What this calculator does
Scientific notation writes any number as a value between 1 and 10 multiplied by a power of ten. It keeps extremely large and extremely small quantities readable, and makes their order of magnitude immediately visible: which is usually the thing that matters when quantities span many powers of ten.
Engineering notation is a variant that restricts the exponent to multiples of three, aligning it with the SI prefixes: kilo, mega, milli, micro. That makes it the more practical form whenever a result will be spoken aloud or labelled on a component.
The formula
The exponent is the number of places the decimal point must move to leave a single non-zero digit before it. Moving left gives a positive exponent, moving right a negative one. Engineering notation then rounds the exponent down to the nearest multiple of three, adjusting the coefficient to compensate.
| Term | Meaning |
|---|---|
| Coefficient | The value between 1 and 10. |
| Exponent | The power of ten. |
| E-notation | The calculator form: 3.45E−4. |
| Engineering notation | Exponent restricted to multiples of three. |
| Order of magnitude | The exponent alone: a rough size class. |
The inputs explained
| Field | What to enter |
|---|---|
| Number | The number to convert. Very large and very small values are exactly what this is for. |
When to use it
Recording scientific measurements
Quantities in physics and chemistry routinely span dozens of orders of magnitude. Scientific notation is the only practical way to write them consistently.
Labelling engineering values
Engineering notation maps directly onto SI prefixes, so 4.7 × 10⁻³ farads is 4.7 millifarads. That is how components are actually marked.
Comparing sizes quickly
The order of magnitude alone often answers the question. Two quantities three orders apart differ by a factor of a thousand, whatever the leading digits are.
Reading calculator output
When a display shows 6.022E23, the E-notation line explains what that means and gives the expanded form.
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.
Small numbers in scientific notation
Small quantities and the notation forms they take.
| Number | Scientific notation | E-notation | Engineering notation | Order of magnitude |
|---|---|---|---|---|
| 0.5 | 5.000 × 10^-1 | 5.000000e-1 | 500.000 × 10^-3 | 10^-1: nearest SI prefix: N/A |
| 0.05 | 5.000 × 10^-2 | 5.000000e-2 | 50.000 × 10^-3 | 10^-2: nearest SI prefix: milli |
| 0.00345 | 3.450 × 10^-3 | 3.450000e-3 | 3.450 × 10^-3 | 10^-3: nearest SI prefix: milli |
| 0.000001 | 1.000 × 10^-6 | 1.000000e-6 | 1.000 × 10^-6 | 10^-6: nearest SI prefix: micro |
| 2e-9 | 2.000 × 10^-9 | 2.000000e-9 | 2.000 × 10^-9 | 10^-9: nearest SI prefix: nano |
Large numbers
Large quantities in the same forms.
| Number | Scientific notation | Engineering notation | Order of magnitude |
|---|---|---|---|
| 1,500 | 1.500 × 10^3 | 1.500 × 10^3 | 10^3: nearest SI prefix: kilo |
| 93,000 | 9.300 × 10^4 | 93.000 × 10^3 | 10^4: nearest SI prefix: kilo |
| 4,200,000 | 4.200 × 10^6 | 4.200 × 10^6 | 10^6: nearest SI prefix: mega |
| 7,500,000,000 | 7.500 × 10^9 | 7.500 × 10^9 | 10^9: nearest SI prefix: giga |
| 300,000,000,000 | 3.000 × 10^11 | 300.000 × 10^9 | 10^11: nearest SI prefix: tera |
Questions
What is standard form?
Another name for scientific notation, used more commonly in British and Australian curricula. Both mean a coefficient between 1 and 10 multiplied by a power of ten.
What is the difference between scientific and engineering notation?
Scientific notation keeps the coefficient between 1 and 10. Engineering notation allows it between 1 and 1000 so the exponent stays a multiple of three, matching the SI prefixes.
What does the E mean on a calculator?
It is shorthand for "times ten to the power of". 6.022E23 means 6.022 × 10²³. It exists because calculator displays cannot easily show superscripts.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. For division, divide the coefficients and subtract the exponents. Then adjust so the coefficient falls back between 1 and 10.
What is an order of magnitude?
A factor of ten. Two quantities differing by three orders of magnitude differ by a factor of a thousand. It is a deliberately rough measure, useful precisely because it ignores the detail.
For powers and roots, see the exponent calculator. For controlling precision, use rounding and significant figures.