ns to Hz Converter
A signal with a period of 1,000 ns repeats 1,000,000 times a second, which is 1 MHz.
Quick answer: Divide 1,000,000,000 by the period in nanoseconds. For example, 1,000 ns is 1,000,000 Hz, 100 ns is 10,000,000 Hz and 20 ns is 50,000,000 Hz.
The ns to Hz formula
Frequency in hertz equals 1,000,000,000 divided by the period in nanoseconds.
A nanosecond is one billionth of a second, so there are a billion of them in each second.
Take 1,000 ns. 1,000,000,000 ÷ 1,000 gives 1,000,000 Hz.
Take 100 ns. 1,000,000,000 ÷ 100 gives 10,000,000 Hz.
Frequency is the reciprocal of the period
The period is the time for one cycle, and the frequency is the number of cycles in one second, so f equals 1 divided by T (Wikipedia: Frequency).
A nanosecond is one billionth of a second (Wikipedia: Nanosecond). So a period of T ns gives a frequency of 1,000,000,000 divided by T hertz.
How to convert ns to Hz step by step
- Read the period in nanoseconds.
- Divide 1,000,000,000 by it to get hertz.
- Divide the hertz by 1,000,000 for megahertz, or use the last column.
- Write the unit after the answer.
Example 1: 1,000 ns
- Start with 1,000 ns.
- 1,000,000,000 ÷ 1,000 = 1,000,000.
- The frequency is 1,000,000 Hz.
1,000 ns = 1,000,000 Hz
Example 2: 100 ns
- Start with 100 ns.
- 1,000,000,000 ÷ 100 = 10,000,000.
- The frequency is 10,000,000 Hz.
100 ns = 10,000,000 Hz
Example 3: 20 ns
- Start with 20 ns.
- 1,000,000,000 ÷ 20 = 50,000,000.
- The frequency is 50,000,000 Hz.
20 ns = 50,000,000 Hz
The three examples below use common sizes.
Each one shows the sum in full.
ns to Hz conversion table
| Period | Frequency (Hz) | Frequency (MHz) |
|---|---|---|
| 1 ns | 1,000,000,000 Hz | 1,000 MHz |
| 2 ns | 500,000,000 Hz | 500 MHz |
| 5 ns | 200,000,000 Hz | 200 MHz |
| 10 ns | 100,000,000 Hz | 100 MHz |
| 20 ns | 50,000,000 Hz | 50 MHz |
| 40 ns | 25,000,000 Hz | 25 MHz |
| 50 ns | 20,000,000 Hz | 20 MHz |
| 100 ns | 10,000,000 Hz | 10 MHz |
| 250 ns | 4,000,000 Hz | 4 MHz |
| 500 ns | 2,000,000 Hz | 2 MHz |
| 1,000 ns | 1,000,000 Hz | 1 MHz |
| 10,000 ns | 100,000 Hz | 0.1 MHz |
The highlighted row is the default of the calculator. The last column gives MHz.
A quick mental shortcut for ns to Hz
Use the shortcut that 1,000 divided by the period in ns gives MHz. A period of 20 ns is 50 MHz.
A shorter period always means a higher frequency.
Clock examples
A period of 1 ns is 1 GHz, a period of 10 ns is 100 MHz and a period of 100 ns is 10 MHz (Wikipedia: Nanosecond).
A frequency of 3 MHz has a period of about 333 ns, so a period of 333 ns is about 3 MHz.
Worked examples
A period of 50 ns is 20,000,000 Hz, which is 20 MHz. A period of 250 ns is 4,000,000 Hz, which is 4 MHz.
A period of 2,000 ns is 500,000 Hz, which is 0.5 MHz.
Going the other way
To turn a frequency into a period, divide 1,000,000,000 by the frequency in hertz. So 20 MHz, which is 20,000,000 Hz, has a period of 50 ns.
The MHz to ns page does this step directly.
A sense of scale
Light travels about 0.3 m in a nanosecond, so a period of a few ns is the time light needs to cross a short cable (Wikipedia: Nanosecond).
This is one reason fast circuits care about wire length.
Quick conversion answers
| Conversion | Result |
|---|---|
| 1,000 ns | 1,000,000 Hz |
| 100 ns | 10,000,000 Hz |
| 20 ns | 50,000,000 Hz |
| 10 ns | 100,000,000 Hz |
Where this conversion is used
Engineers turn a measured period on a scope into a frequency.
Students link timing in nanoseconds to clock speed.
Common mistakes to avoid
- Using microseconds. A period in us needs 1,000,000 on top, not 1,000,000,000.
- Multiplying instead of dividing. A longer period gives a lower frequency.
- Forgetting the unit. The answer is in Hz unless you read the MHz column.
- Mixing period and half period. Use the time for a full cycle.
Related converters
More periods in nanoseconds
4 ns is 250,000,000 Hz. 8 ns is 125,000,000 Hz. 16 ns is 62,500,000 Hz.
25 ns is 40,000,000 Hz. 80 ns is 12,500,000 Hz. 200 ns is 5,000,000 Hz.
400 ns is 2,500,000 Hz. 800 ns is 1,250,000 Hz. 2,000 ns is 500,000 Hz.
Doubling the first number
8 ns is 125,000,000 Hz. 16 ns is 62,500,000 Hz. 32 ns is 31,250,000 Hz.
50 ns is 20,000,000 Hz. 160 ns is 6,250,000 Hz. 400 ns is 2,500,000 Hz.
800 ns is 1,250,000 Hz. 1,600 ns is 625,000 Hz. 4,000 ns is 250,000 Hz.
More worked examples
A period of 4 ns is 250,000,000 Hz, which is 250 MHz. A period of 8 ns is 125 MHz, and a period of 16 ns is 62.5 MHz.
A period of 80 ns is 12.5 MHz, and a period of 400 ns is 2.5 MHz. A period of 10,000 ns is 100,000 Hz, which is 100 kHz.
Checking your answer
Multiply the frequency by the period in seconds and you should get 1. For 125 MHz and 8 ns, 125,000,000 times 0.000000008 is 1.
If the result is not 1, a zero has slipped. Count the digits again.
Which way the answer moves
Cut the period in half and the frequency doubles. A period of 40 ns is 25 MHz, and a period of 20 ns is 50 MHz.
This is why fast clocks have such short periods.
Frequently asked questions
How do I convert ns to Hz?
Divide 1,000,000,000 by the period in nanoseconds.
What frequency is a 10 ns period?
100 MHz, which is 100,000,000 Hz.
What frequency is a 1,000 ns period?
1 MHz.
How do I get MHz from ns?
Divide 1,000 by the period in ns.
Why does a shorter period mean a higher frequency?
Because more cycles fit into each second.
Is this the same as sampling rate?
It is the same sum, if the period is the time between samples.
Sources
- Wikipedia: Frequency (en.wikipedia.org)
- Wikipedia: Nanosecond (en.wikipedia.org)
