How frequency conversion works (with the exact formulas)

Frequency answers a simple question: how many cycles happen in a unit of time? If you clap once per second, that’s 1 Hz. If a signal oscillates one million times per second, that’s 1 MHz. Converting frequency is mostly about converting the time base.

The easiest way to convert is to pick a common reference unit and convert everything through it. For frequency, the natural reference is hertz (Hz), meaning cycles per second. This calculator converts your input into Hz first, then converts from Hz into the target unit.

Metric prefixes are powers of 10:

• kilo (k) = 10³ → 1 kHz = 1,000 Hz
• mega (M) = 10⁶ → 1 MHz = 1,000,000 Hz
• giga (G) = 10⁹ → 1 GHz = 1,000,000,000 Hz
• tera (T) = 10¹² → 1 THz = 1,000,000,000,000 Hz

So the conversion rule is:

• Hz → kHz: divide by 1,000
• kHz → Hz: multiply by 1,000
• Hz → MHz: divide by 1,000,000
• MHz → Hz: multiply by 1,000,000
• …and so on for GHz and THz.

Sometimes frequency is described as “per minute” or “per hour”. That’s common for engines, motors, fans, turntables, and any rotating system. Here’s the conversion logic:

• RPM means revolutions per minute. If you assume one revolution equals one cycle, then Hz = RPM / 60 and RPM = 60 × Hz.
• CPM means cycles per minute. This is numerically the same conversion as RPM: Hz = CPM / 60.
• CPH means cycles per hour. Convert hours to seconds: Hz = CPH / 3600 and CPH = 3600 × Hz.

Physics and engineering often use angular frequency, written as ω (omega), measured in radians per second (rad/s). It’s connected to frequency in Hz by the factor 2π:

• ω = 2π f
• f = ω / (2π)

Why the 2π? Because one full cycle corresponds to 2π radians around a circle. When you convert rad/s to Hz, you’re converting “radians per second” into “cycles per second.”

The period T is the time for one complete cycle. It is the inverse of frequency:

• T = 1 / f (if f is in Hz, T is in seconds)

This is one of the most helpful “feel” conversions. Frequency tells you how fast something repeats; period tells you how long you wait for it to repeat once. For example, a 50 Hz power line has a period of 1/50 = 0.02 s (20 milliseconds) per cycle.

If you’re roughly estimating, remember: kHz ≈ thousands per second, MHz ≈ millions per second, and GHz ≈ billions per second. Then use the inverse to estimate period. A 1 kHz signal has a period of about 1 millisecond; a 1 MHz signal has a period of about 1 microsecond; a 1 GHz signal has a period of about 1 nanosecond. Those “milli/micro/nano” patterns are extremely common in electronics and timing diagrams.

Real examples you can copy (with step-by-step math)

Problem: Convert 440 Hz to kHz.
Rule: kHz = Hz / 1000
Answer: 440 / 1000 = 0.44 kHz
Period: T = 1/440 ≈ 0.0022727 s (≈ 2.27 ms)

Problem: Convert 2.4 GHz to Hz.
Rule: Hz = GHz × 10^9
Answer: 2.4 × 10^9 = 2,400,000,000 Hz
Period: T = 1 / (2.4×10^9) ≈ 4.17×10^-10 s (≈ 0.417 ns)

Problem: Convert 3000 RPM to Hz.
Rule: Hz = RPM / 60
Answer: 3000 / 60 = 50 Hz
Period: T = 1/50 = 0.02 s
Interpretation: One full rotation takes 0.02 seconds (20 ms).

Problem: Convert ω = 200 rad/s to Hz.
Rule: f = ω / (2π)
Answer: 200 / (2π) ≈ 31.83 Hz
Check: If f ≈ 31.83 Hz, then ω = 2πf ≈ 200 rad/s. ✔

Problem: Convert 7200 CPH to CPM.
Step 1: Convert CPH to Hz: Hz = 7200 / 3600 = 2 Hz
Step 2: Convert Hz to CPM: CPM = 60 × Hz = 120 CPM
Answer: 7200 CPH = 120 CPM

Tip: The calculator automates these steps by converting everything through Hz first. That’s why it can handle any “from → to” pair cleanly.

The converter’s “two-step” method (simple but powerful)

Even though the UI feels like a direct conversion, the engine under the hood does something very consistent: it converts from your selected unit to Hz, then converts from Hz to your selected output unit. This is the same approach used in professional unit conversion libraries because it reduces errors and makes the code easier to trust.

The converter reads your input number and your “From unit.” Then it applies the correct formula: multiply/divide by powers of 10 for metric prefixes, divide by 60 for RPM/CPM, divide by 3600 for CPH, or divide by 2π if you started with rad/s.

Once everything is in Hz, converting to the target is easy: multiply/divide again by powers of 10, multiply by 60 to get RPM/CPM, multiply by 3600 to get CPH, or multiply by 2π to get rad/s.

After it finds f in Hz, it also computes: T = 1/f and ω = 2πf. That’s why period and angular frequency remain consistent even if your input/output unit changes.

The colored bar is not a scientific rating—it’s a quick visual cue. We map the frequency (in Hz) onto a log scale so that both small and huge frequencies (like audio vs Wi‑Fi) still “move” the bar. It’s purely for intuition and shareability: higher frequency → “faster” → the bar fills more.

Privacy note: Your values never leave your device. The share buttons only share the text you see (and the public tool URL).

Frequently Asked Questions

• What is the difference between Hz and rad/s?

  Hz measures cycles per second. rad/s measures radians per second. One cycle equals 2π radians, so they’re related by ω = 2πf. If you see formulas in physics using ω, this calculator can convert it back to regular frequency.

• Is RPM always the same as cycles per minute?

  Numerically, yes—RPM and CPM convert the same way. Conceptually, RPM emphasizes rotation (revolutions), while CPM emphasizes repeating events (cycles). If one revolution equals one cycle in your system, they match exactly.

• How do I convert frequency to period?

  Use T = 1/f where f is in Hz. This tool shows period automatically. If your input is in kHz/MHz/GHz/RPM, the tool converts it to Hz first, then computes period in seconds.

• Why does a high frequency create a tiny period?

  Because frequency counts how many cycles occur per second. If many cycles happen each second (high frequency), each cycle must be short—so the time per cycle (period) becomes small.

• Can frequency be negative?

  In many practical contexts, frequency is reported as a non‑negative magnitude. Some math/physics conventions can attach a sign to represent direction or phase, but the unit conversion itself typically uses absolute values. This calculator accepts negative inputs, but period is reported using the magnitude (because “time per cycle” is a positive quantity).

• How accurate are the results?

  The conversions here are exact for the unit definitions (powers of ten, 60 seconds/minute, 3600 seconds/hour, and π). Any rounding you see is just display formatting. If you choose “Scientific,” it will show results in scientific notation.

• What’s a “good” frequency for Wi‑Fi or audio?

  That depends on what you mean. Wi‑Fi commonly uses bands around 2.4 GHz and 5 GHz, while typical audio ranges from about 20 Hz to 20 kHz. This tool is best for converting units and understanding the associated timing (period), not judging quality.