Frequency Converter

What is frequency?

Frequency is how often a repeating event occurs per unit of time — cycles per second. A swinging pendulum, an alternating current, a radio wave, a spinning motor, and a musical note all have a frequency. The hertz (Hz) is the SI unit: one cycle per second. Because frequencies span from fractions of a Hz (ocean tides) to gigahertz (computer clocks) and beyond, we use prefixes and separate units like RPM and rad/s. A frequency converter connects them all through the hertz.

Why so many frequency units?

Electronics and radio use Hz, kHz, MHz, GHz because signals range from audio to microwave. Rotating machinery uses RPM (revolutions per minute) — intuitive for shafts and wheels. Physics and engineering dynamics use radian per second (rad/s) because calculus with angles is cleaner in radians. The choice is about convenience for the field, not different physics. Our tool unifies them.

The base-unit method

Every value is converted into hertz (the base) using each unit's Hz factor, then divided by the target's factor. Simple ratios give six-decimal accuracy. For example, 1 kHz = 1000 Hz and 1 MHz = 1,000,000 Hz, so 1 MHz = 1000 kHz. For RPM: 1 RPM = 1 revolution/60 s = 1/60 Hz. For rad/s: 1 Hz = 2π rad/s, so 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz.

Key conversion factors (to Hz)

• 1 hertz = 1 Hz (base)
• 1 kilohertz = 1000 Hz
• 1 megahertz = 1,000,000 Hz
• 1 gigahertz = 1,000,000,000 Hz
• 1 RPM = 1/60 Hz ≈ 0.0166667 Hz
• 1 rad/s = 1/(2π) Hz ≈ 0.159155 Hz

Hz and RPM

The swap between cycles per second and revolutions per minute is just ×60 or ÷60. 1 Hz = 60 RPM (one spin per second = 60 per minute). A 50 Hz mains frequency drives a 3000 RPM synchronous motor (two-pole); a 60 Hz grid drives 3600 RPM. A hard-drive platter at 7200 RPM is 120 Hz. Remember the direction: frequency (Hz) is per second, RPM is per minute, hence the 60× factor.

Hertz and rad/s

Angular frequency ω (rad/s) and ordinary frequency f (Hz) are linked by ω = 2πf. One full cycle is 2π radians, so 1 Hz = 2π rad/s ≈ 6.283185 rad/s, and 1 rad/s = 0.159155 Hz. This matters in vibration analysis, filter design, and AC circuit theory, where equations use ω. Our converter keeps both so you can move between "cycles per second" and "radians per second" without error.

Real-world examples

A Wi-Fi band at 2.4 GHz = 2,400,000,000 Hz = 2,400,000 kHz. A processor at 3.5 GHz is 3.5 billion cycles/s. AM radio at 1000 kHz = 1 MHz. A ceiling fan at 300 RPM = 5 Hz. A turntable at 33⅓ RPM = 0.5556 Hz. Earth's rotation is 1/86400 Hz ≈ 1.157×10⁻⁵ Hz, or 7.272×10⁻⁵ rad/s. These spans — from tectonic to terahertz — are exactly what a single converter handles.

Common mistakes

The main error is dropping the 2π when switching Hz ↔ rad/s — they are not equal; 1 Hz is 6.28 rad/s. Another is forgetting RPM is per minute, so converting to Hz needs the ÷60 (or ×60 the other way). A third is miscounting SI prefixes: 1 GHz is 10⁹ Hz, not 10⁶. Finally, don't confuse bandwidth (Hz, a range) with a center frequency (Hz, a point) — both use Hz but mean different things. Use the converter's exact factors to stay precise.

Frequently asked questions