cps Calculator

Convert any frequency between cps, Hz, RPM, rad/s and more.

Supports nine frequency units with metric and angular scales.

Updated August 19, 2026
Frank Zhao - Creator
CreatorFrank Zhao
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Introduction

Frequency is how often something repeats in one second, and the same physical rate can be written in several different units depending on where it comes from. Audio gear and radios are usually labelled in hertz, kilohertz or megahertz, motors and fans are rated in revolutions per minute, and physics formulas expect radians per second. This calculator accepts any of them and instantly shows the same frequency in every other unit.

One shared base keeps every unit exact

Internally the calculator works in hertz, the SI unit of frequency, so a whole-hertz input like 60 Hz60\ \mathrm{Hz} stays exact end-to-end: it reads back 60 cps60\ \mathrm{cps}, 3600 RPM3600\ \mathrm{RPM} and 0.06 kHz0.06\ \mathrm{kHz} with no rounding residue. Only the radian-based reading is genuinely approximate, because π\pi is irrational.

Every field is a two-way input

There is no fixed "input" and "output" here. Type a frequency into any of the nine fields and the other eight re-solve around it. If you later correct a different value, the whole set rotates around the value you changed — you never re-enter the full frequency by hand.

Audio engineers checking a sample rate, electronics hobbyists reading a crystal oscillator, motor technicians comparing a nameplate speed, and students converting between Hz and rad/s will all find every field updates together, so a single frequency is never re-typed into a different unit by hand.

How to use / quick start

  1. 1Type the frequency you already have into any field — cps, cpm, RPM, Hz, kHz, MHz, GHz, deg/s or rad/s.
  2. 2Every other field updates instantly. Read whichever unit your equipment, spreadsheet, code or formula needs and copy it.
  3. 3Correct any single value later — because every field is editable, the whole set re-solves around the value you changed.

Worked example — read a 60 Hz mains frequency in every unit

Type 6060 into the Frequency in hertz field. The calculator fills the rest from the same rate:

60 Hz60\ \mathrm{Hz}==60 cps60\ \mathrm{cps}==3600 RPM3600\ \mathrm{RPM}==3600 cpm3600\ \mathrm{cpm}
60 Hz60\ \mathrm{Hz}==0.06 kHz0.06\ \mathrm{kHz}==21600 deg/s21600\ \mathrm{deg/s}==376.991 rad/s376.991\ \mathrm{rad/s}

So the fields show 36003600 in RPM and cpm, 0.060.06 in kHz, 2160021600 in deg/s and 376.991376.991 in rad/s. The rad/s value carries an ≈\approx marker because it is 60×2π60 \times 2\pi.

Calculation method

One hertz is one cycle per second

The hertz is the SI unit of frequency, defined as one cycle per second. Every other unit in this calculator is a fixed multiple of that base:

1 Hz1\ \mathrm{Hz}==1 cps1\ \mathrm{cps}==60 cpm60\ \mathrm{cpm}==60 RPM60\ \mathrm{RPM}
1 Hz1\ \mathrm{Hz}==0.001 kHz0.001\ \mathrm{kHz}==10−6 MHz10^{-6}\ \mathrm{MHz}==10−9 GHz10^{-9}\ \mathrm{GHz}
1 Hz1\ \mathrm{Hz}==360 deg/s360\ \mathrm{deg/s}==2π rad/s2\pi\ \mathrm{rad/s}

Between any two units the calculator applies the same ratio, so you can convert in either direction without remembering a separate formula:

AtargetA_{\mathrm{target}}==AsourceA_{\mathrm{source}}×\timesfsourceftarget\frac{f_{\mathrm{source}}}{f_{\mathrm{target}}}

For example, to go from RPM to hertz you divide by 6060, and to go from kilohertz to hertz you multiply by 10001000. The calculator does this automatically for all nine fields.

Why the rad/s reading is marked approximate

One full cycle is 2π2\pi radians, so converting to radians per second always involves π\pi, an irrational number. The calculator uses the exact π\pi at full working precision, then shows a rounded preview:

1 Hz1\ \mathrm{Hz}==2π rad/s2\pi\ \mathrm{rad/s}≈\approx6.28319 rad/s6.28319\ \mathrm{rad/s}

The ≈\approx marker simply means the displayed value is a rounded preview of an exact irrational result — the full working value is one precision toggle away.

Real-world examples

Audio: a 440 Hz tuning note in kilohertz

The standard tuning note A4 is 440 Hz440\ \mathrm{Hz}, but audio software often displays frequencies in kilohertz. Type 440440 into Frequency in hertz and read the kHz field:

440 Hz440\ \mathrm{Hz}==0.44 kHz0.44\ \mathrm{kHz}==0.00044 MHz0.00044\ \mathrm{MHz}

The human hearing range spans roughly 15 Hz15\ \mathrm{Hz} to 20 kHz20\ \mathrm{kHz}, so a 20 kHz20\ \mathrm{kHz} upper limit converts to 20000 Hz20000\ \mathrm{Hz} — a useful sanity check when setting up audio equipment.

Machinery: a 3000 RPM spindle in hertz and rad/s

A machine spindle rated at 3000 RPM3000\ \mathrm{RPM} is easier to compare with electrical or control signals once it is in hertz. Type 30003000 into Frequency in revolutions per minute:

3000 RPM3000\ \mathrm{RPM}==50 Hz50\ \mathrm{Hz}==314.159 rad/s314.159\ \mathrm{rad/s}

Because 60 RPM=1 Hz60\ \mathrm{RPM} = 1\ \mathrm{Hz}, dividing the RPM by 6060 gives the frequency directly. The rad/s reading is 50×2π≈314.15950 \times 2\pi \approx 314.159.

Tips & best practices

  • Remember the 60× jump between RPM and Hz

    One hertz equals 6060 revolutions per minute, so a value that looks like 36003600 in RPM is only 60 Hz60\ \mathrm{Hz}. If a result is unexpectedly large or small by a factor of 6060, you are almost certainly mixing RPM with Hz.

  • Use the field whose unit you already have

    There is no wrong field to type into. If your source is a nameplate in RPM, type into RPM; if it is a crystal in MHz, type into MHz. The rest of the calculator follows.

  • Understand the ≈ on rad/s and its reverse

    Any value that passes through π\pi — the rad/s reading, or hertz when you type into rad/s — is shown as a rounded preview with an ≈\approx marker. The full working value is one precision toggle away, so nothing is lost.

  • Zero is a valid frequency

    A frequency of 00 is meaningful (nothing repeating) and is kept visible without an error, so you can use it as a starting point or a placeholder.

Frequently asked questions

Why does the rad/s value show an ≈\approx marker?

Converting to radians per second multiplies by 2π2\pi, and π\pi is irrational. The calculator works with the exact value at full precision and shows a rounded preview, so the marker tells you the visible number is a preview rather than the complete value.

How many hertz is one revolution per minute?

Exactly 160 Hz\frac{1}{60}\ \mathrm{Hz}. So 60 RPM=1 Hz60\ \mathrm{RPM} = 1\ \mathrm{Hz}, 3600 RPM=60 Hz3600\ \mathrm{RPM} = 60\ \mathrm{Hz}, and 1 Hz=60 RPM1\ \mathrm{Hz} = 60\ \mathrm{RPM}.

Why does 1 Hz show as 0.001 in the kHz field?

Because one kilohertz is 10001000 hertz. Dividing 11 by 10001000 gives 0.001 kHz0.001\ \mathrm{kHz} — the same frequency written in a larger unit, not a rounding error.

Limitations

  • This calculator changes how a frequency is written; it does not measure frequency or add accuracy beyond the numbers you type. The result is only as precise as the input.
  • Any value that involves π\pi — the rad/s reading, or hertz derived from rad/s — is shown as a rounded preview marked with ≈\approx, because π\pi is irrational.
  • Very long inputs (over 10,000 digits) are kept on screen with a friendly error rather than being converted, so an accidental paste never silently corrupts the result.

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cps Calculator – Convert Cycles per Second to Hz, RPM & More