Reference

Glossary & formulas

Every term the site uses, in plain English, each linked to the chapter that explains it properly. Below the glossary: the fifteen equations that run the whole subject, the constants they need, and a converter for the numbers you’ll actually want.

299,792,458meters per second: the speed of light, exact by definition since 1983
1239.84eV·nm: divide by a wavelength in nm to get photon energy in eV
+3 dBis double the power; +10 dB is ten times; +20 dB a hundred

Common mix-up: dB and dBm are not the same thing. A decibel is a ratio between two powers (“the wall cost 10 dB”). dBm is an absolute power, measured against one milliwatt: 0 dBm = 1 mW, 20 dBm = 100 mW, −70 dBm = 0.1 nanowatt. You can subtract dB from dBm, but you can’t add two dBm values.

Glossary

Terms, A to Z

Formulas

Fifteen equations that run it all

Each one in the form you’d use, with what it means in a sentence and a worked number. Symbols are defined in the constants table below.

Wave relation · Ch 05
c = f λ
Speed equals frequency times wavelength. 2.4 GHz → λ = 299,792,458 ÷ 2.4×10⁹ = 12.5 cm.
Photon energy · Ch 06
E = h f
Energy of one photon. Green light at 545 THz: 6.626×10⁻³⁴ × 5.45×10¹⁴ = 3.6×10⁻¹⁹ J = 2.25 eV.
Coulomb’s law · Ch 01
F = k q₁ q₂ ÷ r²
Force between two point charges. Two 1 µC charges 10 cm apart: 8.988×10⁹ × 10⁻¹² ÷ 0.01 ≈ 0.9 N.
Gauss’s law · Ch 03
∮ E · dA = Qenc ÷ ε₀
Electric flux out of any closed surface equals the charge inside divided by ε₀. Charges are where field lines begin and end.
Faraday’s law · Ch 02
∮ E · dl = − dΦB ÷ dt
A changing magnetic flux drives an electric field around a loop. Generators, transformers, wireless chargers.
Ampère–Maxwell law · Ch 03
∮ B · dl = μ₀ Ienc + μ₀ε₀ dΦE ÷ dt
Currents and changing electric fields both make magnetic fields. The second term, Maxwell’s, is what lets waves exist.
Speed of light · Ch 03
c = 1 ÷ √(μ₀ ε₀)
Two bench-top constants fix the wave speed: 1 ÷ √(1.25664×10⁻⁶ × 8.854×10⁻¹²) = 2.998×10⁸ m/s.
Larmor formula · Ch 04
P = q² a² ÷ (6π ε₀ c³)
Power radiated by a charge q with acceleration a (non-relativistic). No acceleration, no radiation.
Inverse-square law · Ch 08
S = P ÷ (4π r²)
Power density from an isotropic source. 100 mW at 10 m: 0.1 ÷ 1,257 = 80 µW/m².
Free-space path loss · Ch 08
FSPL[dB] = 20 log₁₀ d + 20 log₁₀ f − 147.55
d in meters, f in hertz (it is 20 log₁₀(4π d f ÷ c)). 2.4 GHz over 10 m: 20 + 187.60 − 147.55 ≈ 60 dB.
Power in dBm · Ch 08
P[dBm] = 10 log₁₀(P ÷ 1 mW)
Absolute power on a log scale. 1 W = 30 dBm, 100 mW = 20 dBm, 1 µW = −30 dBm.
Shannon–Hartley · Ch 09
C = B log₂(1 + S/N)
Maximum error-free bit rate. 20 MHz at S/N = 1,000 (30 dB): 20×10⁶ × 9.97 ≈ 199 Mbit/s.
Snell’s law · Ch 11
n₁ sin θ₁ = n₂ sin θ₂
How much a ray bends crossing a boundary. Air to water (n = 1.33) at 45°: sin θ₂ = 0.707 ÷ 1.33 → 32°.
Rayleigh scattering · Ch 11
Iscattered ∝ 1 ÷ λ⁴
Small particles scatter short waves far more. Blue 450 nm vs red 700 nm: (700 ÷ 450)⁴ ≈ 5.9× more. Why the sky is blue.
Wien’s law · Ch 05
λpeak = b ÷ T
Where a hot body’s glow peaks, b = 2.898×10⁻³ m·K. Sun at 5,772 K → 502 nm; you at 310 K → 9.3 µm infrared.
Constants

The numbers in those equations

SymbolNameSI valueNote
cSpeed of light in vacuum299,792,458 m/sExact; defines the meter
hPlanck constant6.626 070 15 × 10⁻³⁴ J·sExact since 2019; = 4.135 667 × 10⁻¹⁵ eV·s
eElementary charge1.602 176 634 × 10⁻¹⁹ CExact since 2019; 1 eV = this many joules
ε₀Vacuum permittivity8.854 187 8188 × 10⁻¹² F/mMeasured (CODATA 2022)
μ₀Vacuum permeability1.256 637 061 27 × 10⁻⁶ N/A²Measured; within 10⁻¹⁰ of the old exact 4π × 10⁻⁷
kCoulomb constant, 1/(4πε₀)8.987 551 786 × 10⁹ N·m²/C²Usually rounded to 8.988 × 10⁹
Z₀Impedance of free space, √(μ₀/ε₀)376.730 ΩRatio of E to H in a plane wave
kBBoltzmann constant1.380 649 × 10⁻²³ J/KExact; kBT at 310 K = 0.0267 eV
meElectron mass9.109 383 7139 × 10⁻³¹ kgRest energy mec² = 510.999 keV
hcHandy product1239.842 eV·nmE[eV] = 1239.84 ÷ λ[nm]
bWien displacement constant2.897 771 955 × 10⁻³ m·KExact (derived from h, c, kB)
σStefan–Boltzmann constant5.670 374 419 × 10⁻⁸ W/(m²·K⁴)Total power radiated by a black body: σT⁴
Instrument

Unit converter

Type in any box, or drag the slider; the others follow. The strip shows where you are on the spectrum and on the power scale.

Region
Photon energy in joules
Ionizing?
dBm

Photon energy uses E = h f; wavelength uses c = f λ in vacuum. dBm = 10 log₁₀(P ÷ 1 mW). Numbers accept forms like 2.4, 1e-9 or 6.5e14.