CPM To Hz
A machine running at 30 CPM completes a cycle every 2 seconds, which is 0.5 Hz.
Quick answer: Divide the CPM by 60. For example, 30 CPM is 0.5 Hz, 300 CPM is 5 Hz and 3,000 CPM is 50 Hz.
The CPM to Hz formula
Hertz equal CPM divided by 60.
CPM here means cycles per minute.
Take 30 CPM. 30 × 0.01666667 gives 0.5 Hz.
Take 300 CPM. 300 × 0.01666667 gives 5 Hz.
Counting cycles in a second
The hertz is one cycle per second (Wikipedia: Frequency). A rate in CPM counts cycles in a minute, so divide by 60 to count them in one second.
The time for one cycle is the reciprocal of the frequency, which is 60 divided by the CPM in seconds (Wikipedia: Frequency).
How to convert CPM to Hz step by step
- Read the rate in CPM.
- Divide it by 60.
- Write Hz after the answer.
- Divide 60 by the CPM for the seconds per cycle.
Example 1: 30 CPM
- Start with 30 CPM.
- 30 × 0.01666667 = 0.5.
- The frequency is 0.5 Hz.
30 CPM = 0.5 Hz
Example 2: 300 CPM
- Start with 300 CPM.
- 300 × 0.01666667 = 5.
- The frequency is 5 Hz.
300 CPM = 5 Hz
Example 3: 3,000 CPM
- Start with 3,000 CPM.
- 3,000 × 0.01666667 = 50.
- The frequency is 50 Hz.
3,000 CPM = 50 Hz
Example 4: 150 CPM
- Start with 150 CPM.
- 150 × 0.01666667 = 2.5.
- The frequency is 2.5 Hz.
150 CPM = 2.5 Hz
Example 5: 1,500 CPM
- Start with 1,500 CPM.
- 1,500 × 0.01666667 = 25.
- The frequency is 25 Hz.
1,500 CPM = 25 Hz
Example 6: 60 CPM
- Start with 60 CPM.
- 60 × 0.01666667 = 1.
- The frequency is 1 Hz.
60 CPM = 1 Hz
Round only at the end. Rounding in the middle of a sum adds small errors that grow.
CPM to Hz conversion table
| Cycles per minute (CPM) | Hertz (Hz) | Cycles per hour |
|---|---|---|
| 3 CPM | 0.05 Hz | 180 Cycles per hour |
| 7.5 CPM | 0.125 Hz | 450 Cycles per hour |
| 15 CPM | 0.25 Hz | 900 Cycles per hour |
| 30 CPM | 0.5 Hz | 1,800 Cycles per hour |
| 60 CPM | 1 Hz | 3,600 Cycles per hour |
| 150 CPM | 2.5 Hz | 9,000 Cycles per hour |
| 300 CPM | 5 Hz | 18,000 Cycles per hour |
| 600 CPM | 10 Hz | 36,000 Cycles per hour |
| 1,500 CPM | 25 Hz | 90,000 Cycles per hour |
| 3,000 CPM | 50 Hz | 180,000 Cycles per hour |
| 7,500 CPM | 125 Hz | 450,000 Cycles per hour |
| 15,000 CPM | 250 Hz | 900,000 Cycles per hour |
The highlighted row is the default of the calculator. The last column gives Cycles per hour.
A quick mental shortcut for CPM to Hz
Divide by 60. 12 CPM is 0.2 Hz.
To get the seconds per cycle, divide 60 by the CPM. 12 CPM is 5 seconds per cycle.
Seconds per cycle
A rate of 30 CPM is one cycle every 2 seconds. A rate of 20 CPM is one cycle every 3 seconds, and 15 CPM is one cycle every 4 seconds.
A rate of 6 CPM is one cycle every 10 seconds.
The CPM name
The letters CPM also stand for other things, such as counts per minute. This page uses cycles per minute.
Always check what a source means by CPM before you convert.
Cycles per hour
The last column gives cycles per hour, which is the CPM times 60. So 30 CPM is 1,800 cycles per hour.
This is handy when a machine is rated per hour.
Quick conversion answers
| Conversion | Result |
|---|---|
| 30 CPM | 0.5 Hz |
| 300 CPM | 5 Hz |
| 3,000 CPM | 50 Hz |
| 30,000 CPM | 500 Hz |
Where this conversion is used
Engineers turn a machine cycle rate into hertz.
Makers find the time between cycles.
Common mistakes to avoid
- Multiplying by 60. You divide by 60 to get hertz.
- Reading CPM as counts per minute. This page is for cycles.
- Mixing hertz with cycles per hour. Check the column.
- Counting half cycles. Use full cycles only.
Related converters
More values at a glance
0.6 CPM is 0.01 Hz. 9 CPM is 0.15 Hz. 22.5 CPM is 0.375 Hz.
45 CPM is 0.75 Hz. 90 CPM is 1.5 Hz. 120 CPM is 2 Hz.
450 CPM is 7.5 Hz. 750 CPM is 12.5 Hz. 6,000 CPM is 100 Hz.
Common rates
3 CPM is 0.05 Hz. 6 CPM is 0.1 Hz. 12 CPM is 0.2 Hz.
15 CPM is 0.25 Hz. 20 CPM is 0.3333 Hz. 45 CPM is 0.75 Hz.
75 CPM is 1.25 Hz. 150 CPM is 2.5 Hz. 240 CPM is 4 Hz.
More worked examples
A rate of 3 CPM is 0.05 Hz, and a rate of 6 CPM is 0.1 Hz. A rate of 15 CPM is 0.25 Hz, and a rate of 45 CPM is 0.75 Hz.
A rate of 75 CPM is 1.25 Hz, and a rate of 150 CPM is 2.5 Hz. A rate of 240 CPM is exactly 4 Hz.
Cycles per hour
A rate of 12 CPM is 720 cycles per hour, and a rate of 45 CPM is 2,700 cycles per hour.
Multiply the CPM by 60 for the hourly figure.
Checking your answer
Multiply the hertz by 60 and you should get the CPM. For 0.25 Hz, the product is 15.
If it is not, the divide step slipped.
Two rates side by side
Compare 30 CPM and 60 CPM. The first is 0.5 Hz and the second is 1 Hz.
Doubling the CPM doubles the hertz, and it halves the seconds per cycle from 2 to 1.
Rounding
Some rates give long decimals. A rate of 7 CPM is about 0.1167 Hz, and it gives about 8.571 seconds per cycle.
Keep the extra digits while you work and round only at the end.
Frequently asked questions
How many Hertz is 1 CPM?
1 CPM is 0.01666667 Hz.
How many Hertz is 300 CPM?
300 CPM is 5 Hz.
How many Cycles per minute is 1 Hz?
1 Hz is 60 CPM.
How do I convert CPM to Hz?
Divide the CPM by 60.
What is 30 CPM in Hz?
0.5 Hz.
How many seconds is one cycle at 30 CPM?
2 seconds.
Sources
- Wikipedia: Frequency (en.wikipedia.org)
