1,000, the resulting exponent maps directly onto a prefix such as k (kilo, 10³), M (mega, 10⁶) or m (milli, 10⁻³).
| Term | Meaning |
|---|---|
| Mantissa | The leading number in front of the power of 10, kept between 1 and 1,000 in engineering notation. |
| Exponent | The power of 10, constrained to a multiple of 3 (…, −6, −3, 0, 3, 6, 9, …). |
| SI prefix | The standard unit prefix, such as kilo or milli, that corresponds to a given multiple-of-3 exponent. |
The inputs explained
| Field | What to enter |
|---|---|
| Number | The number to convert to engineering notation. Negative numbers and decimals are both accepted. |
When to use it
Reading component values in electronics
Resistor, capacitor and inductor values are almost always quoted with SI prefixes (4.7 kΩ, 100 nF, 10 µH). Engineering notation is the mathematical form that sits directly behind those everyday component labels.
Converting a raw calculation into a labelled unit
A calculation that produces a raw result such as 0.0000456 amps is far more readable once converted to engineering notation, which shows immediately that it is 45.6 microamps.
Standardising figures for a report or spreadsheet
Where scientific notation would leave inconsistent exponents scattered across a table, converting every figure to engineering notation aligns them all on multiples of 3, ready to relabel with a matching SI prefix.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How different numbers convert to engineering notation
A range of numbers spanning several orders of magnitude, each converted to engineering notation.
| Number | Engineering notation | SI prefix |
|---|---|---|
| 45600 | 45.600 × 10³ | k (kilo) |
| 0.0000456 | 45.600 × 10⁻⁶ | µ (micro) |
| 3200000 | 3.200 × 10⁶ | M (mega) |
| 0.075 | 75.000 × 10⁻³ | m (milli) |
| 981 | 981.000 × 10⁰ | none (base unit) |
| 12500000000 | 12.500 × 10⁹ | G (giga) |
Questions
How is engineering notation different from scientific notation?
Scientific notation keeps the mantissa between 1 and 10, so the exponent can be any integer. Engineering notation relaxes the mantissa range to between 1 and 1,000, in exchange for forcing the exponent to always be a multiple of 3, which lines it up with SI prefixes.
Why does the exponent have to be a multiple of 3?
SI prefixes such as kilo, mega, giga, milli and micro are themselves defined in steps of 1,000 (10³). Restricting the exponent to a multiple of 3 means every engineering-notation figure maps directly onto one of those standard prefixes, with no in-between exponents to translate.
What if the exponent falls outside the common SI prefixes?
Standard SI prefixes cover roughly 10⁻²⁴ (yocto) to 10²⁴ (yotta), which handles essentially every practical measurement. A number outside that enormous range will still convert correctly, but the calculator will note that it falls outside the standard prefix table.
Does engineering notation work for negative numbers?
Yes. The sign is kept on the mantissa and does not affect the exponent, so −45,600 converts to −45.6 × 10³, the same magnitude and exponent as the positive case with a negative sign carried through.
For a simpler reference table of powers of 10 without the mantissa or SI prefix step, see the power of 10 calculator. For roots and general scientific notation of a calculation result, see the exponents & roots calculator.