# 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.

Interactive version: https://www.calcopenly.com/conversion/frequency-converter
Subject: Unit converters

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.

## Inputs

- **Value**: A number in the “from” unit, or with its own unit
- **From** (options: hertz (Hz), kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz), revolution per minute (rpm), beat per minute (BPM), radian per second (rad/s))
- **To** (options: hertz (Hz), kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz), revolution per minute (rpm), beat per minute (BPM), radian per second (rad/s))

## Results

- Converted value — main result
- Conversion
- Conversion factor
- Exactness

## Formula

$$
\begin{gathered} x_{\text{to}} = x_{\text{from}} \times \dfrac{f_{\text{from}}}{f_{\text{to}}} \\ f = \text{one unit expressed in } \text{Hz} \end{gathered}
$$

## Worked examples

### 3000 rpm in Hz

- Value: 3000 rpm
- From: revolution per minute (rpm)
- To: hertz (Hz)
- **Converted value: 50 Hz**
- Checked against: 3000 / 60 = 50

### 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… (Python decimal)

### 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 rule applies to heart rate: the American Heart Association's normal adult resting range of 60 to 100 beats per minute is 1 to 1.67 Hz.

### How many MHz are in a GHz?

1,000. 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 binary 1,024 used for some memory sizes.

### How accurate is the frequency converter?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 4 worked examples whose answers come from independent sources; for example, “3000 rpm in Hz” is checked against 3000 / 60 = 50.

### Where does the method come from?

NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors; NIST Handbook 44, Appendix C — General tables of units of measurement.

## Sources

- [NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors](https://www.nist.gov/pml/special-publication-811)
- [NIST Handbook 44, Appendix C — General tables of units of measurement](https://www.nist.gov/pml/owm/nist-handbook-44-current-edition)