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=LOGEST()

The equation for the curve is: y = b*m^x or y = (b*(m1^x1)*(m2^x2)*_) if there are multiple x-values, where the dependent y-value is a function of the independent x-values. The m-values are bases corresponding to each exponent x-value, and b is a constant value. Note that y, x, and m can be vectors. The array that LOGEST returns is {mn,mn-1,...,m1,b}.

Applies To: Excel for Microsoft 365Excel for Microsoft 365 for MacExcel 2024Excel 2024 for MacExcel 2021Excel 2021 for MacExcel 2019Excel 2016
=LOGEST(known_y's, [known_x's], [const], [stats])
Hover argument names in the table for details.
Output typeArray
Popularity6 / 100
VolatileNo
Dynamic ArrayNo
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◧ Arguments

ArgumentTypeRequiredDescription
known_y's Range Required The set of y-values you already know in the relationship y = b*m^x. If the array known_y's is in a single column, then each column of known_x's is interpreted as a separate variable. If the array known_y's is in a single row, then each row of known_x's is interpreted as a separate variable.
known_x's Range Optional An optional set of x-values that you may already know in the relationship y = b*m^x. The array known_x's can include one or more sets of variables. If only one variable is used, known_y's and known_x's can be ranges of any shape, as long as they have equal dimensions. If more than one variable is used, known_y's must be a range of cells with a height of one row or a width of one column (which is also known as a vector). If known_x's is omitted, it is assumed to be the array {1,2,3,...} that is the same size as known_y's.
const Logical Optional A logical value specifying whether to force the constant b to equal 1. If const is TRUE or omitted, b is calculated normally. If const is FALSE, b is set equal to 1, and the m-values are fitted to y = m^x.
stats Logical Optional A logical value specifying whether to return additional regression statistics. If stats is TRUE, LOGEST returns the additional regression statistics, so the returned array is {mn,mn-1,...,m1,b;sen,sen-1,...,se1,seb;r 2,sey; F,df;ssreg,ssresid}. If stats is FALSE or omitted, LOGEST returns only the m-coefficients and the constant b.

▣ Examples

Example 1 =LOGEST(B2:B25, A2:A25)
Example 2 =INDEX(LOGEST(B2:B25, A2:A25), 1) - 1

§ Remarks

  • The more a plot of your data resembles an exponential curve, the better the calculated line will fit your data. Like LINEST, LOGEST returns an array of values that describes a relationship among the values, but LINEST fits a straight line to your data; LOGEST fits an exponential curve. For more information, see LINEST.
  • When you have only one independent x-variable, you can obtain y-intercept (b) values directly by using the following formula: Y-intercept (b): INDEX(LOGEST(known_y's,known_x's),2) You can use the y = b*m^x equation to predict future values of y, but Microsoft Excel provides the GROWTH function to do this for you. For more information, see GROWTH function.
  • When entering an array constant such as known_x's as an argument, use commas to separate values in the same row and semicolons to separate rows. Separator characters may be different depending on your regional settings.
  • You should note that the y-values predicted by the regression equation may not be valid if they are outside the range of y-values you used to determine the equation.

✦ Tips

  • The more a plot of your data resembles an exponential curve, the better the calculated line will fit your data. Like LINEST, LOGEST returns an array of values that describes a relationship among the values, but LINEST fits a straight line to your data; LOGEST fits an exponential curve. For more information, see LINEST.
  • When you have only one independent x-variable, you can obtain y-intercept (b) values directly by using the following formula: Y-intercept (b): INDEX(LOGEST(known_y's,known_x's),2) You can use the y = b*m^x equation to predict future values of y, but Microsoft Excel provides the GROWTH function to do this for you. For more information, see GROWTH function.
  • When entering an array constant such as known_x's as an argument, use commas to separate values in the same row and semicolons to separate rows. Separator characters may be different depending on your regional settings.
  • You should note that the y-values predicted by the regression equation may not be valid if they are outside the range of y-values you used to determine the equation.

⇄ Related Functions

=GROWTH() Calculates predicted exponential growth by using existing data. GROWTH returns the y-values for a series of new x-values that you specify by using existing x-values and y-values. You can also use the GROWTH worksheet function to fit an exponential curve to existing x-values and y-values. =LINEST() The LINEST function calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data, and then returns an array that describes the line. You can also combine LINEST with other functions to calculate the statistics for other types of models that are linear in the unknown parameters, including polynomial, logarithmic, exponential, and power series. Because this function returns an array of values, it must be entered as an array formula. Instructions follow the examples in this article. The equation for the line is: y = mx + b –or– y = m1x1 + m2x2 + ... + b if there are multiple ranges of x-values, where the dependent y-values are a function of the independent x-values. The m-values are coefficients corresponding to each x-value, and b is a constant value. Note that y, x, and m can be vectors. The array that the LINEST function returns is {mn,mn-1,...,m1,b}. LINEST can also return additional regression statistics. =RRI() Returns an equivalent interest rate for the growth of an investment.

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