Minimum alveolar concentration or MAC is the concentration of a vapour in the alveoli of the lungs that is needed to prevent movement (motor response) in 50% of subjects in response to surgical (pain) stimulus. MAC is used to compare the strengths, or potency, of anaesthetic vapours.^[1] The concept of MAC was first introduced in 1965.^[2]

MAC actually is a median value, not a minimum as term implies. The original paper proposed MAC as the minimal alveolar concentration,^[3] which was shortly thereafter revised to minimum alveolar concentration.^[4] A lower MAC value represents a more potent volatile anesthetic.

Other uses of MAC include MAC-BAR (1.7-2.0 MAC), which is the concentration required to block autonomic reflexes to nociceptive stimuli, and MAC-awake (0.3-0.5 MAC), the concentration required to block voluntary reflexes and control perceptive awareness.

Returns the number of days between two dates based on twelve 30‑day months and a 360‑day year. Returns a date that is some number of months before or after a given date.

Formal definition[edit]

The MAC is the concentration of the vapour (measured as a percentage at 1 atmosphere, i.e. the partial pressure) that prevents patient movement in response to a supramaximal ^[5] stimulus (traditionally a set depth and width of skin incisions) in 50% of subjects. This measurement is done at steady state (assuming a constant alveolar concentration for 15 minutes), under the assumption that this allows for an equilibration between the gasses in the alveoli, the blood and the brain. MAC is accepted as a valid measure of potency of inhalational general anaesthetics because it remains fairly constant for a given species even under varying conditions.

Meyer-Overton hypothesis[edit]

The MAC of a volatile substance is inversely proportional to its lipid solubility (oil:gas coefficient), in most cases. This is the Meyer-Overton hypothesis put forward in 1899–1901 by Hans Horst Meyer and Charles Ernest Overton. MAC is inversely related to potency, i.e. high MAC equals low potency.

The hypothesis correlates lipid solubility of an anaesthetic agent with potency (1/MAC) and suggests that onset of anaesthesia occurs when sufficient molecules of the anaesthetic agent have dissolved in the cell's lipid membranes, resulting in anaesthesia. Exceptions to the Meyer-Overton hypothesis can result from:

• convulsant property of an agent
• specific receptor (various agents may exhibit an additional effect through specific receptors)
• co-administration of Alpha₂ agonists (dexmedetomidine) and/or opioid receptor agonists (morphine/fentanyl) can decrease the MAC^[6][7]
• Mullin's critical volume hypothesis
• Positive modulation of GABA at GABA_A receptors by barbiturates or benzodiazepines

Factors affecting MAC[edit]

Certain physiological and pathological states may alter MAC. For example, MAC increases with hyperthermia and hypernatremia. interestingly, human subjects with red hair have also been found to have increased MAC. Conversely, anemia, hypercarbia, hypoxia, hypothermia, hypotension (MAP < 40 mmHg), and pregnancy seem to decrease MAC. Duration of anesthesia, gender, height and weight seem to have little effect on MAC.

Age has been shown to affect MAC. MAC begins to rise at one month of age with a peak at approximately 6 months of age. There is a subsequent steady decline in MAC with increasing age, with the exception of another peak during puberty.^[4] There is a linear model that describes the change in MAC of approximately 6% per decade of age.

Medications, illicit drugs, and prior substance use history have also been found to affect MAC. For example, acute use of amphetamines, cocaine, ephedrine, and chronic use of alcohol increase MAC. Whereas, administration of propofol, etomidate, barbiturates, benzodiazepines, ketamine, opiates, local anesthetics, lithium, verapamil, and alpha 2-agonists (dexmedetomidine, clonidine) decrease MAC. Acute alcohol intoxication and chronic amphetamine use have also been found to decrease MAC.

MAC values are additive. For instance, when applying 0.3 MAC of drug X and 1 MAC of drug Y the total MAC achieved is 1.3 MAC. In this way nitrous oxide is often used as a 'carrier' gas to decrease the anesthetic requirement of other drugs.

Common MAC values[edit]

Values are known to decrease with age and the following are given are based on a 40-year-old (MAC₄₀):^[8]

• Nitrous oxide - 104 ^[8]
• Xenon - 72 ^[8]
• Desflurane - 6.6 ^[8]
• Ethyl Ether - 3.2
• Sevoflurane - 1.8 ^[8]
• Enflurane - 1.63 ^[8]
• Isoflurane - 1.17 ^[8]
• Halothane - 0.75 ^[8]
• Chloroform - 0.5
• Methoxyflurane - 0.16

References[edit]

1. ^'Policy: Ban on Use of Ether'. Laboratory Animal Science Center. Archived from the original on 2008-06-09. Retrieved 2008-11-10.
2. ^Eger EI, Saidman LJ, Brandstater B (1965). 'Minimum alveolar anesthetic concentration: a standard of anesthetic potency'. Anesthesiology. 26 (6): 756–63. doi:10.1097/00000542-196511000-00010. PMID5844267.
3. ^Merkel, Giles; Eger, Edmond I. (1963-05-01). 'A Comparative Study of Halothane and Halopropane AnesthesiaIncluding Method for Determining Equipotency'. The Journal of the American Society of Anesthesiologists. 24 (3): 346–357. doi:10.1097/00000542-196305000-00016. ISSN0003-3022. PMID13935000.
4. ^ ^abEger, Edmond I.; Saidman, Lawrence J.; Brandstater, Bernard (1965-11-01). 'Minimum Alveolar Anesthetic ConcentrationA Standard of Anesthetic Potency'. The Journal of the American Society of Anesthesiologists. 26 (6): 756–763. doi:10.1097/00000542-196511000-00010. ISSN0003-3022. PMID5844267.
5. ^Miller ANESTHESIOLOGY
6. ^* Daniel M, Weiskopf RB, Noorani M, Eger EI (January 1998). 'Fentanyl augments the blockade of the sympathetic response to incision (MAC-BAR) produced by desflurane and isoflurane: desflurane and isoflurane MAC-BAR without and with fentanyl'. Anesthesiology. 88 (1): 43–9. doi:10.1097/00000542-199801000-00009. PMID9447854.
7. ^Katoh T, Kobayashi S, Suzuki A, Iwamoto T, Bito H, Ikeda K (February 1999). 'The effect of fentanyl on sevoflurane requirements for somatic and sympathetic responses to surgical incision'. Anesthesiology. 90 (2): 398–405. doi:10.1097/00000542-199902000-00012. PMID9952144.
8. ^ ^abcdefgh* Nickalls, R. W. D., & Mapleson, W. W. (August 2003). 'Age-related iso-MAC charts for isoflurane, sevoflurane, and desflurane in man'. British Journal of Anaesthesia. 91 (2): 170–4. doi:10.1093/bja/aeg132. PMID12878613.CS1 maint: multiple names: authors list (link)

DATE

Combines separate values for year, month, and day and returns a date/time value.

DATEDIF

Returns the number of days, months, or years between two dates.

DATEVALUE

Converts a date text string and returns a date/time value. This function is provided for compatibility with other spreadsheet programs.

DAY

Returns the day of the month for a given date/time value.

DAYNAME

Returns the name of the day of the week from a date/time value or a number. Day 1 is Sunday.

DAYS360

Returns the number of days between two dates based on twelve 30‑day months and a 360‑day year.

EDATE

Returns a date that is some number of months before or after a given date.

EOMONTH

Returns a date that is the last day of the month some number of months before or after a given date.

HOUR

Returns the hour for a given date/time value.

MINUTE

Returns the minutes for a given date/time value.

MONTH

Returns the month for a given date/time value.

MONTHNAME

Returns the name of the month from a number. Month 1 is January.

NETWORKDAYS

Returns the number of working days between two dates. Working days exclude weekends and any other specified dates.

NOW

Returns the current date/time value from the system clock.

SECOND

Returns the seconds for a given date/time value.

TIME

Converts separate values for hours, minutes, and seconds into a date/time value.

TIMEVALUE

Returns the time as a decimal fraction of a 24‑hour day from a given date/time value or from a text string.

TODAY

Returns the current system date. The time is set to 12:00 a.m.

WEEKDAY

Returns a number that is the day of the week for a given date.

WEEKNUM

Returns the number of the week within the year for a given date.

WORKDAY

Returns the date that is the given number of working days before or after a given date. Working days exclude weekends and any other dates specifically excluded.

YEAR

Returns the year for a given date/time value.

YEARFRAC

Finds the fraction of a year represented by the number of whole days between two dates.

DUR2DAYS

Converts a duration value to a number of days.

DUR2HOURS

Converts a duration value to a number of hours.

DUR2MILLISECONDS

Converts a duration value to a number of milliseconds.

DUR2MINUTES

Converts a duration value to a number of minutes.

DUR2SECONDS

Converts a duration value to a number of seconds.

DUR2WEEKS

Converts a duration value to a number of weeks.

DURATION

Combines separate values for weeks, days, hours, minutes, seconds, and milliseconds and returns a duration value.

STRIPDURATION

Evaluates a given value and returns either the number of days represented, if a duration value; or the given value. This function is included for compatibility with other spreadsheet applications.

BASETONUM

Converts a number of the specified base into a number in base 10.

BESSELJ

Returns the integer Bessel function Jn(x).

BESSELY

Returns the integer Bessel function Yn(x).

BIN2DEC

Converts a binary number to the corresponding decimal number.

BIN2HEX

Converts a binary number to the corresponding hexadecimal number.

BIN2OCT

Converts a binary number to the corresponding octal number.

CONVERT

Converts a number from one measurement system to its corresponding value in another measurement system.

DEC2BIN

Converts a decimal number to the corresponding binary number.

DEC2HEX

Converts a decimal number to the corresponding hexadecimal number.

DEC2OCT

Converts a decimal number to the corresponding octal number.

DELTA

Determines whether two values are exactly equal.

ERF

Returns the error function integrated between two values.

ERFC

Returns the complementary ERF function integrated between a given lower bound and infinity.

GESTEP

Determines if one value is greater than or exactly equal to another value.

HEX2BIN

Converts a hexadecimal number to the corresponding binary number.

HEX2DEC

Converts a hexadecimal number to the corresponding decimal number.

HEX2OCT

Converts a hexadecimal number to the corresponding octal number.

NUMTOBASE

Converts a number from base 10 into a number in the specified base.

OCT2BIN

Converts an octal number to the corresponding binary number.

OCT2DEC

Converts an octal number to the corresponding decimal number.

OCT2HEX

Converts an octal number to the corresponding hexadecimal number.

ACCRINT

Calculates the accrued interest added to the purchase price of a security and paid to the seller when the security pays periodic interest.

ACCRINTM

Calculates the total accrued interest added to the purchase price of a security and paid to the seller when the security pays interest only at maturity.

BONDDURATION

Calculates the weighted average of the present value of the cash flows for an assumed par value of $100.

BONDMDURATION

Calculates the modified weighted average of the present value of the cash flows for an assumed par value of $100.

COUPDAYBS

Returns the number of days between the beginning of the coupon period in which settlement occurs and the settlement date.

COUPDAYS

Returns the number of days in the coupon period in which settlement occurs.

COUPDAYSNC

Returns the number of days between the settlement date and the end of the coupon period in which settlement occurs.

COUPNUM

Returns the number of coupons remaining to be paid between the settlement date and the maturity date.

CUMIPMT

Returns the total interest included in loan or annuity payments over a chosen time interval based on fixed periodic payments and a fixed interest rate.

CUMPRINC

Returns the total principal included in loan or annuity payments over a chosen time interval based on fixed periodic payments and a fixed interest rate.

DB

Returns the amount of depreciation of an asset for a specified period using the fixed‑declining balance method.

DDB

Returns the amount of depreciation of an asset based on a specified depreciation rate.

DISC

Returns the annual discount rate of a security that pays no interest and is sold at a discount to its redemption value.

EFFECT

Returns the effective annual interest rate from the nominal annual interest rate based on the number of compounding periods per year.

FV

Returns the future value of an investment based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate.

INTRATE

Returns the effective annual interest rate for a security that pays interest only at maturity.

IPMT

Returns the interest portion of a specified loan or annuity payment based on fixed, periodic payments and a fixed interest rate.

IRR

Returns the internal rate of return for an investment that is based on a series of potentially irregular cash flows that occur at regular time intervals.

ISPMT

Returns the interest portion of a specified loan or annuity payment based on fixed, periodic payments and a fixed interest rate. This function is provided for compatibility with tables imported from other spreadsheet applications.

MIRR

Returns the modified internal rate of return for an investment that is based on a series of potentially irregular cash flows that occur at regular time intervals. The rate earned on positive cash flows and the rate paid to finance negative cash flows can differ.

NOMINAL

Returns the nominal annual interest rate from the effective annual interest rate based on the number of compounding periods per year.

NPER

Returns the number of payment periods for a loan or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate.

NPV

Returns the net present value of an investment based on a series of potentially irregular cash flows that occur at regular time intervals.

PMT

Returns the fixed periodic payment for a loan or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate.

PPMT

Returns the principal portion of a specified loan or annuity payment based on fixed periodic payments and a fixed interest rate.

PRICE

Returns the price of a security that pays periodic interest per $100 of redemption (par) value.

PRICEDISC

Returns the price of a security that is sold at a discount to redemption value and does not pay interest per $100 of redemption (par) value.

PRICEMAT

Returns the price of a security that pays interest only at maturity per $100 of redemption (par) value.

PV

Returns the present value of an investment or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate.

RATE

Returns the interest rate of an investment, loan, or annuity based on a series of regular periodic cash flows (payments of a constant amount and all cash flows at constant intervals) and a fixed interest rate.

RECEIVED

Returns the maturity value for a security that pays interest only at maturity.

SLN

Returns the amount of depreciation of an asset for a single period using the straight‑line method.

SYD

Returns the amount of depreciation of an asset for a specified period using the sum‑of‑the‑years‑digits method.

VDB

Returns the amount of depreciation of an asset over a chosen time interval, based on a specified depreciation rate.

YIELD

Returns the effective annual interest rate for a security that pays regular periodic interest.

YIELDDISC

Returns the effective annual interest rate for a security that is sold at a discount to redemption value and pays no interest.

YIELDMAT

Returns the effective annual interest rate for a security that pays interest only at maturity.

AND

Returns TRUE if all arguments are true; otherwise it returns FALSE.

FALSE

Returns the Boolean value FALSE. This function is included for compatibility with tables imported from other spreadsheet applications.

IF

Returns one of two values depending on whether a specified expression evaluates to a Boolean value of TRUE or FALSE.

IFERROR

Returns a value that you specify if a given value evaluates to an error; otherwise it returns the given value.

ISBLANK

Returns TRUE if the specified cell is empty; otherwise it returns FALSE.

ISERROR

Returns TRUE if a given expression evaluates to an error; otherwise it returns FALSE.

ISEVEN

Returns TRUE if the value is even (leaves no remainder when divided by 2); otherwise it returns FALSE.

ISODD

Returns TRUE if the value is odd (leaves a remainder when divided by 2); otherwise it returns FALSE.

NOT

Returns the opposite of the Boolean value of a specified expression.

OR

Returns TRUE if any argument is true; otherwise it returns FALSE.

TRUE

Returns the Boolean value TRUE. This function is included for compatibility with tables imported from other spreadsheet applications.

ABS

Returns the absolute value of a number or duration.

CEILING

Rounds a number away from zero to the nearest multiple of the specified factor.

COMBIN

Returns the number of different ways you can combine a number of items into groups of a specific size, ignoring the order within the groups.

EVEN

Rounds a number away from zero to the next even number.

EXP

Returns e (the base of natural logarithms) raised to the specified power.

FACT

Returns the factorial of a number.

FACTDOUBLE

Returns the double factorial of a number.

FLOOR

Rounds a number toward zero to the nearest multiple of the specified factor.

GCD

Returns the greatest common divisor of the specified numbers.

INT

Returns the nearest integer that is less than or equal to the number.

LCM

Returns the least common multiple of the specified numbers.

LN

Returns the natural logarithm of a number, the power to which e must be raised to result in the number.

LOG

Returns the logarithm of a number using a specified base.

LOG10

Returns the base‑10 logarithm of a number.

MOD

Returns the remainder from a division.

MROUND

Rounds a number to the nearest multiple of a specified factor.

MULTINOMIAL

Returns the closed form of the multinomial coefficient of the given numbers.

ODD

Rounds a number away from zero to the next odd number.

PI

Returns the approximate value of π (pi), the ratio of a circle’s circumference to its diameter.

POLYNOMIAL

Evaluates a polynomial at a given point.

POWER

Returns a number raised to a power.

PRODUCT

Returns the product of one or more numbers.

QUOTIENT

Returns the integer quotient of two numbers.

RAND

Returns a random number that is greater than or equal to 0 and less than 1.

RANDBETWEEN

Returns a random integer within the specified range.

ROMAN

Converts a number to Roman numerals.

ROUND

Returns a number rounded to the specified number of places.

ROUNDDOWN

Returns a number rounded toward zero (rounded down) to the specified number of places.

ROUNDUP

Returns a number rounded away from zero (rounded up) to the specified number of places.

SERIESSUM

Computes and returns the sum of a power series.

SIGN

Returns 1 when a given number is positive, –1 when it is negative, and 0 when it is zero.

SQRT

Returns the square root of a number.

SQRTPI

Returns the square root of a number multiplied by π (pi).

SUM

Returns the sum of a collection of numbers.

SUMIF

Returns the sum of a collection of numbers, including only numbers that satisfy a specified condition.

SUMIFS

Returns the sum of the cells in a collection where the test values meet the given conditions.

SUMPRODUCT

Returns the sum of the products of corresponding numbers in one or more ranges.

Mkv player mac os x 10.5.8. All that you need is a program called.

SUMSQ

Returns the sum of the squares of a collection of numbers.

SUMX2MY2

Returns the sum of the difference of the squares of corresponding values in two collections.

SUMX2PY2

Returns the sum of the squares of corresponding values in two collections.

SUMXMY2

Returns the sum of the squares of the differences between corresponding values in two collections.

TRUNC

Truncates a number to the specified number of digits.

ADDRESS

Constructs a cell address string from separate row, column, and table identifiers.

AREAS

Returns the number of ranges the function references.

CHOOSE

Returns a value from a collection of values based on a specified index value.

COLUMN

Returns the column number of the column containing a specified cell.

COLUMNS

Returns the number of columns included in a specified range of cells.

HLOOKUP

Returns a value from a range of rows by using the top row of values to pick a column and a row number to pick a row within that column.

INDEX

Returns the value in the cell located at the intersection of the specified row and column within a range of cells.

INDIRECT

Returns the contents of a cell or range referenced by an address specified as a string.

INTERSECT.RANGES

Returns a range that is the intersection of the specified ranges.

LOOKUP

Finds a match for a given search value in one range, then returns the value in the cell with the same relative position in a second range.

MATCH

Returns the position of a value within a range.

OFFSET

Returns a range of cells that is the specified number of rows and columns away from the specified base cell.

ROW

Returns the row number of the row containing a specified cell.

ROWS

Returns the number of rows included in a specified range of cells.

TRANSPOSE

Returns a vertical range of cells as a horizontal range of cells, or vice versa.

UNION.RANGES

Returns a range that represents a range representing the union of the specified ranges.

VLOOKUP

Returns a value from a range of columns by using the left column of values to pick a row and a column number to pick a column in that row.

AVEDEV

Returns the average of the difference of a collection of numbers from their average (arithmetic mean).

AVERAGE

Returns the average (arithmetic mean) of a collection of numbers.

AVERAGEA

Returns the average (arithmetic mean) of a collection of values, including text and Boolean values.

AVERAGEIF

Returns the average (arithmetic mean) of the cells in a range that meet a given condition.

AVERAGEIFS

Returns the average (arithmetic mean) of the cells in a collection that meet all the given conditions.

BETADIST

Returns the cumulative beta distribution probability value.

BETAINV

Returns the inverse of the given cumulative beta distribution probability value.

BINOMDIST

Returns the individual term binomial distribution probability of the specified form.

CHIDIST

Returns the one‑tailed probability of the chi‑square distribution.

CHIINV

Returns the inverse of the one‑tailed probability of the chi‑square distribution.

CHITEST

Returns the value from the chi‑square distribution for the given data.

CONFIDENCE

Returns a value for creating a statistical confidence interval for a sample from a population with a known standard deviation.

CORREL

Returns the correlation between two collections using linear regression analysis.

COUNT

Returns the number of its arguments that contain numbers, numeric expressions, or dates.

COUNTA

Returns the number of its arguments that are not empty.

COUNTBLANK

Returns the number of cells in a range that are empty.

COUNTIF

Returns the number of cells in a range that satisfy a given condition.

COUNTIFS

Returns the number of cells in one or more ranges that satisfy given conditions (one condition per range).

COVAR

Returns the covariance of two collections.

CRITBINOM

Returns the smallest value for which the cumulative binomial distribution is greater than or equal to a given value.

DEVSQ

Returns the sum of the squares of deviations of a collection of numbers from their average (arithmetic mean).

EXPONDIST

Returns the exponential distribution of the specified form.

FDIST

Returns the F probability distribution.

FINV

Returns the inverse of the F probability distribution.

FORECAST

Returns the forecasted y value for a given x value based on sample values using linear regression analysis.

FREQUENCY

Returns an array of how often data values occur within a range of interval values.

GAMMADIST

Returns the gamma distribution in the specified form.

GAMMAINV

Returns the inverse gamma cumulative distribution.

GAMMALN

Returns the natural logarithm of the gamma function, G(x).

GEOMEAN

Returns the geometric mean.

HARMEAN

Returns the harmonic mean.

INTERCEPT

Returns the y‑intercept of the best‑fit line for the collection using linear regression analysis.

LARGE

Returns the nth‑largest value within a collection. The largest value is ranked number 1.

LINEST

Returns an array of the statistics for a straight line that best fits the given data using the least squares method.

LOGINV

Returns the inverse of the log‑normal cumulative distribution function of x.

LOGNORMDIST

Returns the log‑normal distribution.

MAX

Returns the largest number in a collection.

MAXA

Returns the largest number in a collection of values that may include text and Boolean values.

MEDIAN

Returns the median value in a collection of numbers. The median is the value where half the numbers in the collection are less than the median and half are greater.

MIN

Returns the smallest number in a collection.

MINA

Returns the smallest number in a collection of values that may include text and Boolean values.

MODE

Returns the most frequently occurring value in a collection of numbers.

NEGBINOMDIST

Returns the negative binomial distribution.

NORMDIST

Returns the normal distribution of the specified function form.

NORMINV

Returns the inverse of the cumulative normal distribution.

NORMSDIST

Returns the standard normal distribution.

NORMSINV

Returns the inverse of the cumulative standard normal distribution.

PERCENTILE

Returns the value within a collection that corresponds to a particular percentile.

PERCENTRANK

Returns the rank of a value in a collection as a percentage of the collection.

PERMUT

Returns the number of permutations for a given number of objects that can be selected from a total number of objects.

POISSON

Returns the probability that a specific number of events will occur using the Poisson distribution.

PROB

Returns the probability of a range of values if you know the probabilities of the individual values.

QUARTILE

Returns the value for the specified quartile of a given collection.

RANK

Returns the rank of a number within a range of numbers.

SLOPE

Returns the slope of the best‑fit line for the collection using linear regression analysis.

SMALL

Returns the nth‑smallest value within a range. The smallest value is ranked number 1.

STANDARDIZE

Returns a normalized value from a distribution characterized by a given mean and standard deviation.

STDEV

Returns the standard deviation, a measure of dispersion, of a collection of values based on their sample (unbiased) variance.

STDEVA

Returns the standard deviation, a measure of dispersion, of a collection of values that may include text and Boolean values, based on the sample (unbiased) variance.

STDEVP

Returns the standard deviation, a measure of dispersion, of a collection of values based on their population (true) variance.

STDEVPA

Returns the standard deviation, a measure of dispersion, of a collection of values that may include text and Boolean values, based on the population (true) variance.

TDIST

Returns the probability from the Student’s t‑distribution.

TINV

Returns the t value (a function of the probability and degrees of freedom) from the Student’s t‑distribution.

TTEST

Returns the probability associated with a Student’s t‑test, based on the t‑distribution function.

VAR

Returns the sample (unbiased) variance, a measure of dispersion, of a collection of values.

VARA

Returns the sample (unbiased) variance, a measure of dispersion, of a collection of values, including text and Boolean values.

VARP

Returns the population (true) variance, a measure of dispersion, of a collection of values.

VARPA

Returns the sample (unbiased) variance, a measure of dispersion, of a collection of values, including text and Boolean values.

WEIBULL

Returns the values of the Weibull distribution.

ZTEST

Returns the one‑tailed probability value of the Z‑test.

CHAR

Returns the character that corresponds to a decimal Unicode character code.

CLEAN

Removes most common nonprinting characters (Unicode character codes 0–31) from text.

CODE

Returns the decimal Unicode number of the first character in a specified string.

CONCATENATE

Joins (concatenates) strings.

DOLLAR

Returns a string formatted as a dollar amount from a given number.

EXACT

Returns TRUE if the argument strings are identical in case and content.

FIND

Returns the starting position of one string within another.

FIXED

Rounds a number to the specified number of decimal places and then returns the result as a string value.

LEFT

Returns a string consisting of the specified number of characters from the left end of a given string.

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LEN

Returns the number of characters in a string.

LOWER

Returns a string that is entirely lowercase, regardless of the case of the characters in the specified string.

MID

Returns a string consisting of the given number of characters from a string starting at the specified position.

PROPER

Returns a string where the first letter of each word is uppercase and all remaining characters are lowercase, regardless of the case of the characters in the specified string.

REPLACE

Returns a string where a specified number of characters of a given string have been replaced with a new string.

REPT

Returns a string that contains a given string repeated a specified number of times.

RIGHT

Returns a string consisting of the given number of characters from the right end of a specified string.

SEARCH

Returns the starting position of one string within another, ignoring case and allowing wildcards.

SUBSTITUTE

Returns a string where the specified characters of a given string have been replaced with a new string.

T

Returns the text contained in a cell. This function is included for compatibility with tables imported from other spreadsheet applications.

TRIM

Returns a string based on a given string, after removing extra spaces.

UPPER

Returns a string that is entirely uppercase, regardless of the case of the characters in the specified string.

VALUE

Returns a number value even if the argument is formatted as text.

ACOS

Returns the inverse cosine (arccosine) of a number.

ACOSH

Returns the inverse hyperbolic cosine (hyperbolic arccosine) of a number.

ASIN

Returns the arcsine (the inverse sine) of a number.

ASINH

Returns the inverse hyperbolic sine of a number.

ATAN

Returns the inverse tangent (arctangent) of a number.

ATAN2

Returns the angle, relative to the positive x‑axis, of the line passing through the origin and the specified point.

ATANH

Returns the inverse hyperbolic tangent of a number.

COS

Returns the cosine of an angle that is expressed in radians.

COSH

Returns the hyperbolic cosine of a number.

DEGREES

Returns the number of degrees in an angle expressed in radians.

RADIANS

Returns the number of radians in an angle expressed in degrees.

SIN

Returns the sine of an angle that is expressed in radians.

SINH

Returns the hyperbolic sine of the specified number.

TAN

Returns the tangent of an angle that is expressed in radians.

TANH

Returns the hyperbolic tangent of the specified number.