Calculator
Example data table
| Scenario | Duration (D) | Interval (T) | Frequency (f) | Cycles (N) | Notes |
|---|---|---|---|---|---|
| AC mains signal | 1 s | 0.02 s | 50 Hz | 50 | 50 cycles occur in one second. |
| Motor rotation | 10 s | — | 1800 rpm | 300 | 1800 rpm equals 30 Hz. |
| Pulsed sensor | 2 min | 0.5 s | 2 Hz | 240 | N = D/T = 120/0.5. |
| High-speed clock | — | 1 µs | 1 MHz | — | Interval of 1 microsecond equals 1 MHz. |
You can reproduce any row using the solve selector and the matching inputs.
Formula used
- Frequency from interval: f = 1 / T
- Interval from frequency: T = 1 / f
- Duration for N cycles: D = N · T or D = N / f
- Cycles in a duration: N = D / T or N = f · D
Units: seconds for time, and hertz (1/second) for frequency. The calculator converts your inputs to base units, solves, then converts results back to your chosen output units.
How to use this calculator
- Select what you want to solve for.
- Enter the values you already know and choose units.
- If you are solving for duration, provide cycles (or leave it blank for one).
- Pick output units, or keep Auto for readability.
- Press Calculate to see results above the form.
- Use the download buttons to export CSV or PDF.
Article
1) What duration, interval, and frequency mean
Duration (D) is the total time window you observe. Interval or period (T) is the time for one repeat. Frequency (f) is the repeat rate per second. These three describe the same repeating event, so changing one value immediately changes the others.
2) Core relationship you can trust
The most useful link is f = 1/T. A 50 Hz signal repeats every 0.02 s, while a 60 Hz signal repeats every 0.0166667 s. If a sensor triggers every 250 ms, the rate is 4 Hz. If a rotation is 1800 rpm, that equals 30 Hz because 1800/60 = 30.
3) Cycles connect rate to a time window
Cycles (N) tells how many repeats occur in a duration. Use N = f·D when you know the rate and the time window. For example, at 2 Hz over 2 minutes (120 s), N = 2×120 = 240 events. If you know N and D, you can flip it to f = N/D to recover the average frequency.
4) Choosing practical units
Small periods are easier in milliseconds: 5 ms corresponds to 200 Hz. Very fast clocks are clearer in kilohertz or megahertz: 1 MHz has a period of 1 microsecond. Longer observations are easier in minutes or hours: a 0.5 s interval stays 0.5 s, but a 1 hour duration becomes 3600 s internally.
5) Where this is used
Engineers use these conversions for AC power, rotating machines, sampling, and pulse trains. A data logger set to 100 Hz records every 10 ms. A conveyor sensor with a 3 s interval triggers 0.3333 Hz. In test reports, exporting results helps keep unit choices consistent.
6) Accuracy checks that prevent mistakes
First confirm your units: mixing ms and s is the most common error. Next sanity-check magnitudes: if T halves, f should double. If you increase duration while keeping frequency fixed, cycles should increase proportionally. Finally, remember this tool assumes steady repetition; bursty events need averaging.
When solving for duration, cycles can default to one event, which is helpful for single-shot timing. For periodic motion, enter cycles to predict run time and schedule measurements with fewer surprises. This keeps scheduling, logging, and calibration steps consistent.
FAQs
1) Can I solve frequency without entering cycles?
Yes. Enter the interval (period) and the tool uses f = 1/T. Cycles are only needed when you want to link a duration window to how many events occur.
2) What if I only know duration and cycles?
Choose Frequency as the solve target, then enter duration and cycles. The tool calculates f = N/D and also reports the matching interval T = 1/f.
3) Why does Auto output change units?
Auto selects a readable scale. Very small times may switch to milliseconds, and very large rates may switch to kilohertz or megahertz, without changing the underlying value.
4) How do rpm and hertz relate?
Hertz means cycles per second. Rpm means cycles per minute. Convert with Hz = rpm/60 and rpm = Hz×60.
5) Does this handle irregular or burst signals?
It assumes steady repetition. For bursts, compute an average frequency over a measured duration, or count events in a fixed window and use f = N/D as an estimate.
6) Why do I see scientific notation sometimes?
Extremely large or tiny results are displayed in scientific notation to stay readable. You can change input units or output units to bring values into a familiar range.