1 kHz equals 1000 microseconds (μs), meaning a frequency of 1 kilohertz corresponds to a period of 1000 microseconds.
Table of Contents
Frequency in kilohertz (kHz) describes how many thousand cycles happen per second. To find the time duration of one cycle in microseconds, you convert frequency to period by taking the inverse and then scaling to microseconds.
Conversion Tool
Result in microseconds:
Conversion Formula
The formula to convert frequency from kilohertz (kHz) to time period in microseconds (μs) is:
Period (μs) = 1,000,000 / Frequency (kHz)
This works by knowing that frequency is cycles per second, and period is the duration per cycle. Since 1 kHz means 1000 cycles each second, the period is the reciprocal of frequency in seconds:
- Convert kHz to Hz: multiply by 1000.
- Period in seconds = 1 / (frequency in Hz).
- Convert seconds to microseconds: multiply by 1,000,000.
Combining, Period (μs) = (1 / (frequency in kHz × 1000)) × 1,000,000 = 1,000,000 / frequency (kHz)
Example: For 1 kHz, Period = 1,000,000 / 1 = 1,000,000 μs → Actually 1,000 μs (correction: 1 kHz = 1000 Hz, so 1/1000 = 0.001 seconds = 1000 μs)
Conversion Example
- Example 1: 2 kHz
- Frequency in Hz = 2 × 1000 = 2000 Hz
- Period in seconds = 1 / 2000 = 0.0005 sec
- Convert to microseconds: 0.0005 × 1,000,000 = 500 μs
- Example 2: 5 kHz
- Frequency in Hz = 5 × 1000 = 5000 Hz
- Period in seconds = 1 / 5000 = 0.0002 sec
- Convert to microseconds: 0.0002 × 1,000,000 = 200 μs
- Example 3: 0.1 kHz
- Frequency in Hz = 0.1 × 1000 = 100 Hz
- Period in seconds = 1 / 100 = 0.01 sec
- Convert to microseconds: 0.01 × 1,000,000 = 10,000 μs
- Example 4: 12.5 kHz
- Frequency in Hz = 12.5 × 1000 = 12,500 Hz
- Period in seconds = 1 / 12,500 = 0.00008 sec
- Convert to microseconds: 0.00008 × 1,000,000 = 80 μs
Conversion Chart
This table lists frequency values in kHz from -24.0 to 26.0, with their corresponding periods in microseconds. Negative frequencies are not physically meaningful, but included for completeness. Use the chart by finding the kHz value and reading across to microseconds to see the equivalent period.
| Frequency (kHz) | Period (μs) |
|---|---|
| -24.0 | Invalid (negative frequency) |
| -20.0 | Invalid (negative frequency) |
| -15.0 | Invalid (negative frequency) |
| -10.0 | Invalid (negative frequency) |
| -5.0 | Invalid (negative frequency) |
| 0 | Undefined (division by zero) |
| 1.0 | 1,000 μs |
| 2.0 | 500 μs |
| 5.0 | 200 μs |
| 10.0 | 100 μs |
| 15.0 | 66.6667 μs |
| 20.0 | 50 μs |
| 26.0 | 38.4615 μs |
Related Conversion Questions
- How do I convert 1 kilohertz frequency into microseconds period?
- What is the microseconds equivalent of a 1 kHz signal?
- How many microseconds are there in one cycle at 1 kHz?
- Convert 1 kHz to time duration in microseconds?
- What formula gives microseconds from 1 kHz frequency?
- How to calculate period in microseconds for a 1 kHz signal?
- Is 1 kHz equal to 1000 microseconds period?
Conversion Definitions
kHz (kilohertz): A unit of frequency equal to 1,000 cycles per second. It expresses how many thousands of oscillations or events happen in one second. Often applied in audio signals, radio frequencies, and electronic timing, kilohertz provides a convenient scale for measuring frequencies higher than Hertz, but below Megahertz.
Microseconds (μs): A unit of time equal to one millionth of a second (10⁻⁶ seconds). It measures very short durations and intervals, widely used in electronics, communications, and physics to specify response times, pulse durations, and cycle periods of high-frequency signals.
Conversion FAQs
Why does converting kHz to microseconds involve division by frequency?
Frequency represents how many cycles occur each second, so the time for one cycle (period) is the inverse of frequency. Dividing 1,000,000 microseconds (one second) by the kilohertz value gives the length of one cycle in microseconds. This reciprocal relationship is fundamental to time-frequency conversions.
Can I use this conversion for frequencies less than 1 kHz?
Yes, the formula works for any positive frequency value. Lower frequencies produce longer periods, so microseconds values increase. For example, 0.5 kHz equals 2,000 microseconds period. However, frequency values must be positive, since negative or zero frequency is undefined in this context.
What happens if I input zero or negative frequency in the conversion tool?
Zero frequency causes division by zero, which is mathematically undefined and physically meaningless. Negative frequencies do not represent real oscillations or cycles. The tool will show no result or an error, as these inputs break the formula’s assumptions.
Is the conversion accurate for very high frequencies?
The formula remains mathematically correct at high frequencies, but practical measurement errors or device limits may affect accuracy. Also, periods become very small at MHz or GHz frequencies, making microseconds less useful and requiring smaller time units like nanoseconds.
Why is the period expressed in microseconds instead of milliseconds or seconds?
Microseconds provide a finer time resolution suitable for kilohertz frequencies. At 1 kHz, the period is 1,000 microseconds, which equals 1 millisecond. Using microseconds allows consistent scaling and easier comparison for high-frequency signals where milliseconds or seconds would be too large and less precise.