Inverse second

The inverse second or reciprocal second (s⁻¹), also called per second, is a unit defined as the multiplicative inverse of the second (a unit of time). It is applicable for physical quantities of dimension reciprocal time, such as frequency and strain rate.

inverse second
Unit system	SI
Unit of	frequency
Symbol	s-1
Conversions
1 s-1 in ...	... is equal to ...
SI units	1 Hz

It is dimensionally equivalent to:

• hertz (Hz), historically known as cycles per second – the SI unit for frequency and rotational frequency
• becquerel (Bq) – the SI unit for the rate of occurrence of aperiodic or stochastic radionuclide events
• baud (Bd) – the unit for symbol rate over a communication link
• bits per second (bit/s) – the unit of bit rate

However, the special names and symbols above for s⁻¹ are recommend for clarity.^{[lower-alpha 1][lower-alpha 2]}

Reciprocal second should not be confused with radian per second (rad⋅s⁻¹), the SI unit for angular frequency and angular velocity. As the radian is a dimensionless unit, radian per second is dimensionally consistent with reciprocal second. However, they are used for different kinds of quantity, frequency and angular frequency, whose numerical value differs by 2π.

The inverse minute or reciprocal minute (min⁻¹), also called per minute, is 60⁻¹ s⁻¹, as 1 min = 60 s; it is used in quantities of type "counts per minute", such as:

• Actions per minute
• Beats per minute
• Counts per minute
• Revolutions per minute (rpm)
• Words per minute

Inverse square second (s^-2) is involved in the units of linear acceleration, angular acceleration, and rotational acceleration.

See also

Main category: Units of frequency

• Aperiodic frequency
• Inverse metre
• Reciprocal length
• Unit of time

Notes

1. "The SI unit of frequency is given as the hertz, implying the unit cycles per second; the SI unit of angular velocity is given as the radian per second; and the SI unit of activity is designated the becquerel, implying the unit counts per second. Although it would be formally correct to write all three of these units as the reciprocal second, the use of the different names emphasises the different nature of the quantities concerned."^[1]
2. "(d) The hertz is used only for periodic phenomena, and the becquerel (Bq) is used only for stochastic processes in activity referred to a radionuclide."^[2]

References

1. "Units with special names and symbols; units that incorporate special names and symbols".
2. "BIPM - Table 3". BIPM. Retrieved 2012-10-24.