TOOL 02 / FREQUENCY & PROPAGATION

Frequency, Time & Wavelength

One cycle. Every unit. From timing to distance, with the maths in view.

Frequency ↔ period

ONE COMPLETE CYCLE

Input value

Input unit

Display precision

Enter frequency or the time for one cycle. Dot decimal or scientific notation, e.g. 2.4 or 1e-9. Changing unit reinterprets the number.

Try

Frequency · f

Hz—

kHz—

MHz—

GHz—

Period · T

s—

ms—

µs—

ns—

ps—

T = 1 / f · f = 1 / T

Positive finite inputs only: 1e-15 to 1e18 Hz, or 1e-18 to 1e15 s. Zero has no finite reciprocal and is rejected. Rounding affects the display only.

Wavelength

λ = v / f

Spatial length of one cycle. Vacuum uses the exact speed of light, c = 299 792 458 m/s.

Wavelength portion

Applies to both vacuum and medium lengths and the reference table. Frequency and full-cycle period stay the same.

IN VACUUM · λ₀

—m

— cm
— mm

Apply a velocity factor

Velocity factor · VF

v / c as a fraction, from 0.000001 to 1. Examples are illustrative; use the phase velocity factor for your medium and frequency.

IN MEDIUM · λ

—m

— cm
— mm

Enable velocity factor to calculate in a medium.

AT A GLANCE

Quick references

Rounded to the selected display precision

Frequency, period & wavelength

Vacuum

Frequency and period anchors, with vacuum and optional medium wavelength in metres
Frequency	Period	λ₀ (m)	λ medium (m)

Both length columns follow the selected wavelength portion. Only the medium column follows VF. Frequency and full-cycle period stay the same.

Unit ladder

Exact decimal scales

Frequency and time unit definitions
Unit	In base units
1 GHz	10⁹ Hz
1 MHz	10⁶ Hz
1 kHz	10³ Hz
1 ms	10⁻³ s
1 µs	10⁻⁶ s
1 ns	10⁻⁹ s
1 ps	10⁻¹² s

µs means microseconds: one millionth of a second.

Equations & assumptions

SHOW THE WORK

Frequency & time

f [Hz] = 1 / T [s] · T [s] = 1 / f [Hz]

1 Hz = 1 cycle per second

1 s = 10³ ms = 10⁶ µs = 10⁹ ns = 10¹² ps

Time here means the period of a repeating signal: one complete cycle. It is not pulse width, rise time or propagation delay. Convert the input to Hz or seconds before taking its reciprocal.

Wavelength & propagation

c = 299 792 458 m/s (exact)

λ₀ [m] = c / f [Hz] = c · T [s]

VF = v / c · λ = VF · λ₀

Full: L = λ · Half: L = λ / 2

Quarter: L = λ / 4

1 m = 100 cm = 1000 mm

The optional medium model uses the entered phase velocity factor at the signal frequency. Frequency and period stay fixed; wave speed and wavelength scale with VF. It does not infer a material or model dispersion. This tool supports 0 < VF ≤ 1 within the numerical bound below.

Supported ranges, rounding & verification

Frequency: 1e-15 to 1e18 Hz. Period: 1e-18 to 1e15 s. Bounds are inclusive and apply after unit scaling. VF: 1e-6 to 1, inclusive, only when enabled. These are numerical limits, not equipment or material ratings.

Invalid input: zero (including −0), negatives, blanks, malformed numbers, nonfinite values and out-of-range inputs clear dependent results. Invalid VF clears only medium values. A disabled VF is ignored. Use dot decimals or scientific notation; commas, percentages and unit suffixes are rejected.

Display: 3, 6 or 9 significant figures. Scientific notation is used below 0.001 or from 1,000,000 after rounding. Calculations use JavaScript double precision without intermediate display rounding. Digits shown do not imply measurement accuracy.

Verification: calculation checks cover fixed reference values, units, invalid inputs and numerical boundaries, with separate high-precision numerical comparisons. These checks do not establish equipment or material performance.

Primary references: BIPM SI base units · NIST SP 330 §2 (Hz = s⁻¹; exact c) · BIPM SI Brochure, 8th ed., Appendix 1, p. 167 (λ = c / f). External references need internet access; calculations run in your browser after the page loads.