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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a rate is a ratio
Ratio

A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared....
 between two measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
s, often with different units.. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
, or per unit of length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 or mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 or an other quantity. The most common type of rate is "per unit time", such as speed
Speed

Speed is the rate of Motion , or equivalently the rate of change of distance.Speed is a Scalar quantity with dimensions length/time; the equivalent Vector quantity to speed is velocity....
, heart rate
Heart rate

Heart rate is a measure of the number of heart beats per minute . The average resting human heart rate is about 70 bpm for adult males and 75 bpm for adult females....
 and flux
Flux

In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.*In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time....
. Rates that have a non-time denominator include exchange rate
Exchange rate

In finance, the exchange rates between two currency specifies how much one currency is worth in terms of the other. It is the value of a foreign nation?s currency in terms of the home nation?s currency....
s, literacy rate
Literacy rate

In economics, the literacy rate is the proportion of the population over age fifteen that can read and write....
s and electric flux
Electric flux

In electromagnetism, electric flux is the flux of the electric field. Electric flux is proportional to the number of electric field lines going through a virtual surface....
.

In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate
Heart rate

Heart rate is a measure of the number of heart beats per minute . The average resting human heart rate is about 70 bpm for adult males and 75 bpm for adult females....
 is expressed "beats per minute").






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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a rate is a ratio
Ratio

A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared....
 between two measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
s, often with different units.. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
, or per unit of length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 or mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 or an other quantity. The most common type of rate is "per unit time", such as speed
Speed

Speed is the rate of Motion , or equivalently the rate of change of distance.Speed is a Scalar quantity with dimensions length/time; the equivalent Vector quantity to speed is velocity....
, heart rate
Heart rate

Heart rate is a measure of the number of heart beats per minute . The average resting human heart rate is about 70 bpm for adult males and 75 bpm for adult females....
 and flux
Flux

In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.*In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time....
. Rates that have a non-time denominator include exchange rate
Exchange rate

In finance, the exchange rates between two currency specifies how much one currency is worth in terms of the other. It is the value of a foreign nation?s currency in terms of the home nation?s currency....
s, literacy rate
Literacy rate

In economics, the literacy rate is the proportion of the population over age fifteen that can read and write....
s and electric flux
Electric flux

In electromagnetism, electric flux is the flux of the electric field. Electric flux is proportional to the number of electric field lines going through a virtual surface....
.

In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate
Heart rate

Heart rate is a measure of the number of heart beats per minute . The average resting human heart rate is about 70 bpm for adult males and 75 bpm for adult females....
 is expressed "beats per minute"). A rate defined using two numbers of the same units
Units of measurement

The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day....
 (such as tax rates) or counts (such as literacy rate
Literacy rate

In economics, the literacy rate is the proportion of the population over age fifteen that can read and write....
) will result in a dimensionless quantity
Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity without any physical units and thus a pure number. Such a number is typically defined as a product or ratio of quantity which do have units, in such a way that all the units cancel out....
, which can be expressed as a percentage
Percentage

In mathematics, a percentage is a way of expressing a number as a fraction of 100 . It is often denoted using the percent sign, "%". For example, 45% is equal to 45 / 100, or 0.45....
 (for example, the global literacy rate
Literacy rate

In economics, the literacy rate is the proportion of the population over age fifteen that can read and write....
 in 1998 was 80%) or fraction
Fraction

In common usage a fraction is any part of a Units of measurement.Fraction may also mean:*Fraction , a quotient of numbers, e.g. "?"; or, more generally, an element of a quotient field...
 or as a multiple
Multiple

The word multiple can refer to:*Multiple of numbers.*List of independent discoveries, instances of scientists, working independently of each other, reaching similar findings....
.

Often "rate" is a synonym of rhythm
Rhythm

Rhythm is the variation of the length and accentuation of a series of sounds or other events....
 or frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
, a count per second
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
 (i.e. Hertz
Hertz

The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
) e.g. radio frequencies or heart rate
Heart rate

Heart rate is a measure of the number of heart beats per minute . The average resting human heart rate is about 70 bpm for adult males and 75 bpm for adult females....
 or sample rate.

Rate of change

A rate of change can be formally defined in two ways:

where f(x) is the function with respect to x over the interval from a to a+h. An instantaneous rate of change is equivalent to a derivative
Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point....
.

An example to contrast the differences between the average and instantaneous definitions: the speed
Speed

Speed is the rate of Motion , or equivalently the rate of change of distance.Speed is a Scalar quantity with dimensions length/time; the equivalent Vector quantity to speed is velocity....
 of a car can be calculated:
  1. An average rate can be calculated using the total distance travelled between a and b, divided by the travel time
  2. An instantaneous rate can be determined by viewing a speedometer
    Speedometer

    A speedometer is a device that measures the instantaneous speed of a land vehicle.Now universally fitted to motor vehicles, they started to be available as options in the 1900s, and as standard equipment from about 1910 onwards....


Terms based on rates


In chemistry and physics:
  • Speed
    Speed

    Speed is the rate of Motion , or equivalently the rate of change of distance.Speed is a Scalar quantity with dimensions length/time; the equivalent Vector quantity to speed is velocity....
    , being the distance covered per unit time, e.g. miles per hour
    Miles per hour

    The mile per hour is a physical unit of speed, expressing the number of Mile covered per hour.It is currently the Unit of measurement used for speed limits, and speeds, on roads in the United Kingdom and United States....
     and meters per second
  • Acceleration
    Acceleration

    File:Acceleration.JPGFile:Acceleration components.JPGIn physics, and more specifically kinematics, acceleration is the change in velocity over time....
    , the rate of change in speed, or the change in speed per unit time


  • Radioactive decay
    Radioactive decay

    Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide....
    , the amount of radioactive material in which one nucleus decays per second, measured in Becquerel
    Becquerel

    The becquerel is the SI derived unit of Radioactive decay. 1 Bq is defined as the activity of a quantity of radioactive material in which one atomic nucleus decays per second....
    s
  • Reaction rate
    Reaction rate

    The reaction rate or rate of reaction for a reactant or product in a particular chemical reaction is intuitively defined as how fast a reaction takes place....
    , the speed at which chemical reactions occur
  • Volumetric flow rate
    Volumetric flow rate

    The volumetric flow rate in fluid dynamics and hydrometry, is the volume of fluid which passes through a given surface per unit time Volumetric flow rate should not be confused with volumetric flux, as defined by Darcy's law and represented by the symbol q, with units of m3/, that is, m s-1....
    , the volume of fluid which passes through a given surface per unit time, e.g. cubic meters per second


In computing:
  • Bit rate, the number of bits that are conveyed or processed by a computer per unit of time
  • Symbol rate
    Symbol rate

    In digital communications, symbol rate, also known as baud or modulation rate; is the number of symbol changes made to the transmission medium per second using a digitally modulation signal or a line code....
    , the number of symbol changes (signalling events) made to the transmission medium per second
  • Sampling rate
    Sampling rate

    The sampling rate, sample rate, or sampling frequency defines the number of sample per second taken from a continuous signal to make a discrete signal....
    , the number of samples (signal measurements) per second


In finance:
  • Interest rate
    Interest rate

    An interest rate is the price a borrower pays for the use of money they do not own, for instance a small company might borrow from a bank to kick start their business, and the return a lender receives for deferring the use of funds, by lending it to the borrower....
    , the price a borrower pays for the use of money they do not own, usually expressed as a percentage rate over the period of one year; see also for related rates
  • Exchange rate
    Exchange rate

    In finance, the exchange rates between two currency specifies how much one currency is worth in terms of the other. It is the value of a foreign nation?s currency in terms of the home nation?s currency....
    , how much one currency is worth in terms of the other
  • Inflation rate
    Inflation rate

    In economics, the inflation rate is a measure of inflation, the rate of increase of a price index .It is the percentage rate of change in price level overtime....
    , a measure of inflation change per year
  • Rate of return
    Rate of return

    In finance, rate of return , also known as return on investment , rate of profit or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested....
    , the ratio of money gained or lost on an investment relative to the amount of money invested
  • Tax rate, the tax amount divided by the taxable income


Miscellaneous definitions:
  • Rate of reinforcement
    Rate of reinforcement

    In behaviorism, rate of reinforcement is number of reinforcements per time, usually per minute. Symbol of this rate is usually Rf. Its first major exponent was B....
    , number of reinforcements per time, usually per minute
  • Heart rate
    Heart rate

    Heart rate is a measure of the number of heart beats per minute . The average resting human heart rate is about 70 bpm for adult males and 75 bpm for adult females....
    , usually measured in beats per minute
  • Unemployment rate, a ratio between those in the labor force to those who are unemployed
  • Birth rate
    Birth rate

    Crude birth rate is the natality or childbirths per 1,000 people per year.It can be represented by number of childbirths in that year, and p is the current population....
     and mortality rate
    Mortality rate

    Mortality rate is a measure of the number of deaths in some population, scaled to the size of that population, per unit time. Mortality rate is typically expressed in units of deaths per 1000 individuals per year; thus, a mortality rate of 9.5 in a population of 100,000 would mean 950 deaths per year in that entire population....
    , the number of births or deaths scaled to the size of that population, per unit time
  • Literacy rate
    Literacy rate

    In economics, the literacy rate is the proportion of the population over age fifteen that can read and write....
    , the proportion of the population over age fifteen that can read and write


See also

  • Derivative
    Derivative

    In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point....
  • Flux
    Flux

    In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.*In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time....
  • Gradient
    Gradient

    In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
  • Slope
    Slope

    Slope is used to describe the steepness, incline, gradient, or grade of a line . A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two point...