# Convert Radian to Second

Please provide values below to convert radian [rad] to second ["], or *vice versa*.

### Radian

**Definition:** A radian (symbol: rad) is the standard unit of angular measure. It is a derived unit (meaning that it is a unit that is derived from one of the seven SI base units) in the International System of Units. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. One radian is equal to 180/π (~57.296) degrees.

**History/origin:** Measuring angles in terms of arc length has been used by mathematicians since as early as the year 1400. The concept of the radian specifically however, is credited to Roger Cotes who described the measure in 1714. Although he described the unit, Cotes did not name the radian, and it was not until 1873 that the term "radian" first appeared in print.

**Current use:** The radian is widely used throughout mathematics as well as in many branches of physics that involve angular measurements. Although the symbol "rad" is the accepted SI symbol, in practice, radians are often written without the symbol since a radian is a ratio of two lengths and is therefore, a dimensionless quantity. As such, when angle measures are written, the lack of a symbol implies that the measurement is in radians, while a ° symbol would be added if the measurement were in degrees.

### Second

**Definition:** A second is the base unit of time in the International System of Units (SI). It is defined as exactly "9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."

**History/origin:** Unlike many units that have had numerous definitions throughout history, the second has only had three different definitions.

The second was historically defined as 1/86400 of a day in 1832, which was based on the definition of a day as the approximate amount of time required for the Earth to complete a full rotation cycle relative to the sun.

The second was also defined as a fraction of an extrapolated year in the late 1940s with the advent of quartz crystal oscillator clocks. This resulted in a second defined as "1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time," in 1956. This definition was adopted as part of SI in 1960.

In 1967, the current definition of the second was adopted and is defined exactly as "9,192,631,770 times the period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."

**Current use:** As the SI base unit of time, the second and its multiples are ubiquitous. There are few, if any, modern applications in which time is measured in a form other than the second and its multiples.

**Possible future changes:** The definition of some SI base units may change in the near future. The International Committee for Weights and Measures (CIPM) has proposed re-definition of some of the SI base units in an attempt to further improve the system. Although the definitions of some units may change, the actual size of the units would remain the same; the change in definition will not have much (if any) effect on the daily use of these units.

The second is one of the units that is being considered for another re-definition. If the proposed re-definition of the SI base units is passed, the second will be re-defined by taking the fixed numerical value of cesium frequency to be 9,192,631,770 when expressed in the unit of Hz, which is equal to s^{-1}.

### Radian to Second Conversion Table

Radian [rad] | Second ["] |
---|---|

0.01 rad | 2062.648062471 " |

0.1 rad | 20626.48062471 " |

1 rad | 206264.8062471 " |

2 rad | 412529.61249419 " |

3 rad | 618794.41874129 " |

5 rad | 1031324.0312355 " |

10 rad | 2062648.062471 " |

20 rad | 4125296.1249419 " |

50 rad | 10313240.312355 " |

100 rad | 20626480.62471 " |

1000 rad | 206264806.2471 " |

### How to Convert Radian to Second

1 rad = 206264.8062471 "

1 " = 4.8481368110954E-6 rad

**Example:** convert 15 rad to ":

15 rad = 15 × 206264.8062471 " = 3093972.0937064 "