Engineering Units, SI Prefixes and Decibels

Engineering numbers are rarely written in plain metres, farads or watts. They come with prefixes (4.7 nF, 2.4 GHz), in derived electrical units (ohms, henries, siemens) and, for gains and power levels, in decibels. This page collects the conversions that come up in circuits, signals and communications, and in the Units and Measurements chapter of JEE Physics, with worked examples. Values marked ≈ are rounded; the rest are exact.

SI prefixes

SI prefixes used in engineering

Prefix	Symbol	Factor	Typical use
tera	T	$10^{12}$	Data rates and storage
giga	G	$10^{9}$	Wi-Fi at 2.4 GHz
mega	M	$10^{6}$	1 MΩ input resistance
kilo	k	$10^{3}$	10 kΩ resistors
milli	m	$10^{-3}$	Currents in mA, time in ms
micro	μ	$10^{-6}$	Electrolytic capacitors in μF
nano	n	$10^{-9}$	Gate delays in ns, capacitors in nF
pico	p	$10^{-12}$	Small capacitors in pF
femto	f	$10^{-15}$	Tiny charges, in fC

Converting between prefixes. Move through the base unit: $4.7\text{ nF} = 4.7 \times 10^{-9}\text{ F} = 4700\text{ pF} = 0.0047\text{ μF}$ .

Prefixes in a product. A 10 kΩ resistor with a 100 nF capacitor has time constant $RC = (10 \times 10^{3})(100 \times 10^{-9}) = 10^{-3}$ s, which is 1 ms. Multiply the numbers, add the powers of ten.

Squared and cubed units. The prefix is squared too: $1\text{ mm}^2 = (10^{-3}\text{ m})^2 = 10^{-6}\text{ m}^2$ , not $10^{-3}\text{ m}^2$ .

Electrical units and what they are made of

Derived electrical units

Quantity	Unit	In other units
Charge	coulomb (C)	A·s
Potential difference	volt (V)	J/C = W/A
Resistance	ohm (Ω)	V/A
Conductance	siemens (S)	A/V = 1/Ω
Capacitance	farad (F)	C/V
Inductance	henry (H)	V·s/A = Wb/A
Power	watt (W)	J/s = V·A
Energy	joule (J)	W·s
Magnetic flux	weber (Wb)	V·s
Flux density	tesla (T)	Wb/m²
Frequency	hertz (Hz)	1/s

A siemens is the reciprocal of an ohm, so a 20 Ω resistor has conductance 0.05 S. Transconductance $g_m$ of a transistor is quoted in siemens (often mS or mA/V, which is the same thing).

Checking a formula with its units

Units are a fast check that a formula, or your answer, makes sense:

$RC$ : $\Omega \cdot \text{F} = \dfrac{\text{V}}{\text{A}} \cdot \dfrac{\text{C}}{\text{V}} = \dfrac{\text{C}}{\text{A}} = \text{s}$ , so a time constant comes out in seconds
$\dfrac{L}{R}$ : $\dfrac{\text{V·s/A}}{\text{V/A}} = \text{s}$ , also a time constant
$\dfrac{1}{2}CV^2$ : $\text{F} \cdot \text{V}^2 = \dfrac{\text{C}}{\text{V}} \cdot \text{V}^2 = \text{C·V} = \text{J}$ , an energy. A 10 μF capacitor at 12 V stores $\tfrac{1}{2}(10 \times 10^{-6})(12^2) = 0.72$ mJ
$\dfrac{1}{2\pi\sqrt{LC}}$ : $\sqrt{\text{H·F}} = \sqrt{\text{s}^2} = \text{s}$ , so this is a frequency. With 10 mH and 100 nF it is about 5.03 kHz

Decibels

A decibel compares two quantities on a log scale. For powers, and for voltages or currents across the same impedance:

\text{dB} = 10\log_{10}\dfrac{P_2}{P_1}, \qquad \text{dB} = 20\log_{10}\dfrac{V_2}{V_1}

The factor is 20 for voltage because power goes as voltage squared, and the log of a square is twice the log.

Decibel values worth remembering

dB	Power ratio	Voltage ratio
+3	≈ 2	≈ 1.41
+6	≈ 4	≈ 2
+10	10	≈ 3.16
+20	100	10
−3	≈ 0.5 (half power)	≈ 0.707
−20	0.01	0.1

Worked example. An amplifier turns 10 mV into 500 mV, a voltage gain of 50. In decibels that is $20\log_{10} 50 \approx 34.0$ dB.

Gains in a chain add in dB. Multiplying ratios becomes adding decibels, which is why link budgets are written in dB.

dBm and dBW: absolute power levels

Adding a reference turns a ratio into a level. dBm is relative to 1 mW and dBW to 1 W:

P_{\text{dBm}} = 10\log_{10}\dfrac{P}{1\text{ mW}}, \qquad 0\text{ dBm} = 1\text{ mW}, \quad 20\text{ dBm} = 100\text{ mW}, \quad 30\text{ dBm} = 1\text{ W} = 0\text{ dBW}

Worked example. A −10 dBm signal passes an amplifier with 20 dB gain, then a cable with 3 dB loss. The output is $-10 + 20 - 3 = 7$ dBm, which is $10^{0.7} \approx 5.0$ mW.

A level plus a gain is a level (dBm + dB = dBm). Two levels don't add in dB: 0 dBm plus 0 dBm of uncorrelated power is 2 mW, about 3 dBm, not 0 dBm.

Everyday conversions

Length, energy and time

Unit	Equals
1 nanometre	$10^{-9}$ m
1 ångström	$10^{-10}$ m
1 inch	2.54 cm
1 electronvolt (eV)	≈ $1.602 \times 10^{-19}$ J
1 kilowatt-hour (kWh)	$3.6 \times 10^{6}$ J
1 calorie	4.184 J
1 day	86,400 s
1 year (365 days)	≈ $3.15 \times 10^{7}$ s

Common mistakes

Using 20 log for a power ratio. Power ratios take $10\log_{10}$ ; voltage and current ratios take $20\log_{10}$ .
Adding two dBm values. Levels in dBm don't add; convert to milliwatts, add, and convert back.
Mixing up m and μ, or n and p. A factor of 1000 each time. 4.7 nF is 4700 pF, not 4.7 pF.
Forgetting to square the prefix. $1\text{ cm}^2$ is $10^{-4}\text{ m}^2$ .
Reading −3 dB as "3 times smaller". It is half the power, about 0.707 of the voltage.

Practice questions

An amplifier has a voltage gain of 1000. What is its gain in dB?
What power, in watts, is −20 dBm?
What is the time constant of a 2.2 kΩ resistor with a 47 μF capacitor?
A 0 dBm source feeds a 25 dB amplifier, a 6 dB attenuator and a 12 dB amplifier. What is the output level in dBm, and roughly how many watts?

Answers

$20\log_{10} 1000 = 60$ dB.
$10^{-20/10}$ mW $= 0.01$ mW, which is $10\ \mu$ W or $10^{-5}$ W.
$RC = (2.2 \times 10^{3})(47 \times 10^{-6}) = 0.1034$ s, about 103 ms.
$0 + 25 - 6 + 12 = 31$ dBm, which is $10^{3.1}$ mW, about 1.26 W.

Where this comes up in exams

JEE Main 2026 opens its Physics syllabus with Units and Measurements. In GATE EC, gains and losses, signal-to-noise ratios (Section 7, Communications) and Bode plots (Section 6, Control Systems) are routinely given in decibels, and every circuits question uses prefixed SI units.

Checked against JEE (Main) 2026 syllabus (NTA) and GATE 2027 EC syllabus. Syllabi can change from year to year, so confirm with the latest official notification for your exam.

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