cps Calculator

How to use this cycles per second converter

What this calculator does. This tool takes one ordinary frequency expressed in cycles per second (cps) and converts it into equivalent linear-frequency and angular-frequency units. It is useful for translating older technical notation, comparing motor or shaft speed with oscillation rate, checking vibration specifications, and moving between hertz and angular speed. It does not measure a real device, account for slip in a motor, or determine whether a rotating system is safe; it performs exact unit relationships from the value you enter.

When to use it. Use it when a manual or historical document lists cps instead of hertz, when a laboratory frequency must be compared with RPM, when a vibration rate needs an angular-frequency value in rad/s, or when a frequency must be scaled into kHz, MHz, or GHz for a report.

How to calculate. The converter opens with a complete demonstration value of 4 cps, so every output and the Excel workbook are available immediately. Follow these steps:

1. Replace Frequency in cycles per second with your non-negative decimal value. Use a period for decimals, such as 2.5. Scientific notation and decimal commas are intentionally rejected to avoid ambiguous input.
2. Read Frequency in hertz as the primary result. Review the remaining cards for cycles per minute, RPM, radians per second, degrees per second, kHz, MHz, and GHz.
3. Use the conversion table to see each value, its unit, and the factor applied to cps. Select Download Excel to export the current validated inputs and results to a real XLSX workbook.
4. Select Reset to clear the demonstration and calculated state. Excel export is then disabled until you enter a complete valid frequency again.

Input guide. Frequency in cycles per second is required. Enter a finite number from 0 through 1×10¹⁵ cps. Zero is valid and means no repeating cycles. A realistic example is 60 cps, which is exactly 60 Hz. Increasing the input scales every output proportionally. Negative values are invalid because this converter represents the magnitude of a repetition rate, and values that would produce a non-finite derived result are rejected.

Output guide. Frequency in hertz is an exact identity because 1 cps equals 1 Hz. Cycles per minute and Revolutions per minute multiply cps by 60; RPM assumes one revolution corresponds to one complete cycle. Radians per second multiplies cps by 2π, while Degrees per second multiplies it by 360. Kilohertz, Megahertz, and Gigahertz divide hertz by 10³, 10⁶, and 10⁹ respectively. The summary pills repeat three high-value results for quick scanning. All are exact conversions in principle; displayed decimals are rounded for readability.

Worked example. At startup, the input is 4 cps. The hertz result is 4 Hz. Multiplying by 60 gives 240 cpm and 240 RPM. Multiplying by 2π gives 25.132741 rad/s at the displayed precision, and multiplying by 360 gives 1,440 °/s. Dividing 4 Hz by 1,000 gives 0.004 kHz; dividing by one million gives 0.000004 MHz; and dividing by one billion gives 0.000000004 GHz. These same typed values appear in the startup workbook.

Learn more. The BIPM SI Brochure defines the International System of Units, while the NIST explanation of the SI second provides the time basis underlying hertz. For angular quantities, see the NIST reference on SI units.