Period to Frequency Calculator
Convert a time period to frequency using the formula f = 1/T. Enter a period in seconds, milliseconds, microseconds, nanoseconds, minutes, hours, or days to calculate frequency in Hz, kHz, MHz, GHz, RPM, and angular frequency instantly.
Complete Unit Conversion Matrix
All period and frequency equivalents for the current value.
| Period Unit | Period (T) | Frequency Unit | Frequency (f) |
|---|---|---|---|
| Femtoseconds (fs) | 1.666670e13 | Nanohertz (nHz) | 5.999988e10 |
| Picoseconds (ps) | 1.666670e10 | Microhertz (μHz) | 5.999988e7 |
| Nanoseconds (ns) | 1.666670e7 | Millihertz (mHz) | 59,999.88 |
| Microseconds (μs) | 16,666.7 | Hertz (Hz) | 59.99988 |
| Milliseconds (ms) | 16.6667 | Kilohertz (kHz) | 0.06 |
| Seconds (s) | 0.016667 | Megahertz (MHz) | 5.999988e-5 |
| Minutes (min) | 0.000278 | Gigahertz (GHz) | 5.999988e-8 |
| Hours (hr) | 4.629639e-6 | Terahertz (THz) | 5.999988e-11 |
| Days (d) | 1.929016e-7 | Revolutions / Min (RPM) | 3,599.9928 |
How to Use This Calculator
Convert any time period to frequency — or frequency to period — in seconds using the reciprocal relationship between period and frequency: f = 1/T. Works across nanoseconds, milliseconds, Hz, GHz, RPM, and more.
Enter the time period (T) in any unit — ns, ms, seconds, days, etc.
The frequency (f) is calculated instantly using f = 1 / T.
Select a different frequency unit to see the result in Hz, kHz, MHz, GHz, RPM, or rad/s.
Switch to the Wave & Wavelength tab to calculate the spatial wavelength λ.
Use the preset chips to load common real-world examples instantly.
Why Calculate Frequency?
Frequency and period are fundamental to every field of physics and engineering. Accurate calculation ensures:
- Signal Processing: Match sampling rates to signal bandwidth.
- RF Engineering: Design antennas to correct wavelengths.
- AC Power: Verify power line cycle timing and harmonics.
- Acoustics: Tune musical instruments and speaker systems.
Period & Frequency Formulas
Period and frequency are exact reciprocals. For waves, the relationship between wavelength and frequency is expressed by λ = v/f.
Formula 1: Period to Frequency
f = 1 / TFrequency f in Hertz equals one divided by the period T in seconds.
Formula 2: Frequency to Period
T = 1 / fPeriod T equals one divided by frequency f.
Formula 3: Angular Frequency
ω = 2π × f = 2π / TAngular frequency ω in radians per second.
Formula 4: Wavelength
λ = v / f = v × TWavelength λ equals wave speed divided by frequency.
Identify the known value
Determine whether you know the period (T) or frequency (f).
Apply the reciprocal
Use f = 1/T to find frequency, or T = 1/f to find period.
Convert units if needed
Multiply or divide by unit scale factors (e.g. 1 kHz = 1000 Hz).
Extend to wavelength
Use λ = v/f to find spatial wavelength if wave speed is known.
Worked Example
Suppose a pendulum completes one full swing in 0.5 seconds. What is its oscillation frequency?
Common Frequency Reference Values
Typical frequencies across science and engineering domains.
| Signal / Phenomenon | Frequency | Period |
|---|---|---|
| US Power Grid (AC) | 60 Hz | 16.67 ms |
| EU Power Grid (AC) | 50 Hz | 20 ms |
| ISO standard tuning frequency of 440 Hz | 440 Hz | 2.27 ms |
| Human Hearing (Low) | 20 Hz | 50 ms |
| Human Hearing (High) | 20 kHz | 50 μs |
| Wi-Fi 2.4 GHz Band | 2.4 GHz | 0.417 ns |
Frequency & Wave Relationships
Frequency connects every branch of physics — from mechanical oscillations and acoustic waves to electromagnetic radiation and quantum energy levels.
Key Principle
“Higher frequency means shorter period. Double the frequency and you halve the period — always.”
Wave Properties
A wave's spatial properties are determined by its frequency and the medium through which it travels. The wavelength λ = v/f links time-domain behavior to spatial structure. For electromagnetic waves in vacuum, use the exact speed of light in vacuum: 299,792,458 m/s.
Period & Frequency FAQ
Essential answers about converting period to frequency and wave calculations.
What is the formula for converting period to frequency?
The formula is f = 1 / T. Frequency (f) in Hertz equals one divided by the period (T) in seconds. For example, a period of 0.5 seconds gives a frequency of 2 Hz.
How do you convert frequency to period?
The formula is T = 1 / f. A 60 Hz signal has a period of 1/60 ≈ 0.01667 seconds (16.67 milliseconds).
What is Hertz (Hz)?
The SI unit of frequency, the hertz, is named after Heinrich Hertz. One hertz (1 Hz) means one complete cycle per second.
How do you convert RPM to Hertz?
Divide RPM by 60: f (Hz) = RPM / 60. So 3600 RPM = 60 Hz. Equivalently, T = 60 / RPM in seconds.
What is angular frequency (ω)?
Angular frequency ω = 2πf measures how fast the phase angle changes, in radians per second (rad/s). It relates to frequency by ω = 2π / T.
How is wavelength related to period?
Wavelength λ = v × T, where v is wave propagation speed. For light (v = 3×10⁸ m/s) at 600 THz, λ = 500 nm (green visible light).
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