diff --git a/NEWS.md b/NEWS.md
index 4dd574e37..bf51d48dd 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -12,6 +12,7 @@
 - The interface for defining delay distributions has been generalised to also cater for continuous distributions
 - When defining probability distributions these can now be truncated using the `tolerance` argument
 - Ornstein-Uhlenbeck and 5 / 2 Matérn kernels have been added. By @sbfnk in # and reviewed by @.
+- Switch to broadcasting from random walks and added unit tests. By @seabbs in #747 and reviewed by @jamesmbaazam.
 - Optimised convolution code to take into account the relative length of the vectors being convolved. See #745 by @seabbs and reviewed by @jamesmbaazam.
 - Switch to broadcasting the day of the week effect. By @seabbs in #746 and reviewed by @jamesmbaazam.
 - A warning is now thrown if nonparametric PMFs passed to delay options have consecutive tail values that are below a certain low threshold as these lead to loss in speed with little gain in accuracy. By @jamesmbaazam in #752 and reviewed by @seabbs.
@@ -28,6 +29,7 @@
 
 - Updated the documentation of the dots argument of the `stan_sampling_opts()` to add that the dots are passed to `cmdstanr::sample()`. By @jamesmbaazam in #699 and reviewed by @sbfnk.
 - `generation_time_opts()` has been shortened to `gt_opts()` to make it easier to specify. Calls to both functions are equivalent. By @jamesmbaazam in #698 and reviewed by @seabbs and @sbfnk .
+- Added stan documentation for `update_rt()`. By @seabbs in #747 and reviewed by @jamesmbaazam.
 
 # EpiNow2 1.5.2
 
diff --git a/R/create.R b/R/create.R
index 89c61a67c..d3e8bedc6 100644
--- a/R/create.R
+++ b/R/create.R
@@ -261,15 +261,20 @@ create_future_rt <- function(future = c("latest", "project", "estimate"),
 #'
 #' # using breakpoints
 #' create_rt_data(rt_opts(use_breakpoints = TRUE), breakpoints = rep(1, 10))
+#'
+#' # using random walk
+#' create_rt_data(rt_opts(rw = 7), breakpoints = rep(1, 10))
 #' }
 create_rt_data <- function(rt = rt_opts(), breakpoints = NULL,
                            delay = 0, horizon = 0) {
+
   # Define if GP is on or off
   if (is.null(rt)) {
     rt <- rt_opts(
       use_rt = FALSE,
       future = "project",
-      gp_on = "R0"
+      gp_on = "R0",
+      rw = 0
     )
   }
   # define future Rt arguments
@@ -279,24 +284,34 @@ create_rt_data <- function(rt = rt_opts(), breakpoints = NULL,
   )
   # apply random walk
   if (rt$rw != 0) {
-    breakpoints <- as.integer(seq_along(breakpoints) %% rt$rw == 0)
+    if (is.null(breakpoints)) {
+      stop("breakpoints must be supplied when using random walk")
+    }
+
+    breakpoints <- seq_along(breakpoints)
+    breakpoints <- floor(breakpoints / rt$rw)
     if (!(rt$future == "project")) {
       max_bps <- length(breakpoints) - horizon + future_rt$from
       if (max_bps < length(breakpoints)) {
-        breakpoints[(max_bps + 1):length(breakpoints)] <- 0
+        breakpoints[(max_bps + 1):length(breakpoints)] <- breakpoints[max_bps]
       }
     }
+  }else {
+    breakpoints <- cumsum(breakpoints)
   }
-  # check breakpoints
-  if (is.null(breakpoints) || sum(breakpoints) == 0) {
+
+  if (sum(breakpoints) == 0) {
     rt$use_breakpoints <- FALSE
   }
+  # add a shift for 0 effect in breakpoints
+  breakpoints <- breakpoints + 1
+
   # map settings to underlying gp stan requirements
   rt_data <- list(
     r_mean = rt$prior$mean,
     r_sd = rt$prior$sd,
     estimate_r = as.numeric(rt$use_rt),
-    bp_n = ifelse(rt$use_breakpoints, sum(breakpoints, na.rm = TRUE), 0),
+    bp_n = ifelse(rt$use_breakpoints, max(breakpoints) - 1, 0),
     breakpoints = breakpoints,
     future_fixed =  as.numeric(future_rt$fixed),
     fixed_from = future_rt$from,
diff --git a/inst/stan/estimate_infections.stan b/inst/stan/estimate_infections.stan
index 1e97203e4..985cfa9c2 100644
--- a/inst/stan/estimate_infections.stan
+++ b/inst/stan/estimate_infections.stan
@@ -51,7 +51,7 @@ parameters{
   array[estimate_r] real initial_infections ;    // seed infections
   array[estimate_r && seeding_time > 1 ? 1 : 0] real initial_growth; // seed growth rate
   array[bp_n > 0 ? 1 : 0] real<lower = 0> bp_sd; // standard deviation of breakpoint effect
-  array[bp_n] real bp_effects;                   // Rt breakpoint effects
+  vector[bp_n] bp_effects;                   // Rt breakpoint effects
   // observation model
 
   vector<lower = delay_params_lower>[delay_params_length] delay_params; // delay parameters
diff --git a/inst/stan/functions/rt.stan b/inst/stan/functions/rt.stan
index 418c07675..ad2d877b1 100644
--- a/inst/stan/functions/rt.stan
+++ b/inst/stan/functions/rt.stan
@@ -1,26 +1,34 @@
-// update a vector of Rts
+/**
+ * Update a vector of effective reproduction numbers (Rt) based on
+ * an intercept, breakpoints (i.e. a random walk), and a Gaussian
+ * process.
+ *
+ * @param t Length of the time series
+ * @param log_R Logarithm of the base reproduction number
+ * @param noise Vector of Gaussian process noise values
+ * @param bps Array of breakpoint indices
+ * @param bp_effects Vector of breakpoint effects
+ * @param stationary Flag indicating whether the Gaussian process is stationary 
+ * (1) or non-stationary (0)
+ * @return A vector of length t containing the updated Rt values
+ */
 vector update_Rt(int t, real log_R, vector noise, array[] int bps,
-                 array[] real bp_effects, int stationary) {
+                 vector bp_effects, int stationary) {
   // define control parameters
   int bp_n = num_elements(bp_effects);
-  int bp_c = 0;
   int gp_n = num_elements(noise);
-  // define result vectors
-  vector[t] bp = rep_vector(0, t);
-  vector[t] gp = rep_vector(0, t);
-  vector[t] R;
-  // initialise breakpoints
+  // initialise intercept
+  vector[t] R = rep_vector(log_R, t);
+  //initialise breakpoints + rw
   if (bp_n) {
-    for (s in 1:t) {
-      if (bps[s]) {
-        bp_c += bps[s];
-        bp[s] = bp_effects[bp_c];
-      }
-    }
-    bp = cumulative_sum(bp);
+    vector[bp_n + 1] bp0;
+    bp0[1] = 0;
+    bp0[2:(bp_n + 1)] = cumulative_sum(bp_effects);
+    R = R + bp0[bps];
   }
   //initialise gaussian process
   if (gp_n) {
+    vector[t] gp = rep_vector(0, t);
     if (stationary) {
       gp[1:gp_n] = noise;
       // fix future gp based on last estimated
@@ -31,18 +39,31 @@ vector update_Rt(int t, real log_R, vector noise, array[] int bps,
       gp[2:(gp_n + 1)] = noise;
       gp = cumulative_sum(gp);
     }
+    R = R + gp;
   }
-  // Calculate Rt
-  R = rep_vector(log_R, t) + bp + gp;
-  R = exp(R);
-  return(R);
+  
+  return exp(R);
 }
-// Rt priors
+
+/**
+ * Calculate the log-probability of the reproduction number (Rt) priors
+ *
+ * @param log_R Logarithm of the base reproduction number
+ * @param initial_infections Array of initial infection values
+ * @param initial_growth Array of initial growth rates
+ * @param bp_effects Vector of breakpoint effects
+ * @param bp_sd Array of breakpoint standard deviations
+ * @param bp_n Number of breakpoints
+ * @param seeding_time Time point at which seeding occurs
+ * @param r_logmean Log-mean of the prior distribution for the base reproduction number
+ * @param r_logsd Log-standard deviation of the prior distribution for the base reproduction number
+ * @param prior_infections Prior mean for initial infections
+ * @param prior_growth Prior mean for initial growth rates
+ */
 void rt_lp(vector log_R, array[] real initial_infections, array[] real initial_growth,
-           array[] real bp_effects, array[] real bp_sd, int bp_n, int seeding_time,
+           vector bp_effects, array[] real bp_sd, int bp_n, int seeding_time,
            real r_logmean, real r_logsd, real prior_infections,
            real prior_growth) {
-  // prior on R
   log_R ~ normal(r_logmean, r_logsd);
   //breakpoint effects on Rt
   if (bp_n > 0) {
@@ -51,6 +72,7 @@ void rt_lp(vector log_R, array[] real initial_infections, array[] real initial_g
   }
   // initial infections
   initial_infections ~ normal(prior_infections, 0.2);
+  
   if (seeding_time > 1) {
     initial_growth ~ normal(prior_growth, 0.2);
   }
diff --git a/man/EpiNow2-package.Rd b/man/EpiNow2-package.Rd
index 3b1d4e286..f8f7529f3 100644
--- a/man/EpiNow2-package.Rd
+++ b/man/EpiNow2-package.Rd
@@ -43,7 +43,7 @@ Other contributors:
   \item Paul Mee \email{paul.mee@lshtm.ac.uk} [contributor]
   \item Peter Ellis \email{peter.ellis2013nz@gmail.com} [contributor]
   \item Pietro Monticone \email{pietro.monticone@edu.unito.it} [contributor]
-  \item Lloyd Chapman \email{lloyd.chapman1@lshtm.ac.uk} [contributor]
+  \item Lloyd Chapman \email{lloyd.chapman1@lshtm.ac.uk } [contributor]
   \item Andrew Johnson \email{andrew.johnson@arjohnsonau.com} [contributor]
 }
 
diff --git a/man/create_rt_data.Rd b/man/create_rt_data.Rd
index 4a02c1664..3c5233795 100644
--- a/man/create_rt_data.Rd
+++ b/man/create_rt_data.Rd
@@ -36,6 +36,9 @@ create_rt_data(rt = NULL)
 
 # using breakpoints
 create_rt_data(rt_opts(use_breakpoints = TRUE), breakpoints = rep(1, 10))
+
+# using random walk
+create_rt_data(rt_opts(rw = 7), breakpoints = rep(1, 10))
 }
 }
 \seealso{
diff --git a/tests/testthat/test-create_rt_date.R b/tests/testthat/test-create_rt_date.R
new file mode 100644
index 000000000..748ae80d4
--- /dev/null
+++ b/tests/testthat/test-create_rt_date.R
@@ -0,0 +1,88 @@
+test_that("create_rt_data returns expected default values", {
+  result <- create_rt_data()
+  
+  expect_type(result, "list")
+  expect_equal(result$r_mean, 1)
+  expect_equal(result$r_sd, 1)
+  expect_equal(result$estimate_r, 1)
+  expect_equal(result$bp_n, 0)
+  expect_equal(result$breakpoints, numeric(0))
+  expect_equal(result$future_fixed, 1)
+  expect_equal(result$fixed_from, 0)
+  expect_equal(result$pop, 0)
+  expect_equal(result$stationary, 0)
+  expect_equal(result$future_time, 0)
+})
+
+test_that("create_rt_data handles NULL rt input correctly", {
+  result <- create_rt_data(rt = NULL)
+  
+  expect_equal(result$estimate_r, 0)
+  expect_equal(result$future_fixed, 0)
+  expect_equal(result$stationary, 1)
+})
+
+test_that("create_rt_data handles custom rt_opts correctly", {
+  custom_rt <- rt_opts(
+    prior = list(mean = 2, sd = 0.5),
+    use_rt = FALSE,
+    rw = 0,
+    use_breakpoints = FALSE,
+    future = "project",
+    gp_on = "R0",
+    pop = 1000000
+  )
+  
+  result <- create_rt_data(rt = custom_rt, horizon = 7)
+  
+  expect_equal(result$r_mean, 2)
+  expect_equal(result$r_sd, 0.5)
+  expect_equal(result$estimate_r, 0)
+  expect_equal(result$pop, 1000000)
+  expect_equal(result$stationary, 1)
+  expect_equal(result$future_time, 7)
+})
+
+test_that("create_rt_data handles breakpoints correctly", {
+  result <- create_rt_data(rt_opts(use_breakpoints = TRUE), 
+                           breakpoints = c(1, 0, 1, 0, 1))
+  
+  expect_equal(result$bp_n, 3)
+  expect_equal(result$breakpoints, c(2, 2, 3, 3, 4))
+})
+
+test_that("create_rt_data handles random walk correctly", {
+  result <- create_rt_data(rt_opts(rw = 2), 
+                           breakpoints = rep(1, 10))
+  
+  expect_equal(result$bp_n, 5)
+  expect_equal(result$breakpoints, c(1, 2, 2, 3, 3, 4, 4, 5, 5, 6))
+})
+
+test_that("create_rt_data throws error for invalid inputs", {
+  expect_error(create_rt_data(rt_opts(rw = 2)),
+               "breakpoints must be supplied when using random walk")
+})
+
+test_that("create_rt_data handles future projections correctly", {
+  result <- create_rt_data(rt_opts(future = "project"), horizon = 7)
+  
+  expect_equal(result$future_fixed, 0)
+  expect_equal(result$fixed_from, 0)
+  expect_equal(result$future_time, 7)
+})
+
+test_that("create_rt_data handles zero sum breakpoints", {
+  result <- create_rt_data(rt_opts(use_breakpoints = TRUE), 
+                           breakpoints = rep(0, 5))
+  
+  expect_equal(result$bp_n, 0)
+})
+
+test_that("create_rt_data adjusts breakpoints for horizon", {
+  result <- create_rt_data(rt_opts(rw = 2, future = "latest"), 
+                           breakpoints = rep(1, 10),
+                           horizon = 3)
+  
+  expect_equal(result$breakpoints, c(1, 2, 2, 3, 3, 4, 4, 4, 4, 4))
+})
diff --git a/tests/testthat/test-rt_opts.R b/tests/testthat/test-rt_opts.R
new file mode 100644
index 000000000..2d415ff8e
--- /dev/null
+++ b/tests/testthat/test-rt_opts.R
@@ -0,0 +1,61 @@
+test_that("rt_opts returns expected default values", {
+  result <- rt_opts()
+  
+  expect_s3_class(result, "rt_opts")
+  expect_equal(result$prior, list(mean = 1, sd = 1))
+  expect_true(result$use_rt)
+  expect_equal(result$rw, 0)
+  expect_true(result$use_breakpoints)
+  expect_equal(result$future, "latest")
+  expect_equal(result$pop, 0)
+  expect_equal(result$gp_on, "R_t-1")
+})
+
+test_that("rt_opts handles custom inputs correctly", {
+  result <- rt_opts(
+    prior = list(mean = 2, sd = 0.5),
+    use_rt = FALSE,
+    rw = 7,
+    use_breakpoints = FALSE,
+    future = "project",
+    gp_on = "R0",
+    pop = 1000000
+  )
+  
+  expect_equal(result$prior, list(mean = 2, sd = 0.5))
+  expect_false(result$use_rt)
+  expect_equal(result$rw, 7)
+  expect_true(result$use_breakpoints)  # Should be TRUE when rw > 0
+  expect_equal(result$future, "project")
+  expect_equal(result$pop, 1000000)
+  expect_equal(result$gp_on, "R0")
+})
+
+test_that("rt_opts sets use_breakpoints to TRUE when rw > 0", {
+  result <- rt_opts(rw = 3, use_breakpoints = FALSE)
+  expect_true(result$use_breakpoints)
+})
+
+test_that("rt_opts throws error for invalid prior", {
+  expect_error(rt_opts(prior = list(mean = 1)),
+               "prior must have both a mean and sd specified")
+  expect_error(rt_opts(prior = list(sd = 1)),
+               "prior must have both a mean and sd specified")
+})
+
+test_that("rt_opts validates gp_on argument", {
+  expect_error(rt_opts(gp_on = "invalid"), "must be one")
+})
+
+test_that("rt_opts returns object of correct class", {
+  result <- rt_opts()
+  expect_s3_class(result, "rt_opts")
+  expect_true("list" %in% class(result))
+})
+
+test_that("rt_opts handles edge cases correctly", {
+  result <- rt_opts(rw = 0.1, pop = -1)
+  expect_equal(result$rw, 0.1)
+  expect_equal(result$pop, -1)
+  expect_true(result$use_breakpoints)
+})
diff --git a/tests/testthat/test-stan-rt.R b/tests/testthat/test-stan-rt.R
index cddfa1ef9..1b4c40153 100644
--- a/tests/testthat/test-stan-rt.R
+++ b/tests/testthat/test-stan-rt.R
@@ -32,29 +32,29 @@ test_that("update_Rt works when Rt is fixed", {
 })
 test_that("update_Rt works when Rt is fixed but a breakpoint is present", {
   expect_equal(
-    round(update_Rt(5, log(1.2), numeric(0), c(0, 0, 1, 0, 0), 0.1, 0), 2),
+    round(update_Rt(5, log(1.2), numeric(0), c(1, 1, 2, 2, 2), 0.1, 0), 2),
     c(1.2, 1.2, rep(1.33, 3))
   )
   expect_equal(
-    round(update_Rt(5, log(1.2), numeric(0), c(0, 0, 1, 0, 0), 0.1, 1), 2),
+    round(update_Rt(5, log(1.2), numeric(0), c(1, 1, 2, 2, 2), 0.1, 1), 2),
     c(1.2, 1.2, rep(1.33, 3))
   )
   expect_equal(
-    round(update_Rt(5, log(1.2), numeric(0), c(0, 1, 1, 0, 0), rep(0.1, 2), 0), 2),
+    round(update_Rt(5, log(1.2), numeric(0), c(1, 2, 3, 3, 3), rep(0.1, 2), 0), 2),
     c(1.2, 1.33, rep(1.47, 3))
   )
 })
 test_that("update_Rt works when Rt is variable and a breakpoint is present", {
   expect_equal(
-    round(update_Rt(5, log(1.2), rep(0, 4), c(0, 0, 1, 0, 0), 0.1, 0), 2),
+    round(update_Rt(5, log(1.2), rep(0, 4), c(1, 1, 2, 2, 2), 0.1, 0), 2),
     c(1.2, 1.2, rep(1.33, 3))
   )
   expect_equal(
-    round(update_Rt(5, log(1.2), rep(0, 5), c(0, 0, 1, 0, 0), 0.1, 1), 2),
+    round(update_Rt(5, log(1.2), rep(0, 5), c(1, 1, 2, 2, 2), 0.1, 1), 2),
     c(1.2, 1.2, rep(1.33, 3))
   )
   expect_equal(
-    round(update_Rt(5, log(1.2), rep(0.1, 4), c(0, 0, 1, 0, 0), 0.1, 0), 2),
+    round(update_Rt(5, log(1.2), rep(0.1, 4), c(1, 1, 2, 2, 2), 0.1, 0), 2),
     c(1.20, 1.33, 1.62, 1.79, 1.98)
   )
 })