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The integral length scale measures the correlation distance of a process in terms of space or time.

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The mathematical expressions for integral scales are:

$\mathrm {T} =\int _{0}^{\infty }\rho (\tau )d\tau$

$L=\int _{0}^{\infty }\rho (r)dr$

Where $\tau$ is the integral time scale, L is the integral length scale, and $\rho (\tau )$ and $\rho (r)$ are the autocorrelation with respect to time and space respectively.

^ O’Neill, P. L.; Nicolaides, D.; Honnery, D.; Soria, J. (13–17 December 2004). "Autocorrelation Functions and the Determination of Integral Length with Reference to Experimental and Numerical Data". 15th Australasian Fluid Mechanics Conference.{{cite journal}}: CS1 maint: date format (link)

[1] O’Neill, P. L.; Nicolaides, D.; Honnery, D.; Soria, J. (13–17 December 2004). "Autocorrelation Functions and the Determination of Integral Length with Reference to Experimental and Numerical Data". 15th Australasian Fluid Mechanics Conference.{{cite journal}}: CS1 maint: date format (link)

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