diff --git a/base/math.jl b/base/math.jl
index 981f152ed383d..462e82c8ab443 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -702,6 +702,9 @@ function _hypot(x, y)
     end
     return h*scale*oneunit(axu)
 end
+_hypot(x::Float16, y::Float16) = Float16(_hypot(Float32(x), Float32(y)))
+_hypot(x::ComplexF16, y::ComplexF16) = Float16(_hypot(ComplexF32(x), ComplexF32(y)))
+
 function _hypot(x...)
     maxabs = maximum(abs, x)
     if isnan(maxabs) && any(isinf, x)
diff --git a/test/math.jl b/test/math.jl
index 21f3f34204500..bfe584ed5d340 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -1193,6 +1193,10 @@ end
             @test hypot(x, x*f) ≈ x * hypot(one(f), f) rtol=eps(T)
             @test hypot(x, x*f, x*f) ≈ x * hypot(one(f), f, f) rtol=eps(T)
         end
+        let x = floatmax(T)/2
+            @test (@inferred hypot(x, x/4)) ≈ x * sqrt(17/BigFloat(16))
+            @test (@inferred hypot(x, x/4, x/4)) ≈ x * sqrt(9/BigFloat(8))
+        end
     end
     # hypot on Complex returns Real
     @test (@inferred hypot(3, 4im)) === 5.0