diff --git a/Schema.Test/GeneratedDataEditorTests.cs b/Schema.Test/GeneratedDataEditorTests.cs
index bb644c8..ff410a6 100644
--- a/Schema.Test/GeneratedDataEditorTests.cs
+++ b/Schema.Test/GeneratedDataEditorTests.cs
@@ -308,6 +308,22 @@ public void TestAMissingOrMisshapenValueThrows()
 		Assert.ThrowsExactly<InvalidOperationException>(() => SchemaDataValues.GetString(record, "Missing"));
 	}
 
+	[TestMethod]
+	public void TestANumberPastItsTypesRangeThrowsRatherThanReadingAsInfinity()
+	{
+		JsonObject record = new()
+		{
+			["Speed"] = JsonNode.Parse("1e39"),
+			["D"] = JsonNode.Parse("1e309"),
+			["Position"] = JsonNode.Parse("[1, 1e39, 2]"),
+		};
+
+		Assert.ThrowsExactly<InvalidOperationException>(() => SchemaDataValues.GetFloat(record, "Speed"));
+		Assert.ThrowsExactly<InvalidOperationException>(() => SchemaDataValues.GetDouble(record, "D"));
+		Assert.ThrowsExactly<InvalidOperationException>(() => SchemaDataValues.GetVector3(record, "Position"));
+		Assert.AreEqual(1e39, SchemaDataValues.GetDouble(record, "Speed"));
+	}
+
 	[TestMethod]
 	public void TestVectorsAndColoursRoundTrip()
 	{
diff --git a/Schema.Test/SchemaDataValidatorTypeTests.cs b/Schema.Test/SchemaDataValidatorTypeTests.cs
index 5b42d74..b73610a 100644
--- a/Schema.Test/SchemaDataValidatorTypeTests.cs
+++ b/Schema.Test/SchemaDataValidatorTypeTests.cs
@@ -136,4 +136,60 @@ public void ATypeWithNoStoredFormIsReportedAsUnchecked()
 			Assert.AreEqual(SchemaValidationSeverity.Warning, issues[0].Severity, type.DisplayName);
 		}
 	}
+
+	// ---- floating-point overflow -----------------------------------------------
+
+	[TestMethod]
+	[DataRow("1e39")]
+	[DataRow("-1e39")]
+	public void AFloatPastFloatsRangeIsAnError(string value)
+	{
+		Collection<SchemaValidationIssue> issues = Validate(new Float(), value);
+
+		Assert.HasCount(1, issues, string.Join("; ", issues));
+		Assert.AreEqual(SchemaValidationSeverity.Error, issues[0].Severity);
+		Assert.Contains("range of Float", issues[0].Message);
+	}
+
+	[TestMethod]
+	[DataRow("3.4028234663852886E+38")]
+	[DataRow("1e38")]
+	[DataRow("0")]
+	public void AFloatAtOrInsideFloatsRangeIsAccepted(string value) =>
+		Assert.HasCount(0, Validate(new Float(), value));
+
+	[TestMethod]
+	public void ADoublePastDoublesRangeIsAnError()
+	{
+		Assert.HasCount(1, Validate(new Double(), "1e309"));
+		Assert.HasCount(0, Validate(new Double(), "1e39"));
+	}
+
+	[TestMethod]
+	public void AFloatVectorComponentPastFloatsRangeIsAnError()
+	{
+		Collection<SchemaValidationIssue> issues = Validate(new Vector3(), "[1, 1e39, 2]");
+
+		Assert.HasCount(1, issues, string.Join("; ", issues));
+		Assert.AreEqual("data.Value[1]", issues[0].Path);
+	}
+
+	[TestMethod]
+	public void AColourComponentAndAQuantityPastFloatsRangeAreErrors()
+	{
+		Assert.HasCount(1, Validate(new ColorRGB(), "[0, 1e39, 0]"));
+		Assert.HasCount(1, Validate(Quantity("Mass"), "1e39"));
+	}
+
+	[TestMethod]
+	public void ASemanticTypeOverAFloatIsHeldToFloatsRange()
+	{
+		SchemaClass schemaClass = ClassWith((schema, c) =>
+		{
+			schema.AddSemanticType("Speed".As<SemanticTypeName>())!.SetUnderlyingType(new Float());
+			c.AddMember("Value".As<MemberName>())!.SetType(new Semantic { SemanticTypeName = "Speed".As<SemanticTypeName>() });
+		});
+
+		Assert.HasCount(1, SchemaDataValidator.ValidateData(schemaClass, """{ "Value": 1e39 }""", "data"));
+	}
 }
diff --git a/Schema/Models/SchemaDataValidator.cs b/Schema/Models/SchemaDataValidator.cs
index 3cb401f..ee4b666 100644
--- a/Schema/Models/SchemaDataValidator.cs
+++ b/Schema/Models/SchemaDataValidator.cs
@@ -262,7 +262,7 @@ private static void ValidateValue(BaseType type, JsonElement value, string path,
 				break;
 
 			case Float or Double:
-				Expect(value, JsonValueKind.Number, path, type, issues);
+				ExpectNumber(value, type, path, type, issues);
 				break;
 
 			case Types.String:
@@ -399,7 +399,24 @@ private static void ExpectNumber(JsonElement value, BaseType storage, string pat
 			return;
 		}
 
-		Expect(value, JsonValueKind.Number, path, type, issues);
+		if (value.ValueKind != JsonValueKind.Number)
+		{
+			Expect(value, JsonValueKind.Number, path, type, issues);
+			return;
+		}
+
+		// A number past what the storage holds reads back as an infinity rather than failing, so
+		// "1e39" in a Float passes every reader and arrives as one. Refuse it here, as the
+		// integral types already are and as schema validation already refuses such a default.
+		bool finite = value.TryGetDouble(out double number) && double.IsFinite(number);
+		if (represented is Float && !(finite && Math.Abs(number) <= float.MaxValue))
+		{
+			issues.Add(Error(path, $"Expected a number within the range of Float (±{float.MaxValue.ToString("R", CultureInfo.InvariantCulture)}) for type '{type.DisplayName}' but found {value.GetRawText()}."));
+		}
+		else if (represented is Double && !finite)
+		{
+			issues.Add(Error(path, $"Expected a number within the range of Double (±{double.MaxValue.ToString("R", CultureInfo.InvariantCulture)}) for type '{type.DisplayName}' but found {value.GetRawText()}."));
+		}
 	}
 
 	private static void ValidateEnumValue(Types.Enum enumType, JsonElement value, string path, Collection<SchemaValidationIssue> issues)
diff --git a/Schema/Runtime/SchemaDataValues.cs b/Schema/Runtime/SchemaDataValues.cs
index e106855..5b3ac90 100644
--- a/Schema/Runtime/SchemaDataValues.cs
+++ b/Schema/Runtime/SchemaDataValues.cs
@@ -115,7 +115,7 @@ public static long GetLong(JsonObject record, string name) =>
 	/// <param name="name">The member's declared name.</param>
 	/// <returns>The value.</returns>
 	public static float GetFloat(JsonObject record, string name) =>
-		ReadNumber(record, name, static (JsonElement e, out float v) => e.TryGetSingle(out v));
+		ReadNumber(record, name, static (JsonElement e, out float v) => e.TryGetSingle(out v) && float.IsFinite(v));
 
 	/// <summary>Writes a <c>Float</c> member.</summary>
 	/// <param name="record">The record.</param>
@@ -128,7 +128,7 @@ public static float GetFloat(JsonObject record, string name) =>
 	/// <param name="name">The member's declared name.</param>
 	/// <returns>The value.</returns>
 	public static double GetDouble(JsonObject record, string name) =>
-		ReadNumber(record, name, static (JsonElement e, out double v) => e.TryGetDouble(out v));
+		ReadNumber(record, name, static (JsonElement e, out double v) => e.TryGetDouble(out v) && double.IsFinite(v));
 
 	/// <summary>Writes a <c>Double</c> member.</summary>
 	/// <param name="record">The record.</param>
@@ -342,7 +342,8 @@ private static float[] GetComponents(JsonObject record, string name, int count)
 		{
 			JsonNode? component = array[i];
 			if (component?.GetValueKind() != JsonValueKind.Number
-				|| !JsonSerializer.SerializeToElement(component).TryGetSingle(out components[i]))
+				|| !JsonSerializer.SerializeToElement(component).TryGetSingle(out components[i])
+				|| !float.IsFinite(components[i]))
 			{
 				throw Malformed(name, $"component {i} is not a number");
 			}