diff --git a/NAMESPACE b/NAMESPACE
index 507d28c..f0d4aa4 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -1,5 +1,6 @@
 # Generated by roxygen2: do not edit by hand
 
+S3method(all.equal,Bitset)
 export(Bitset)
 export(CategoricalVariable)
 export(DoubleVariable)
diff --git a/R/bitset.R b/R/bitset.R
index 556c560..fe11a03 100644
--- a/R/bitset.R
+++ b/R/bitset.R
@@ -227,6 +227,17 @@ Bitset <- list(
   }
 )
 
+#' @export
+#' @method all.equal Bitset
+all.equal.Bitset <- function(target, current, ...) {
+  if (target$max_size != current$max_size) {
+    return(paste0(
+      "Bitset capacity differs (", target$max_size, " vs ",
+      current$max_size,  ")"))
+  }
+  all.equal(target$to_vector(), current$to_vector(), ...)
+}
+
 #' @title Filter a bitset
 #' @description This non-modifying function returns a new \code{\link{Bitset}}
 #' object of the same maximum size as the original but which only contains
diff --git a/tests/testthat/test-bitset.R b/tests/testthat/test-bitset.R
index 4199bc2..53ed13c 100644
--- a/tests/testthat/test-bitset.R
+++ b/tests/testthat/test-bitset.R
@@ -358,3 +358,38 @@ test_that("bitset sampling has correctly distributed size", {
     expect_gt(p, threshold)
   }
 })
+
+test_that("bitset equality works", {
+  a <- Bitset$new(10)
+  b <- Bitset$new(10)
+  c <- Bitset$new(10)
+  d <- Bitset$new(10)
+  e <- Bitset$new(10)
+  f <- Bitset$new(10)
+
+  c$insert(c(1, 2, 3))
+  d$insert(c(1, 2, 3))
+  e$insert(c(4, 5, 6))
+  f$insert(c(4, 7))
+
+  expect_equal(a, b)
+  expect_equal(c, d)
+
+  expect_false(isTRUE(all.equal(a, c)))
+  expect_false(isTRUE(all.equal(a, e)))
+  expect_false(isTRUE(all.equal(a, f)))
+  expect_false(isTRUE(all.equal(c, e)))
+  expect_false(isTRUE(all.equal(c, f)))
+  expect_false(isTRUE(all.equal(e, f)))
+
+  expect_equal(a, a$copy())
+  expect_equal(c, c$copy())
+  expect_equal(e, e$copy())
+  expect_equal(f, f$copy())
+})
+
+test_that("bitset with different sizes are not equal", {
+  a <- Bitset$new(10)
+  b <- Bitset$new(11)
+  expect_false(isTRUE(all.equal(a, b)))
+})