diff --git a/docs/src/lib/sets/Interval.md b/docs/src/lib/sets/Interval.md
index 9fd329c8d3..51d4009e02 100644
--- a/docs/src/lib/sets/Interval.md
+++ b/docs/src/lib/sets/Interval.md
@@ -75,6 +75,7 @@ Undocumented implementations:
 * [`radius`](@ref radius(::LazySet, ::Real))
 * [`volume`](@ref volume(::LazySet))
 * [`convex_hull`](@ref convex_hull(::LazySet, ::LazySet))
+* [`distance`](@ref distance(::LazySet, ::LazySet))
 * [`≈`](@ref ≈(::LazySet, ::LazySet))
 * [`isequivalent`](@ref isequivalent(::LazySet, ::LazySet))
 * [`⊂`](@ref ⊂(::LazySet, ::LazySet))
@@ -127,7 +128,6 @@ Inherited from [`AbstractHyperrectangle`](@ref):
 * [`genmat`](@ref genmat(::AbstractHyperrectangle))
 * [`isconvextype`](@ref isconvextype(::Type{<:AbstractHyperrectangle}))
 * [`cartesian_product`](@ref cartesian_product(::AbstractHyperrectangle, ::AbstractHyperrectangle))
-* [`distance`](@ref distance(::AbstractHyperrectangle, ::AbstractHyperrectangle))
 
 Some additional functionality is available for `IntervalArithmetic.Interval`s:
 
diff --git a/src/Sets/Interval/IntervalModule.jl b/src/Sets/Interval/IntervalModule.jl
index 0fe1bcc6de..1ebc741a40 100644
--- a/src/Sets/Interval/IntervalModule.jl
+++ b/src/Sets/Interval/IntervalModule.jl
@@ -16,8 +16,8 @@ import IntervalArithmetic as IA
                         convex_hull, diameter, dim, exponential_map, extrema, high, ∈,
                         isoperationtype, linear_map, low, norm, permute, project, rand,
                         rectify, reflect, scale, ρ, σ, translate, vertices_list, volume,
-                        difference, intersection, ≈, isdisjoint, isequivalent, ⊂, ⊆,
-                        minkowski_difference, minkowski_sum
+                        difference, distance, intersection, ≈, isdisjoint, isequivalent,
+                        ⊂, ⊆, minkowski_difference, minkowski_sum
 @reexport import ..LazySets: chebyshev_center_radius, isflat, ngens, plot_recipe,
                              radius_hyperrectangle, split
 import Base: convert, -, *, min, max
@@ -62,6 +62,7 @@ include("vertices_list.jl")
 include("volume.jl")
 
 include("difference.jl")
+include("distance.jl")
 include("intersection.jl")
 include("isapprox.jl")
 include("isdisjoint.jl")
diff --git a/src/Sets/Interval/distance.jl b/src/Sets/Interval/distance.jl
new file mode 100644
index 0000000000..bcd3392116
--- /dev/null
+++ b/src/Sets/Interval/distance.jl
@@ -0,0 +1,7 @@
+function distance(X::Interval, Y::Interval; p::Real=2)
+    d = max(min(X) - max(Y), min(Y) - max(X))
+    if d < 0
+        return zero(d)
+    end
+    return d
+end
diff --git a/test/Sets/Interval.jl b/test/Sets/Interval.jl
index fe1183a7ba..224acd85b6 100644
--- a/test/Sets/Interval.jl
+++ b/test/Sets/Interval.jl
@@ -352,4 +352,9 @@ for N in [Float64, Float32, Rational{Int}]
 
     # isequivalent
     @test isequivalent(I1, I1) && !isequivalent(I1, I2)
+
+    # distance
+    @test distance(I1, I2) == distance(I2, I1) == N(1)
+    I3 = Interval(N(1//2), N(2))
+    @test distance(I1, I3) == distance(I2, I3) == distance(I1, I1) == N(0)
 end