FMath

struct Core Since unknown

#include "Math/UnrealMathUtility.h"

Description

The primary math utility struct in Unreal Engine, providing static functions for arithmetic, interpolation, trigonometry, random number generation, and geometric operations. Inherits platform-specific implementations from FPlatformMath via FGenericPlatformMath.

Caveats & Gotchas

• Many functions have both float and double overloads. When mixing float/double arguments, UE will promote to the higher-precision type via MIX_FLOATS macros — but implicit promotion can silently increase cost in hot paths.
• Trigonometric functions (Sin, Cos, Atan2) take angles in radians. FRotator stores degrees. Use FMath::DegreesToRadians / FMath::RadiansToDegrees to convert.
• FMath::RandRange seeded by FMath::RandInit — the global seed is shared across the process. For deterministic random sequences, use FRandomStream instead.

Example

Common usage in a tick function C++

void AMyActor::Tick(float DeltaTime)
{
	Super::Tick(DeltaTime);

	// Smoothly interpolate a float toward a target
	CurrentSpeed = FMath::FInterpTo(CurrentSpeed, TargetSpeed, DeltaTime, 5.0f);

	// Clamp health to valid range
	Health = FMath::Clamp(Health, 0.0f, MaxHealth);

	// Random chance per tick (roughly once per second at 60fps)
	if (FMath::RandRange(0, 59) == 0)
	{
		TriggerRandomEvent();
	}
}

Functions (40)

Utility 7 Geometry 11 Math 14 Smoothing 4 Trigonometry 4

Utility

7 ▼

Access	Type	Name	Description
public	function	FMath::ApplyScaleToFloat	Applies a 3D scale delta to a single float in-place, intended for editor gizmo interactions where dragging a uniform scale handle should affect scalar properties.
public	function	FMath::Eval	Evaluates a mathematical expression from a string at runtime.
public	function	FMath: MIX_FLOATS_2_ARGS	Preprocessor macro that injects a two-argument template overload for mixing float/double/integral argument types, promoting all arguments to the highest-precision floating-point type.
public	function	FMath: MIX_FLOATS_3_ARGS	Preprocessor macro that injects a template overload for a three-argument function, allowing mixed float/double/integral argument lists by promoting all arguments to the highest-precision floating-point type among them.
public	function	FMath: RESOLVE_FLOAT_AMBIGUITY_3_ARGS	Preprocessor macro that currently expands to MIX_FLOATS_3_ARGS, injecting mixed float/double overloads for a three-argument function to eliminate compiler ambiguity errors when argument types differ.
public	function	FMath::SetBoolInBitField	Sets or clears a single bit by index within a packed bitfield represented as a uint8 array.
public	function	FMath: UE_REQUIRES	Preprocessor macro that wraps a C++20 requires-clause (or a SFINAE equivalent on older standards) to constrain template overloads inside FMath and other UE template-heavy code.

Geometry

11 ▼

Access	Type	Name	Description
public	function	FMath::CartesianToPolar	Converts a 2D Cartesian coordinate pair to polar form (radius and angle).
public	function	FMath::PointDistToLine	Returns the perpendicular distance from a point to an infinite line defined by an origin and a direction.
public	function	FMath::PolarToCartesian	Converts polar coordinates (radius and angle in radians) to a 2D Cartesian coordinate pair.
public	function	FMath::SegmentDistToSegment	Finds the closest pair of points between two 3D line segments.
public	function	FMath::SegmentDistToSegmentSafe	Safe variant of SegmentDistToSegment that handles degenerate zero-length segments without undefined behaviour.
public	function	FMath::SegmentIntersection2D	Tests whether two 3D segments intersect when projected onto the XY plane and returns the intersection point.
public	function	FMath::SegmentPlaneIntersection	Tests whether a line segment intersects a plane and returns the intersection point.
public	function	FMath::GetDotDistance	Computes the dot-distance of a direction vector relative to a coordinate system, returning the cosine of azimuth and sine of elevation.
public	function	FMath::LineExtentBoxIntersection	Performs a swept-box versus axis-aligned box intersection test and returns the hit location, normal, and parametric hit time.
public	function	FMath::SegmentTriangleIntersection	Tests whether a line segment intersects a triangle and returns both the intersection point and the triangle's face normal.
public	function	FMath::SphereDistToLine	Finds the closest point on a sphere's surface to an infinite line.

Math

14 ▼

Access	Type	Name	Description
public	function	FMath::Abs	Returns the absolute (non-negative) value of A.
public	function	FMath::Cos	Returns the cosine of an angle given in radians.
public	function	FMath::Sin	Returns the sine of an angle given in radians.
public	function	FMath::Atan2	Returns the angle in radians between the positive X axis and the point (X, Y), in the range [-π, π].
public	function	FMath::Clamp	Clamps a value between a minimum and maximum, inclusive on both ends.
public	function	FMath::FInterpTo	Smoothly moves a float toward a target value at a given speed, independent of frame rate.
public	function	FMath::GetMappedRangeValueClamped	Maps a value from one range to another, clamping the input to the source range first.
public	function	FMath::IsNearlyEqual	Returns true if two floating-point numbers are within a given absolute tolerance of each other.
public	function	FMath::IsNearlyZero	Returns true if a floating-point value is within ErrorTolerance of zero.
public	function	FMath::Lerp	Linearly interpolates between two values.
public	function	FMath::RandRange	Returns a random integer in the inclusive range [Min, Max].
public	function	FMath::Sqrt	Returns the square root of Value.
public	function	FMath::Square	Returns A * A.
public	function	FMath::VInterpTo	Smoothly moves an FVector toward a target vector at a given speed, independently on each axis, frame-rate-independently.

Smoothing

4 ▼

Access	Type	Name	Description
public	function	FMath::ExponentialSmoothingApprox	Smooths a value towards a target using an exponential decay approximation.
public	function	FMath::CriticallyDampedSmoothing	Smooths a value using a critically-damped spring, tracking both position and velocity.
public	function	FMath::SpringDamper	Full spring-damper simulation supporting under-, over-, and critically-damped motion.
public	function	FMath::SpringDamperSmoothing	Convenience wrapper around SpringDamper that accepts a SmoothingTime instead of a frequency, matching the CriticallyDampedSmoothing API but adding a tunable damping ratio.

Trigonometry

4 ▼

Access	Type	Name	Description
public	function	FMath::DegreesToRadians	Converts an angle from degrees to radians by multiplying by π/180.
public	function	FMath::RadiansToDegrees	Converts an angle from radians to degrees by multiplying by 180/π.
public	function	FMath::SinCos	Computes both sine and cosine of an angle simultaneously.
public	function	FMath::WindRelativeAnglesDegrees	Adjusts InOutAngle1 so that the difference between it and InAngle0 is at most 180 degrees, preventing large jumps when interpolating rotation components converted from quaternions.

Version History

Introduced in: unknown

Version	Status	Notes
5.6	stable	—

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