Frequency to Period Calculator

Instant conversion between frequency and period. Supports multiple units (Hz, kHz, MHz, GHz, THz) and shows live sine waveform preview.

Relationship: Period (T) = 1 / Frequency (f)    (f in Hz, T in seconds)

Works for any periodic signal: sine, square, pulse, etc.

Frequency (positive number)
Period (positive time)
1 Hz 60 Hz (AC) 1 kHz 1 MHz 1 GHz 2.4 GHz (Wi-Fi)
Conversion Results
Frequency: 1.000 kHz
Period: 1.000 ms
T = 1 / f   →   1 ms = 1 / 1 kHz

* Two cycles of sine wave at current frequency (time domain). One period highlighted between markers.

Understanding Frequency and Period

Frequency (f) is the number of occurrences of a repeating event per unit time. The standard unit is hertz (Hz), where 1 Hz = 1 cycle per second.

Period (T) is the duration of one cycle. It is the reciprocal of frequency: T = 1/f.

Fundamental relation: \( f = \frac{1}{T} \) , \( T = \frac{1}{f} \)

Common Unit Conversions

Frequency Period
1 Hz 1 s
60 Hz 16.667 ms
1 kHz 1 ms
1 MHz 1 µs
1 GHz 1 ns
1 THz 1 ps

Applications in Science & Engineering

1
Electronics: Clock frequencies in processors (GHz → ns), filter design, signal integrity.
2
Acoustics: Audio frequencies (20 Hz – 20 kHz) determine pitch; period relates to time delay.
3
Radio Frequency (RF): Wavelength and antenna size depend on frequency/period.
4
Power systems: 50/60 Hz AC — period 20 ms / 16.67 ms.

Did you know? In 1960, the second was redefined based on the frequency of a specific atomic transition (cesium-133), linking time and frequency with extreme precision.

Frequently Asked Questions

Since 1 MHz = 10⁶ Hz, period T = 1 / (10⁶) = 10⁻⁶ s = 1 µs. So 1 MHz corresponds to exactly 1 microsecond.

T = 1 / (2.4 × 10⁹ Hz) ≈ 4.167 × 10⁻¹⁰ s = 416.7 ps (picoseconds).

Angular frequency ω = 2πf. The period T = 2π/ω. This calculator uses ordinary frequency f. To convert from ω, first compute f = ω/(2π).

The graph displays two full periods to illustrate the repetitive nature. Red markers indicate the start and end of one period, showing the time interval T.