Frequency Converter

Frequency Converter

Frequency measures how many times something repeats per second — a radio wave oscillating, a motor shaft spinning, a speaker cone vibrating, or a processor completing a clock cycle. The base unit is hertz (Hz), and practical values span an enormous range: from the 0.00001 Hz of a tidal cycle to the 300 GHz of millimeter-wave 5G signals. This converter handles hertz, kilohertz, megahertz, gigahertz, terahertz, RPM, and radians per second, covering audio engineering, wireless communications, motor control, and physics applications in one place.

How Frequency Conversion Works

All conversions use hertz (Hz) as the base unit, defined as one complete cycle per second. The formula is: Result = Input x (source factor in Hz) / (target factor in Hz). Key relationships: 1 kHz = 1,000 Hz, 1 MHz = 1,000,000 Hz, 1 GHz = 1,000,000,000 Hz, 1 THz = 1,000,000,000,000 Hz, 1 RPM = 1/60 Hz (approximately 0.01667 Hz), and 1 rad/s = 1/(2pi) Hz (approximately 0.15915 Hz). The rad/s conversion is used in physics and control engineering because angular velocity in radians per second is the natural unit for differential equations describing oscillating systems.

Worked Examples

An audio engineer sets a low-pass filter cutoff at 3,500 Hz on a vocal track. To enter this in a DSP processor that accepts values in kHz, she divides by 1,000: 3,500 / 1,000 = 3.5 kHz. When she also needs the angular frequency for a filter coefficient calculation, she multiplies by 2pi: 3,500 x 6.2832 = 21,991 rad/s.

An HVAC technician works with a 3-phase motor running at 1,750 RPM and needs to program a variable frequency drive (VFD). The required output frequency is: 1,750 / 60 = 29.17 Hz. He programs the VFD to output 29.17 Hz at full speed, then uses the converter to check intermediate speeds for soft-start ramp profiles.

A radio engineer checks whether a 915 MHz signal falls within the ISM (industrial, scientific, medical) band. Converting to GHz: 915 / 1,000 = 0.915 GHz. This confirms the signal is in the 902-928 MHz ISM band, commonly used for long-range IoT devices like LoRa sensors.

Expanded Reference Table

When to Use This Converter

• Audio and DSP — convert Hz to kHz for filter settings, or to rad/s for writing digital signal processing code and filter coefficient formulas
• RF and wireless engineering — translate between MHz and GHz when referencing band plans, antenna specs, or spectrum allocations
• Motor control — convert RPM to Hz to determine the drive frequency for variable frequency drives and verify synchronous motor speeds
• Physics and lab work — convert between Hz and rad/s when matching angular frequency notation in textbooks or simulation software
• CPU and hardware specs — express processor clock speeds in GHz for readability, or convert to Hz for low-level timing calculations in embedded systems

Common Mistakes to Avoid

1. Misplacing the decimal between prefixes. Each prefix step is a factor of 1,000, not 100. A 2.4 GHz WiFi channel is 2,400 MHz, not 240 MHz. Double-check any conversion that crosses a prefix boundary.
2. Confusing Hz with rad/s. 1 Hz is not equal to 1 rad/s. One full cycle spans 2pi radians, so 1 Hz = 6.2832 rad/s. Using Hz directly in angular frequency formulas (like impedance or resonance equations) gives answers off by a factor of 2pi.
3. Forgetting RPM divides by 60 for Hz. A motor at 1,800 RPM runs at 30 Hz, not 1,800 Hz. This matters when setting VFD output frequencies — entering the RPM value directly would command a speed 60x higher than intended.
4. Treating CPU GHz as a direct performance metric. Clock frequency measures cycles per second, not work done per second. Two CPUs at 3.5 GHz can have very different performance due to different numbers of instructions executed per cycle.

Quick Reference Benchmarks

• Human hearing range: 20 Hz to 20,000 Hz (20 kHz)
• Standard AC power: 60 Hz (US/Canada), 50 Hz (Europe/Asia)
• Typical electric motor (4-pole, 60 Hz): 1,800 RPM
• WiFi 2.4 GHz = 2,400,000,000 Hz = 2,400 MHz
• Concert A = 440 Hz; one octave up = 880 Hz; one octave down = 220 Hz
• A 4.0 GHz CPU executes 4,000,000,000 clock cycles per second

Tips

1. For audio work, keep filter values in Hz or kHz and only convert to rad/s at the last step in coefficient calculations — it reduces the chance of a 2pi error in intermediate steps
2. When reading radio datasheets, note that manufacturers sometimes mix MHz and GHz within the same table; always verify the unit label before comparing two rows
3. Converting RPM to Hz for a VFD: the formula is Hz = (RPM x number of poles) / 120 for AC motors — for a 4-pole motor at 1,750 RPM that gives 58.3 Hz
4. In embedded systems programming, clock rates are often specified in Hz but must match the timer register’s maximum count; convert to the right scale before calculating prescaler values
5. Sound frequency doubles with each octave, so if you know one note’s Hz value, the same note one octave higher is exactly 2x that value
6. For spectrum analysis, radians per second and hertz are both legitimate frequency axes; check which axis a plot uses before reading values off it