Frequency and period are reciprocals
T = 1 / f and f = 1 / T. A 1 kHz tone repeats every 1 ms; a 16 MHz microcontroller clock ticks every 62.5 ns; a 2.4 GHz Wi-Fi carrier completes a cycle in about 417 ps. Type either quantity above and the other appears — along with three companions engineers reach for constantly:
- Wavelength λ = v / f, where v is the speed of light times the velocity factor of the medium — 1.0 for free space, ~0.66 for solid polyethylene coax, ~0.95 for open-wire line. At 2.4 GHz in air, λ ≈ 12.5 cm, which is why a quarter-wave Wi-Fi antenna is about 31 mm.
- Angular frequency ω = 2πf, in radians per second — what appears in reactance formulas (XL = ωL, XC = 1/ωC) and control-loop math.
- Clock cycles — how long N ticks take at frequency f. A 1000-cycle delay loop on a 16 MHz AVR runs 62.5 µs; the same loop at 240 MHz takes 4.17 µs.
Worked examples
Timer interrupt: you need a 1 ms tick from a 72 MHz timer — that's 72,000 counts per interrupt (enter 72M, then read the period, or use the cycle field the other way).
Antenna length: a 146 MHz ham transmitter: λ = 2.05 m, so a quarter-wave whip is about 51 cm.
UART bit time: 115200 baud → each bit lasts 8.68 µs — enter 115.2k as the frequency.
Frequently asked questions
- What's the difference between Hz and rad/s?
- Hertz counts complete cycles per second; radians per second measures the same rotation in angle. One cycle is 2π radians, hence ω = 2πf. Filters and reactance formulas want ω; datasheets and dials speak Hz.
- Why does wavelength matter to a digital designer?
- When a trace or cable approaches a notable fraction of a wavelength (rule of thumb: 1/10), it stops being "just a wire" and becomes a transmission line — reflections, termination, and impedance suddenly matter. This is also why fast edges (short equivalent wavelengths) cause trouble on long traces.
- What velocity factor should I use?
- 1.0 for air/vacuum, ~0.66 for common PE-dielectric coax (RG-58, RG-213), ~0.78–0.85 for foam coax, ~0.95 for open-wire ladder line. Your cable's datasheet has the exact number.
- Converting a data rate instead?
- For "how long does this file take", you want the data transfer time calculator — it handles bits vs bytes and GB vs GiB properly.