Engineering Notation Calculator

What Is Engineering Notation?

Engineering notation is a variation of scientific notation in which numbers are expressed as a product of a real coefficient (the mantissa) and a power of ten where the exponent is strictly a multiple of three ($\dots, -9, -6, -3, 0, 3, 6, 9, 12, \dots$).

Formally, any nonzero real number $N$ is represented as:

$$N = m \times 10^e \quad \text{where } 1 \le |m| < 1000 \text{ and } e \in 3\mathbb{Z}$$

Because powers of ten that are multiples of three map directly to International System of Units (SI) metric prefixes (such as kilo, mega, micro, and nano), engineering notation is widely used across electrical engineering, physics, telecommunications, and computing.

Engineering Notation vs. Scientific Notation

While scientific notation constrains the mantissa to the interval $[1, 10)$, engineering notation allows the mantissa to range between $[1, 1000)$ so that the exponent corresponds directly to physical SI prefixes:

Standard Decimal	Scientific Notation	Engineering Notation	SI Metric Prefix Form
475,000	$4.75 \times 10^5$	$475 \times 10^3$	$475\text{ k}$ (kilo)
0.000022	$2.2 \times 10^{-5}$	$22 \times 10^{-6}$	$22\ \mu$ (micro)
1,500,000,000	$1.5 \times 10^9$	$1.5 \times 10^9$	$1.5\text{ G}$ (giga)
0.00000000085	$8.5 \times 10^{-10}$	$850 \times 10^{-12}$	$850\text{ p}$ (pico)

SI Metric Prefixes Reference

Prefix	Symbol	Power of 10	Decimal Value
Tera	T	$10^{12}$	1,000,000,000,000
Giga	G	$10^9$	1,000,000,000
Mega	M	$10^6$	1,000,000
Kilo	k	$10^3$	1,000
Milli	m	$10^{-3}$	0.001
Micro	$\mu$	$10^{-6}$	0.000001
Nano	n	$10^{-9}$	0.000000001
Pico	p	$10^{-12}$	0.000000000001

How to Convert Numbers to Engineering Notation

Identify the base-10 order of magnitude: calculate $\lfloor \log_{10}(|N|) \rfloor$.
Find the closest multiple of 3 that is less than or equal to that exponent: $e = 3 \times \lfloor \text{exponent} / 3 \rfloor$.
Divide the original number by $10^e$ to get the mantissa: $m = N / 10^e$.
Write the result in the standard format: $m \times 10^e$.

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Rounding Significant Figures Calculator: Round arithmetic operations to specified significant figures.

Frequently Asked Questions

Why is engineering notation preferred in engineering?

Engineering notation matches the steps of SI metric units ($10^3 = \text{kilo}, 10^6 = \text{mega}, 10^{-3} = \text{milli}, 10^{-6} = \text{micro}$), making it easy to read resistor values, frequencies, voltages, and computer storage capacities directly.

What is the allowable range for the mantissa in engineering notation?

The absolute value of the mantissa $|m|$ must be greater than or equal to 1 and strictly less than 1000 ($1 \le |m| < 1000$).

Can negative numbers be written in engineering notation?

Yes, negative numbers keep their negative sign in the mantissa, for example $-450,000 = -450 \times 10^3$.

What is E-notation?

E-notation replaces "$\times 10^n$" with the letter "e" or "E", for example $475 \times 10^3$ is written as $475\text{e}+3$. It is commonly used in programming and electronic calculators.

How do you add numbers in engineering notation?

First align both numbers to have the same power of ten exponent (or convert both to standard decimal), add their coefficients, and then re-normalize the sum so that the exponent is a multiple of three with $1 \le |m| < 1000$.

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What Is Engineering Notation?

Engineering Notation vs. Scientific Notation

SI Metric Prefixes Reference

How to Convert Numbers to Engineering Notation

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Frequently Asked Questions

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