How do you convert frequency to period?

Period T = 1/f. If the frequency is 1 kHz (1000 Hz), the period is 1/1000 = 0.001 seconds = 1 millisecond. The two quantities are always the reciprocal of each other.

How do you convert RPM to Hz?

Divide RPM by 60 to get Hz. For example, 3600 RPM = 3600/60 = 60 Hz. RPM measures rotations per minute, Hz measures cycles per second.

How do you convert Hz to rad/s?

Multiply Hz by 2π to get rad/s. Angular frequency ω = 2πf. For example, 50 Hz = 2π × 50 ≈ 314.16 rad/s.

What is the frequency of a 32.768 kHz crystal?

32.768 kHz is 2^15 Hz, which divides evenly by powers of 2 down to exactly 1 Hz. This is why it is the standard frequency for real-time clock (RTC) crystals in watches and microcontrollers.

Frequency & Period Converter

Convert between frequency and period instantly. Hz, kHz, MHz, GHz, RPM, and rad/s.

Enter Frequency

Frequency

Results

Frequency1000.00 Hz

kHz1.00000 kHz

MHz0.00100000 MHz

GHz0.00000100000 GHz

Period0.00100000 s

ms1.00000 ms

µs1000.00 µs

ns1.00000e+6 ns

RPM60000.0 RPM

rad/s6283.19 rad/s

Common Frequencies Reference

Frequency	Period	Description
50 Hz	20.0 ms	Mains (Europe, Asia)
60 Hz	16.7 ms	Mains (Americas)
440 Hz	2.27 ms	Concert pitch (A4)
1 kHz	1.00 ms	Audio test tone
32.768 kHz	0.0305 ms	RTC crystal
1 MHz	1.00 µs	Common MCU clock
2.4 GHz	0.417 ns	WiFi / Bluetooth
5.8 GHz	0.172 ns	WiFi 5 GHz band

Frequency and Period

Frequency and period are two ways of describing the same thing: how fast something repeats. Frequency (f) counts cycles per second in hertz (Hz). Period (T) measures the time for one complete cycle. The relationship is simple: f = 1/T and T = 1/f.

In electronics, you encounter frequencies from sub-hertz (heartbeat sensors) to gigahertz (WiFi, Bluetooth). The 32.768 kHz crystal in every digital watch was chosen because 32768 = 2^15, which a chain of 15 flip-flops divides down to exactly 1 Hz for the seconds counter.

Angular frequency ω = 2πf (in rad/s) appears in formulas for impedance (XL = ωL, XC = 1/ωC) and transfer functions. RPM (revolutions per minute) is common in motors — divide by 60 to get Hz. These are all different units for the same physical quantity.

Conversion Formula

f = 1/T T = 1/f

Key Points

f = 1/T — frequency and period are reciprocals
ω = 2πf — angular frequency in radians per second
RPM = f × 60 — used for rotating machinery
32.768 kHz = 2^15 Hz — standard RTC crystal frequency

Applications

Oscillator and crystal selection
Timer/counter configuration for microcontrollers
Motor speed measurement and control
Audio and RF frequency analysis

Practical Examples

2.4 GHz WiFi antenna length

Calculate the quarter-wave monopole antenna length for 2.4 GHz WiFi. λ = c/f.

λ = 3×10⁸ / 2.4×10⁹ = 0.125 m = 12.5 cm · λ/4 = 3.1 cm

1 kHz audio signal

Express a 1 kHz audio tone as period, angular frequency, and wavelength in air (c = 343 m/s).

T = 1 ms · ω = 6283 rad/s · λ_air = 343/1000 = 34.3 cm

Did you know? The highest frequency ever measured is from gamma-ray bursts: ~10²³ Hz. The lowest measurable frequency is around 10⁻¹⁶ Hz (oscillations that would take longer than the age of the universe per cycle). Electronics typically operates between a few Hz and a few hundred GHz.