diff --git a/lib/graphql.rb b/lib/graphql.rb
index 110a40a54d7..b3fcac42961 100644
--- a/lib/graphql.rb
+++ b/lib/graphql.rb
@@ -93,6 +93,8 @@ class << self
   autoload :AnalysisError, "graphql/analysis_error"
   autoload :CoercionError, "graphql/coercion_error"
   autoload :InvalidNameError, "graphql/invalid_name_error"
+  autoload :FloatDecodingError, "graphql/float_decoding_error"
+  autoload :FloatEncodingError, "graphql/float_encoding_error"
   autoload :IntegerDecodingError, "graphql/integer_decoding_error"
   autoload :IntegerEncodingError, "graphql/integer_encoding_error"
   autoload :StringEncodingError, "graphql/string_encoding_error"
diff --git a/lib/graphql/float_decoding_error.rb b/lib/graphql/float_decoding_error.rb
new file mode 100644
index 00000000000..8e0f9aed53b
--- /dev/null
+++ b/lib/graphql/float_decoding_error.rb
@@ -0,0 +1,13 @@
+# frozen_string_literal: true
+module GraphQL
+  # This error is raised when `Types::Float` is given a non-finite input value.
+  class FloatDecodingError < GraphQL::RuntimeTypeError
+    # The value which couldn't be decoded
+    attr_reader :float_value
+
+    def initialize(value)
+      @float_value = value
+      super("Float is not finite: #{value.inspect}.")
+    end
+  end
+end
diff --git a/lib/graphql/float_encoding_error.rb b/lib/graphql/float_encoding_error.rb
new file mode 100644
index 00000000000..f1c01cb3205
--- /dev/null
+++ b/lib/graphql/float_encoding_error.rb
@@ -0,0 +1,28 @@
+# frozen_string_literal: true
+module GraphQL
+  # This error is raised when `Types::Float` is asked to return a non-finite value.
+  class FloatEncodingError < GraphQL::RuntimeTypeError
+    # The value which couldn't be encoded
+    attr_reader :float_value
+
+    # @return [GraphQL::Schema::Field] The field that returned a non-finite float
+    attr_reader :field
+
+    # @return [Array<String, Integer>] Where the field appeared in the GraphQL response
+    attr_reader :path
+
+    def initialize(value, context:)
+      @float_value = value
+      @field = context[:current_field]
+      @path = context[:current_path]
+      message = "Float is not finite: #{value.inspect}".dup
+      if @path
+        message << " @ #{@path.join(".")}"
+      end
+      if @field
+        message << " (#{@field.path})"
+      end
+      super("#{message}.")
+    end
+  end
+end
diff --git a/lib/graphql/language.rb b/lib/graphql/language.rb
index 5280f9c5d07..d85133cdbbe 100644
--- a/lib/graphql/language.rb
+++ b/lib/graphql/language.rb
@@ -34,8 +34,8 @@ def self.serialize(value)
         JSON.generate(value)
       end
     rescue JSON::GeneratorError
-      if Float::INFINITY == value
-        "Infinity"
+      if value.is_a?(Float) && !value.finite?
+        value.to_s
       else
         raise
       end
diff --git a/lib/graphql/query/variable_validation_error.rb b/lib/graphql/query/variable_validation_error.rb
index 3a934dfc164..41f70e116e5 100644
--- a/lib/graphql/query/variable_validation_error.rb
+++ b/lib/graphql/query/variable_validation_error.rb
@@ -22,7 +22,7 @@ def to_h
         # It is possible there are other extension items in this error, so handle
         # a one level deep merge explicitly. However beyond that only show the
         # latest value and problems.
-        super.merge({ "extensions" => { "value" => value, "problems" => validation_result.problems }}) do |key, oldValue, newValue|
+        super.merge({ "extensions" => { "value" => value_for_extensions, "problems" => validation_result.problems }}) do |key, oldValue, newValue|
           if oldValue.respond_to?(:merge)
             oldValue.merge(newValue)
           else
@@ -33,6 +33,21 @@ def to_h
 
       private
 
+      def value_for_extensions(value = @value)
+        case value
+        when Array
+          value.map { |item| value_for_extensions(item) }
+        when Hash
+          value.each_with_object({}) do |(key, item), result|
+            result[key] = value_for_extensions(item)
+          end
+        when Float
+          value.finite? ? value : value.to_s
+        else
+          value
+        end
+      end
+
       def problem_fields
         @problem_fields ||= @validation_result
           .problems
diff --git a/lib/graphql/schema.rb b/lib/graphql/schema.rb
index f6801ddbfb2..48f502b4475 100644
--- a/lib/graphql/schema.rb
+++ b/lib/graphql/schema.rb
@@ -1338,9 +1338,9 @@ def type_error(type_error, context)
 
           context.errors << execution_error
           execution_error
-        when GraphQL::UnresolvedTypeError, GraphQL::StringEncodingError, GraphQL::IntegerEncodingError
+        when GraphQL::UnresolvedTypeError, GraphQL::StringEncodingError, GraphQL::FloatEncodingError, GraphQL::IntegerEncodingError
           raise type_error
-        when GraphQL::IntegerDecodingError
+        when GraphQL::FloatDecodingError, GraphQL::IntegerDecodingError
           nil
         end
       end
diff --git a/lib/graphql/types/float.rb b/lib/graphql/types/float.rb
index 7551899ed5a..2016aefcbbb 100644
--- a/lib/graphql/types/float.rb
+++ b/lib/graphql/types/float.rb
@@ -5,12 +5,26 @@ module Types
     class Float < GraphQL::Schema::Scalar
       description "Represents signed double-precision fractional values as specified by [IEEE 754](https://en.wikipedia.org/wiki/IEEE_floating_point)."
 
-      def self.coerce_input(value, _ctx)
-        value.is_a?(Numeric) ? value.to_f : nil
+      def self.coerce_input(value, ctx)
+        return if !value.is_a?(Numeric)
+
+        value = value.to_f
+        if value.finite?
+          value
+        else
+          err = GraphQL::FloatDecodingError.new(value)
+          ctx.schema.type_error(err, ctx)
+        end
       end
 
-      def self.coerce_result(value, _ctx)
-        value.to_f
+      def self.coerce_result(value, ctx)
+        value = value.to_f
+        if value.finite?
+          value
+        else
+          err = GraphQL::FloatEncodingError.new(value, context: ctx)
+          ctx.schema.type_error(err, ctx)
+        end
       end
 
       default_scalar true
diff --git a/spec/graphql/query/variable_validation_error_spec.rb b/spec/graphql/query/variable_validation_error_spec.rb
index eea4268db12..f73a826370a 100644
--- a/spec/graphql/query/variable_validation_error_spec.rb
+++ b/spec/graphql/query/variable_validation_error_spec.rb
@@ -47,5 +47,13 @@ def extensions
       }
       assert_equal error.to_h, as_hash
     end
+
+    it 'makes non-finite values JSON-safe' do
+      error = subject.new(ast, type, { "values" => [Float::NAN, Float::INFINITY] }, validation_result)
+      value = error.to_h.dig("extensions", "value")
+
+      assert_equal({ "values" => ["NaN", "Infinity"] }, value)
+      JSON.generate(error.to_h)
+    end
   end
 end
diff --git a/spec/graphql/types/float_spec.rb b/spec/graphql/types/float_spec.rb
index ba2b8028802..7077abd3ff8 100644
--- a/spec/graphql/types/float_spec.rb
+++ b/spec/graphql/types/float_spec.rb
@@ -3,6 +3,28 @@
 
 describe GraphQL::Types::Float do
   let(:enum) { GraphQL::Language::Nodes::Enum.new(name: 'MILK') }
+  let(:schema) {
+    query_type = Class.new(GraphQL::Schema::Object) do
+      graphql_name "Query"
+
+      field :echo, Float do
+        argument :value, Float
+      end
+      field :non_finite, Float, resolve_static: true
+
+      def self.non_finite(_context)
+        ::Float::NAN
+      end
+
+      def non_finite
+        self.class.non_finite(nil)
+      end
+    end
+
+    Class.new(GraphQL::Schema) do
+      query(query_type)
+    end
+  }
 
   describe "coerce_input" do
     it "accepts ints and floats" do
@@ -15,5 +37,49 @@
       assert_nil GraphQL::Types::Float.coerce_isolated_input(true)
       assert_nil GraphQL::Types::Float.coerce_isolated_input(enum)
     end
+
+    it "rejects non-finite values" do
+      assert_nil GraphQL::Types::Float.coerce_isolated_input(Float::NAN)
+      assert_nil GraphQL::Types::Float.coerce_isolated_input(Float::INFINITY)
+      assert_nil GraphQL::Types::Float.coerce_isolated_input(-Float::INFINITY)
+    end
+
+    it "rejects non-finite literals and variables" do
+      literal_result = schema.execute("{ echo(value: 1e400) }")
+      assert_includes literal_result["errors"].first["message"], "has an invalid value"
+
+      variable_result = schema.execute(
+        "query($value: Float!) { echo(value: $value) }",
+        variables: { "value" => Float::NAN },
+      )
+      assert_includes variable_result["errors"].first["message"], "provided invalid value"
+      assert_equal "NaN", variable_result["errors"].first.dig("extensions", "value")
+      [literal_result, variable_result].each { |result| JSON.generate(result.to_h) }
+    end
+  end
+
+  describe "coerce_result" do
+    it "accepts finite values" do
+      assert_equal 1.0, GraphQL::Types::Float.coerce_isolated_result(1)
+      assert_equal 6.1, GraphQL::Types::Float.coerce_isolated_result(6.1)
+    end
+
+    it "raises on non-finite values" do
+      assert_raises(GraphQL::FloatEncodingError) do
+        GraphQL::Types::Float.coerce_isolated_result(Float::INFINITY)
+      end
+      assert_raises(GraphQL::FloatEncodingError) do
+        GraphQL::Types::Float.coerce_isolated_result(-Float::INFINITY)
+      end
+
+      err = assert_raises(GraphQL::FloatEncodingError) do
+        schema.execute("{ nonFinite }")
+      end
+      expected_message = exec_next_error_message(
+        "Query.nonFinite",
+        "Float is not finite: NaN#{if_exec_next("", " @ nonFinite (Query.nonFinite)")}.",
+      )
+      assert_equal expected_message, err.message
+    end
   end
 end