Engineering Notation Calculator
Enter any number in decimal or scientific notation and this calculator instantly converts it to engineering notation (exponent restricted to multiples of 3), shows the matching SI prefix (kilo, mega, nano, pico, and all others), and also outputs standard scientific notation, E-notation, and expanded decimal form. Choose arithmetic mode to add, subtract, multiply or divide two numbers and see all result formats at once.
What is engineering notation?
Engineering notation is a form of scientific notation in which the exponent of 10 is always a multiple of 3: ..., -9, -6, -3, 0, 3, 6, 9, .... That constraint means the mantissa (the number out front) is always between 1 and 999.9 rather than between 1 and 9.9. The payoff is direct alignment with the named SI prefixes: 10^3 is kilo, 10^6 is mega, 10^9 is giga, 10^-3 is milli, 10^-6 is micro, and so on all the way to quetta and yocto at the extremes. Engineers and scientists use it constantly because a capacitor labeled "220 pF" is far more readable on a schematic than one labeled "2.2 x 10^-10 F".
How to convert a number to engineering notation
Start with the number in any form. Find the base-10 exponent by computing the floor of log10 of the absolute value. Round that exponent down to the nearest multiple of 3 - that is the engineering exponent. Divide the original number by 10 raised to that exponent to get the mantissa. For example, 65,000 has log10(65000) = 4.81, so the raw exponent is 4. Round 4 down to 3 (the nearest multiple of 3 that does not exceed 4). The engineering exponent is 3, the mantissa is 65000 / 10^3 = 65, and the result is 65 x 10^3, or 65 kilo in SI prefix form. For 0.000047: log10(0.000047) is about -4.33, raw exponent -5. Round down (more negative) to -6. Mantissa = 0.000047 / 10^-6 = 47. Result: 47 x 10^-6, or 47 micro.
Engineering notation vs. scientific notation
Scientific notation keeps the mantissa strictly between 1 and 10 by allowing any integer exponent. That is compact, but the exponent rarely matches a named prefix. Engineering notation sacrifices the tight mantissa bound in exchange for prefix alignment, so 65,000 V becomes 65 kV rather than 6.5 x 10^4 V. In practice, circuit diagrams, data sheets, lab reports, and metric signage almost always use engineering notation or SI-prefixed form. E-notation (3.5E+4) is a keyboard-friendly shorthand used in spreadsheets and programming languages where superscripts are hard to type. This calculator outputs all three alongside the full decimal expansion so you can choose whichever form a given audience expects.
Arithmetic in engineering notation
Addition and subtraction are easiest when both numbers share the same exponent: convert both to the same power of 10, add or subtract the mantissas, then re-express in engineering form if the result falls outside 1-999.9. Multiplication is simpler in principle: multiply the mantissas and add the exponents, then normalise to the nearest multiple-of-3 exponent. Division works by dividing the mantissas and subtracting the exponents. For powers, raise the mantissa to the power and multiply the exponent by the power, then normalise. This calculator handles all five operations for you, showing the fully converted result.
SI prefix reference
| Prefix | Symbol | Exponent | Value | Common use |
|---|---|---|---|---|
| quetta | Q | 10^30 | 1 000 000 000 000 000 000 000 000 000 000 | Cosmological distances |
| ronna | R | 10^27 | 1 000 000 000 000 000 000 000 000 000 | Planetary masses |
| yotta | Y | 10^24 | 1 000 000 000 000 000 000 000 000 | Global data (yottabytes) |
| zetta | Z | 10^21 | 1 000 000 000 000 000 000 000 | Stars in the observable universe |
| exa | E | 10^18 | 1 000 000 000 000 000 000 | Exabytes (data) |
| peta | P | 10^15 | 1 000 000 000 000 000 | Petabytes (cloud storage) |
| tera | T | 10^12 | 1 000 000 000 000 | Terabytes, terahertz |
| giga | G | 10^9 | 1 000 000 000 | GHz (CPU clock speeds) |
| mega | M | 10^6 | 1 000 000 | MHz, megapixels |
| kilo | k | 10^3 | 1 000 | kV, km, kg |
| (none) | 10^0 | 1 | Base unit | |
| milli | m | 10^-3 | 0.001 | mm, mA, mV |
| micro | u | 10^-6 | 0.000 001 | uF, uH, um |
| nano | n | 10^-9 | 0.000 000 001 | nF, nm (chip features) |
| pico | p | 10^-12 | 0.000 000 000 001 | pF (capacitors) |
| femto | f | 10^-15 | 0.000 000 000 000 001 | Femtoseconds (laser pulses) |
| atto | a | 10^-18 | 0.000 000 000 000 000 001 | Sub-atomic physics |
| zepto | z | 10^-21 | 0.000 000 000 000 000 000 001 | Particle physics |
| yocto | y | 10^-24 | 0.000 000 000 000 000 000 000 001 | Quantum physics |
All named SI prefixes with their engineering-notation exponents and symbols.
Frequently asked questions
What is the difference between engineering notation and scientific notation?
Scientific notation restricts the exponent to any integer and keeps the mantissa between 1 and 9.9 repeating. Engineering notation restricts the exponent to multiples of 3 only, so the mantissa can range from 1 to 999.9. The trade-off is that engineering notation always aligns with a named SI prefix (kilo, mega, milli, micro, etc.), making it far more readable in electrical, mechanical, and scientific contexts.
How do I convert 0.0046 to engineering notation?
Compute log10(0.0046) = -2.34, so the raw exponent is -3 (floor of -2.34). That is already a multiple of 3, so the engineering exponent is -3. The mantissa is 0.0046 / 10^-3 = 4.6. The result is 4.6 x 10^-3, or 4.6 milli (4.6 m in SI prefix notation).
What SI prefix matches 10^6?
10^6 is mega, abbreviated M. So 5 x 10^6 ohms is 5 M-ohm (5 Mohm), and 12 x 10^6 hertz is 12 MHz. The SI prefix table above lists all 20 named prefixes from yocto (10^-24) to quetta (10^30).
Can I use engineering notation with negative numbers?
Yes. Negative numbers are handled exactly the same way. The exponent is determined from the absolute value, and the negative sign stays with the mantissa. For example, -47,000 becomes -47 x 10^3, or -47 kilo.
Why does the mantissa go up to 999 in engineering notation?
Because the exponent must skip in steps of 3, it cannot always be adjusted to bring the mantissa below 10. A number like 500 has a raw exponent of 2, which rounds down to 0 (the nearest lower multiple of 3). So the mantissa stays as 500 and the result is 500 x 10^0. If the raw exponent were 3 instead, the mantissa would be 1, giving 1 x 10^3. The mantissa therefore spans from 1 to just under 1000.
What does the SI-prefixed form output mean?
The SI-prefixed form replaces "x 10^n" with the standard metric prefix symbol. For example, 65 x 10^3 V becomes "65 kV", and 220 x 10^-12 F becomes "220 pF". If you select a unit type in the calculator, the symbol is appended automatically, matching the format used on electronic component datasheets and circuit diagrams.