Engineering Notation Calculator

Convert any number to engineering notation (exponents that are multiples of 3) with SI prefix equivalents.

Enter a Number

Result

Engineering Notation
4.5 x 10^-3
Original Number 0.0045
Scientific Notation 4.5 x 10^-3
Engineering Notation 4.5 x 10^-3
SI Prefix milli (m)
With SI Prefix 4.5 m
Exponent -3
Coefficient 4.5

Step-by-Step Solution

0.0045 = 4.5 x 10^-3

What Is Engineering Notation?

Engineering notation is a version of scientific notation in which the exponent of ten is always a multiple of three (... -9, -6, -3, 0, 3, 6, 9 ...). The coefficient (or significand) is a number between 1 and 999.999. This format aligns directly with the SI metric prefixes, making it extremely practical for engineers and scientists working with physical quantities.

For example, 47,000 ohms in engineering notation is 47 x 103 ohms, or simply 47 kilohms (47 k ohms). This is much more intuitive than the scientific notation form of 4.7 x 104.

SI Prefix Reference

Large Numbers

Prefixes for powers of 10 with positive exponents.

10^3 = kilo (k)
10^6 = mega (M)
10^9 = giga (G)
10^12 = tera (T)

Small Numbers

Prefixes for powers of 10 with negative exponents.

10^-3 = milli (m)
10^-6 = micro (u)
10^-9 = nano (n)
10^-12 = pico (p)

Very Large

Prefixes for extremely large quantities.

10^15 = peta (P)
10^18 = exa (E)
10^21 = zetta (Z)
10^24 = yotta (Y)

Very Small

Prefixes for extremely small quantities.

10^-15 = femto (f)
10^-18 = atto (a)
10^-21 = zepto (z)
10^-24 = yocto (y)

How to Convert to Engineering Notation

  1. Write the number in scientific notation: a x 10n, where 1 ≤ |a| < 10.
  2. If n is already a multiple of 3, you are done.
  3. If not, adjust the exponent down to the nearest multiple of 3 (round toward negative infinity).
  4. Multiply the coefficient by 10 raised to the difference to compensate.
  5. The coefficient should now be between 1 and 999.999, and the exponent a multiple of 3.

Engineering vs. Scientific Notation

Scientific notation uses exponents of any integer, always keeping the coefficient between 1 and 10. Engineering notation restricts the exponent to multiples of 3, which may result in a coefficient between 1 and 999.999. The advantage of engineering notation is its direct correspondence with SI prefixes (kilo, mega, milli, micro, etc.), making it far more practical in technical fields.

Practical Applications

  • Electrical Engineering: Resistor and capacitor values are typically expressed with SI prefixes (e.g., 4.7 kohm, 100 nF, 2.2 uH).
  • Telecommunications: Frequencies are expressed in kHz, MHz, or GHz, which are engineering notation with units.
  • Physics: Measurements like wavelengths (nm), distances (km), and masses (kg) all use SI prefixes.
  • Computer Science: Data sizes use binary-adapted SI prefixes (kB, MB, GB, TB).
  • Chemistry: Concentrations and molecular weights often use milli, micro, and nano prefixes.

Common Examples

  • 1,500 = 1.5 x 103 (1.5 kilo)
  • 0.000047 = 47 x 10-6 (47 micro)
  • 3,600,000 = 3.6 x 106 (3.6 mega)
  • 0.0000000082 = 8.2 x 10-9 (8.2 nano)