3000 rpm in Hz
- Value
- 3000 rpm
- From
- revolution per minute (rpm)
- To
- hertz (Hz)
- Converted value
- 50 Hz
Checked against: 3000 / 60 = 50
Frequency converter
Convert rpm to Hz, Hz to rpm, BPM to Hz, GHz to MHz and hertz to radians per second (ω = 2πf), from Hz to THz.
By AdminDrafted with AI writing toolsUpdated Checked examples: 4
Converted value
Hz
Converted value: 50 Hz
- Conversion
- 3,000 rpm = 50 Hz
- Conversion factor
- 0.0166666666667
- Exactness
- Exact
3,000 rpm is exactly 50 Hz. One revolution per minute is about 0.01666667 Hz.
The same amount counted in each unit
3,000 rpm in every Frequency unit
| Unit | Value | Definition |
|---|---|---|
| hertz (Hz) | 50 | Base unit |
| kilohertz (kHz) | 0.05 | 1 kHz = 1,000 Hz, exact |
| megahertz (MHz) | 0.00005 | 1 MHz = 1,000,000 Hz, exact |
| gigahertz (GHz) | 5 × 10⁻⁸ | 1 GHz = 1,000,000,000 Hz, exact |
| terahertz (THz) | 5 × 10⁻¹¹ | 1 THz = 1,000,000,000,000 Hz, exact |
| revolution per minute (rpm) | 3,000 | 1 rpm = 1/60 Hz, exact |
| beat per minute (BPM) | 3,000 | 1 BPM = 1/60 Hz, exact |
| radian per second (rad/s) | 314.1593 | 1 rad/s = 1/(2π) Hz, exact |
How it's calculated S
Convert revolution per minute to hertz
1 rpm = 1/60 Hz, exact
Both units are defined exactly and the converted mathematical value has a terminating decimal. A displayed result may still be rounded.
About the frequency converter
One hertz is one cycle per second, so revolutions per minute and beats per minute divide by 60 to give hertz, and the SI prefixes step by 1,000 from kHz to THz. Angular frequency in radians per second is ω = 2πf, so 1 Hz is 6.2832 rad/s; conversions to or from rad/s involve π and are shown to 12 significant figures.
The default converts 3,000 rpm to 50 Hz, the speed of a two-pole motor on a 50 Hz supply. Musicians convert tempo the same way (120 BPM is 2 Hz), and radio users move between MHz and GHz: 2.4 GHz Wi-Fi is 2,400 MHz.
Rpm and BPM count whole cycles per minute, while rad/s counts the angle swept per second. A cycle is 2π radians, so 60 rpm is 1 Hz and 6.2832 rad/s.
How to convert rpm to Hz
Divide revolutions per minute by 60: 3,000 rpm = 50 Hz, because a hertz is one cycle per second and a minute has 60 seconds. Multiply Hz by 60 to get rpm. The same rule turns a tempo or heart rate in beats per minute into hertz: 120 BPM is 2 Hz.
- 1,800 rpm = 30 Hz
- 3,000 rpm = 50 Hz
- 3,600 rpm = 60 Hz
- 7,200 rpm = 120 Hz, a common hard-drive spindle speed
How to convert Hz to rad/s
Multiply by 2π, about 6.283185: ω = 2πf. So 1 Hz is 6.283185 rad/s and 50 Hz is 314.16 rad/s. A hertz counts whole cycles, a radian per second counts the angle swept, and one cycle is 2π radians.
rpm to rad/s
Combine the two steps: multiply rpm by 2π/60, which is π/30 or 0.104720. So 60 rpm is 6.283185 rad/s, 1,000 rpm is 104.72 rad/s, and 1 rad/s is 9.549297 rpm. Rotation formulas such as power = torque × ω need rad/s.
kHz, MHz and GHz
SI prefixes step by 1,000: 1 GHz = 1,000 MHz = 1,000,000 kHz = 10⁹ Hz. Wi-Fi's 2.4 GHz band is 2,400 MHz, and a 3.5 GHz processor clock ticks 3.5 billion times a second.
Frequency prefixes are always decimal, never the 1,024 used for some memory sizes (NIST SP 811, chapter 4 lists the hertz and the SI prefixes).
Motor speed and mains frequency
A synchronous AC motor turns at 120 × f ÷ p rpm, where p is the number of poles. A two-pole motor runs at 3,000 rpm on 50 Hz mains and 3,600 rpm on 60 Hz; a four-pole motor at 1,500 or 1,800 rpm.
Induction motors run a few percent below that synchronous speed, for example about 2,900 rpm on 50 Hz, which is 48.33 Hz of shaft rotation.
Frequency conversion chart
Repeating decimals and results involving π are rounded to six places.
| Value | From | To | Converted rate |
|---|---|---|---|
| 3000 | rpm | Hz | 50 |
| 120 | BPM | Hz | 2 |
| 2.4 | GHz | MHz | 2400 |
| 1 | Hz | rad/s | 6.283185 |
| 60 | rpm | rad/s | 6.283185 |
| 1 | rad/s | rpm | 9.549297 |
Period: the reciprocal of frequency
The period of one cycle is T = 1/f. A 50 Hz supply has a 20 ms cycle, 60 Hz a 16.67 ms cycle, and a beat at 120 BPM lasts 0.5 s.
Common mistakes
- Putting Hz where rad/s belongs. 10 rad/s is 1.59 Hz, not 10 Hz; the factor between them is 2π.
- Forgetting the 60. 1,800 rpm is 30 Hz, not 1,800 Hz.
- Using 1,024 for frequency prefixes. 1 GHz is exactly 1,000 MHz.
Related frequency tools
The wavelength, frequency and photon energy calculator turns a frequency into a wavelength with c = fλ. The circular motion calculator handles rpm, rad/s and period for rotating objects, and the angle converter converts radians to degrees.
Worked examples
120 BPM in Hz
- Value
- 120 BPM
- From
- beat per minute (BPM)
- To
- hertz (Hz)
- Converted value
- 2 Hz
Checked against: 120 / 60 = 2
1 Hz in rad/s
- Value
- 1 Hz
- From
- hertz (Hz)
- To
- radian per second (rad/s)
- Converted value
- 6.2831853072 rad/s
- Exactness
- Exact definitions, involves π
Checked against: ω = 2πf = 6.28318530717958647…
2.4 GHz in MHz
- Value
- 2.4 GHz
- From
- gigahertz (GHz)
- To
- megahertz (MHz)
- Converted value
- 2,400 MHz
Checked against: 2.4 × 1000
Questions
How do I convert rpm to Hz?
Divide by 60, because hertz counts cycles per second and rpm cycles per minute. 3,000 rpm is 50 Hz, 1,800 rpm is 30 Hz, and 7,200 rpm, a common hard-drive speed, is 120 Hz. To go from Hz to rpm, multiply by 60.
Why does a motor run at 3,000 or 3,600 rpm?
Because its speed is locked to the supply frequency. A synchronous motor turns at 120 × f ÷ p rpm, where p is the number of poles, so a two-pole motor runs at 3,000 rpm on 50 Hz mains and 3,600 rpm on 60 Hz. Induction motors run a few percent below this synchronous speed, for example 2,900 rpm on 50 Hz.
How do I convert Hz to rad/s?
Multiply by 2π, about 6.28319: ω = 2πf. 50 Hz is 314.16 rad/s and 1 Hz is 6.2832 rad/s. Both units reduce to “per second”, but a hertz counts whole cycles while a radian per second counts the angle swept, and one cycle is 2π radians.
How many Hz is 120 BPM?
2 Hz: 120 beats ÷ 60 seconds. Tempo in beats per minute converts to hertz by dividing by 60, so 90 BPM is 1.5 Hz. The same arithmetic applies to heart rate: the American Heart Association gives a usual resting range of 60 to 100 beats per minute for most adults, corresponding to 1 to approximately 1.67 Hz.
How many MHz are in a GHz?
1,000. The shown GHz/MHz/kHz unit steps are factors of 1,000: 1 GHz = 1,000 MHz = 1,000,000 kHz = 10⁹ Hz. Wi-Fi's 2.4 GHz band is 2,400 MHz, and a 3.5 GHz processor clock ticks 3.5 billion times a second. Frequency prefixes are always decimal, never the binary 1,024 used for some memory sizes.
About this calculator
Sources
Checked against references
This calculator includes 4 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.