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Formula used
The time period T is the inverse of frequency f: T = 1 / f. Frequency must be in hertz (cycles per second) before inversion.
- Hz is cycles per second.
- rpm is cycles per minute, so f(Hz) = rpm / 60.
- Angular frequency is ω = 2πf in rad/s.
How to use this calculator
- Enter the frequency value measured or provided.
- Select the correct unit, such as Hz, kHz, or rpm.
- Pick an output period unit, or keep Auto select.
- Choose decimals and a display style if needed.
- Press Calculate Period to view results above.
- Use CSV or PDF buttons to export the result.
Example data table
| Frequency | Unit | Period (s) | Period (ms) |
|---|---|---|---|
| 50 | Hz | 0.02 | 20 |
| 1 | kHz | 0.001 | 1 |
| 2.5 | MHz | 0.0000004 | 0.0004 |
| 60 | rpm | 1 | 1000 |
| 0.2 | Hz | 5 | 5000 |
Tip: Use scientific display for microsecond and nanosecond periods.
Frequency–period relationship
Frequency tells how many cycles occur each second. Period tells how long one complete cycle takes. They are mathematical inverses, so increasing frequency shortens the period. This calculator converts common frequency units into a readable period, which is useful for timing, vibration analysis, signal generation, and rotating machinery checks.
Why engineers and students use this conversion
Datasheets and lab instruments often specify frequency, while time-domain work needs period. For example, mains electricity at 50 Hz has a 0.02 s period, and a 1 kHz tone repeats every 0.001 s. Converting quickly helps estimate response times, pulse spacing, and cycle counts in experiments.
Unit prefixes and scaling
Prefixes move the decimal point by powers of ten. A kilohertz is 103 Hz, a megahertz is 106 Hz, and a gigahertz is 109 Hz. The resulting periods can shrink from milliseconds to microseconds and nanoseconds, so scientific notation prevents rounding to zero.
Rotation and rpm as frequency
Rotational speed in rpm can be treated as a frequency: divide rpm by 60 to get cycles per second. A shaft at 1200 rpm equals 20 Hz, giving a 0.05 s period per revolution. This is handy for balancing, vibration diagnosis, tachometer validation, and relating blade-pass events to time.
Reading results with sensible precision
Real measurements have uncertainty. If frequency is measured to three significant digits, reporting an eight-decimal period can look precise but be misleading. Use the decimals control to match your instrument’s resolution. For fast signals, fewer decimals plus scientific notation often communicates the value more clearly.
Sampling, timing, and digital systems
In digital acquisition, sampling frequency determines sample spacing. A 10 kHz sample rate means a 0.0001 s (100 µs) interval between samples. Converting frequency to period helps choose timer settings, configure PWM cycles, and confirm that aliasing risk is reduced by keeping sampling far above the signal bandwidth.
Vibration, waves, and resonance context
Mechanical vibration and wave motion are commonly described by frequency, but fatigue and resonance investigations often need time per cycle. Knowing the period allows cycle counting over a time window, estimating dwell times, and comparing to system time constants. Small changes in frequency can create noticeable timing shifts near resonance.
Common reference values
Use these quick anchors: 1 Hz → 1 s, 2 Hz → 0.5 s, 10 Hz → 0.1 s, 50 Hz → 0.02 s, 60 Hz → 0.0167 s, 1 kHz → 1 ms, and 1 MHz → 1 µs. These benchmarks make mental checks easy before exporting results. They also help verify conversions between Hz, rpm, and kilohertz when reviewing field notes, oscilloscopes, and lab reports.
FAQs
1) What is the formula for period from frequency?
Period is the reciprocal of frequency: T = 1/f. Use f in cycles per second (Hz) to get T in seconds, then convert seconds to other time units if needed.
2) Why does higher frequency mean smaller period?
Frequency counts how many cycles fit into one second. If more cycles fit into the same second, each cycle must take less time, so the period decreases.
3) How do I convert rpm to period?
First convert rpm to Hz by dividing by 60. Then compute T = 1/f. For example, 60 rpm → 1 Hz → 1 second per revolution.
4) When should I use milliseconds or microseconds?
Use ms for audio and low-frequency controls, µs for fast timers and switching, and ns for RF or very high-speed digital signals. The calculator’s auto mode helps select a readable unit.
5) What happens if I enter zero or a negative frequency?
A period cannot be computed from zero, and negative frequency is not physically meaningful for this conversion. The calculator will show an error and ask for a positive value.
6) Does period depend on amplitude or voltage?
No. Period depends only on frequency. Amplitude affects signal magnitude, not how long one cycle takes, as long as the waveform remains periodic.
7) How accurate is the period result?
The math is exact, but the accuracy depends on your frequency input. Match the decimals to your measurement resolution, and avoid over-reporting precision beyond what your instrument supports.