diff --git a/R/smoothness.R b/R/smoothness.R
index 28c2f4a0e..7adbc45e6 100644
--- a/R/smoothness.R
+++ b/R/smoothness.R
@@ -2,7 +2,7 @@
 #'
 #' Functions to quantify the smoothness of a vector, which can be used in some cases
 #' as an index of "linearity". A smooth series is one that does not have abrupt changes in
-#' its values. The smoothness of a series can be measured in different ways, such
+#' its values. The smoothness of a series can be approximated in different ways, such
 #' as the standard deviation of the standardized differences or the lag-one
 #' autocorrelation.
 #'
@@ -25,6 +25,10 @@
 #' # When perfectly linear, the "smoothness" is 1
 #' smoothness(1:10)
 #'
+#' # And closer to zero for random
+#' smoothness(rnorm(1000))
+#' smoothness(rnorm(1000), method = "diff")
+#'
 #' @return Value of smoothness.
 #' @references https://stats.stackexchange.com/questions/24607/how-to-measure-smoothness-of-a-time-series-in-r
 #'
@@ -54,7 +58,8 @@ smoothness.numeric <- function(x,
   if (method == "cor") {
     smooth <- stats::cor(utils::head(x, length(x) - lag), utils::tail(x, length(x) - lag))
   } else {
-    smooth <- stats::sd(diff(x, lag = lag)) / abs(mean(diff(x, lag = lag)))
+    diff <- standardize(diff(x))
+    smooth <- 1 - mean((diff(diff) ** 2) / 4)  # Note the reversal to match the other method
   }
 
   if (!is.null(iterations)) {
diff --git a/man/smoothness.Rd b/man/smoothness.Rd
index 5b93db2b5..7d7d208be 100644
--- a/man/smoothness.Rd
+++ b/man/smoothness.Rd
@@ -26,7 +26,7 @@ Value of smoothness.
 \description{
 Functions to quantify the smoothness of a vector, which can be used in some cases
 as an index of "linearity". A smooth series is one that does not have abrupt changes in
-its values. The smoothness of a series can be measured in different ways, such
+its values. The smoothness of a series can be approximated in different ways, such
 as the standard deviation of the standardized differences or the lag-one
 autocorrelation.
 }
@@ -42,6 +42,10 @@ smoothness(x, iterations = 100)
 # When perfectly linear, the "smoothness" is 1
 smoothness(1:10)
 
+# And closer to zero for random
+smoothness(rnorm(1000))
+smoothness(rnorm(1000), method = "diff")
+
 }
 \references{
 https://stats.stackexchange.com/questions/24607/how-to-measure-smoothness-of-a-time-series-in-r