The inverse second or reciprocal second (s⁻¹), also called ''per second'', is a

unit Unit may refer to: General measurement * Unit of measurement, a definite magnitude of a physical quantity, defined and adopted by convention or by law **International System of Units (SI), modern form of the metric system **English units, histo ...

defined as the

multiplicative inverse In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a ra ...

of the

second The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...

(a unit of

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

). It is applicable for

physical quantities A physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a '' numerical value'' and a '' ...

dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...

reciprocal time, such as

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

and

strain rate In mechanics and materials science, strain rate is the time derivative of strain of a material. Strain rate has dimension of inverse time and SI units of inverse second, s−1 (or its multiples). The strain rate at some point within the mat ...

. It is dimensionally equivalent to: *

hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...

(Hz), historically known as

cycles per second The cycle per second is a once-common English name for the unit of frequency now known as the ''hertz'' (Hz). Cycles per second may be denoted by c.p.s., c/s, or, ambiguously, just "cycles" (Cyc., Cy., C, or c). The term comes from repetitive ph ...

– the SI unit for

and

rotational frequency Rotational frequency, also known as rotational speed or rate of rotation (symbols ''ν'', lowercase Greek nu, and also ''n''), is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s−1); other co ...

becquerel The becquerel (; symbol: Bq) is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as an activity of one per second, on average, for aperiodic activity events referred to a radionuclide. For applicatio ...

(Bq) – the SI unit for the rate of occurrence of aperiodic or stochastic

radionuclide A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess numbers of either neutrons or protons, giving it excess nuclear energy, and making it unstable. This excess energy can be used in one of three ...

events *

baud In telecommunications and electronics, baud (; symbol: Bd) is a common unit of measurement of symbol rate, which is one of the components that determine the speed of communication over a data channel. It is the unit for symbol rate or modulat ...

(Bd) – the unit for

symbol rate In a digitally modulated signal or a line code, symbol rate, modulation rate or baud is the number of symbol changes, waveform changes, or signaling events across the transmission medium per unit of time. The symbol rate is measured in '' baud ...

over a communication link *

bit per second In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction ...

(bit/s) – the unit of bit rate However, the special names and symbols above for s⁻¹ are recommend for clarity. Reciprocal second should not be confused with

radian per second The radian per second (symbol: rad⋅s−1 or rad/s) is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency (symbol ''ω'', omega). The radian per second is defin ...

(rad⋅s⁻¹), the SI unit for

angular frequency In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...

and

angular velocity In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i ...

. As the

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...

is a

dimensionless unit Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...

, 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 2. 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 Count (feminine: countess) is a historical title of nobility in certain European countries, varying in relative status, generally of middling rank in the hierarchy of nobility. Pine, L. G. ''Titles: How the King Became His Majesty''. New York: ...

per minute", such as: *

Actions per minute Actions per minute, abbreviated to APM, is a term used in video games, particularly real-time strategy and fighting games which refers to the total number of actions that a player can perform in a minute. Actions per minute are the number of acti ...

Beats per minute Beat, beats, or beating may refer to: Common uses * Assault, inflicting physical harm or unwanted physical contact * Battery (crime), a criminal offense involving unlawful physical contact * Battery (tort), a civil wrong in common law of in ...

Counts per minute The measurement of ionizing radiation is sometimes expressed as being a ''rate'' of counts per unit time as registered by a radiation monitoring instrument, for which counts per minute (cpm) and counts per second (cps) are commonly used quantitie ...

Revolutions per minute Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or r⋅min−1) is a unit of rotational speed (or rotational frequency) for rotating machines. One revolution per minute is equivalent to hertz. Standards ISO 80000-3:2019 de ...

(rpm) *

Words per minute Words per minute, commonly abbreviated as WPM (sometimes lowercased as wpm), is a measure of words processed in a minute, often used as a measurement of the speed of typing, reading or Morse code sending and receiving. Alphanumeric entry Since ...

Inverse square second (s⁻²) is involved in the units of linear

acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...

angular acceleration In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, ''spin angular velocity'' and ''orbital angular velocity'', the respective types of angular accele ...

, and

rotational acceleration Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis interse ...

Notes

References

{{reflist Units of frequency

See also

Notes

References