About Game Math Calculator

Calculate vectors, distances, dot products, lerp, and common game math operations. Part of the DevTools Surf developer suite. Browse more tools in the Game Dev collection.

Use Cases

• Game programmers calculating distances between game entities
• AI developers computing direction vectors for NPC pathfinding
• Physics programmers debugging collision detection math
• Shader developers verifying lighting calculation vectors

Tips

• Use dot product to check if two vectors face the same direction
• Calculate lerp values between 0-1 for smooth interpolation
• Normalize direction vectors before calculating distances

Fun Facts

• Linear interpolation (lerp) is the most-used function in game development — John Carmack once said every game programmer writes lerp within their first week.
• The dot product determines the angle between vectors — a positive value means they point roughly the same direction, zero means perpendicular, negative means opposite.
• The cross product, essential for 3D game math, was formalized by Josiah Willard Gibbs at Yale in 1881 — the same mathematician who founded vector analysis.

FAQ

What operations?

Vector (2D, 3D) arithmetic, dot/cross products, distance, normalize, magnitude, lerp (linear interpolation), slerp (spherical). Plus matrix basics.

Which language output?

C# (Unity/Mathf), JS (three.js-style Vector3), HLSL (shader code), GLSL. Same operation, native syntax per target.

Lerp example?

Position between two points: `Vector3.Lerp(a, b, 0.5f)` gets the midpoint. `0.0` returns a, `1.0` returns b, in-between interpolates linearly.

Is this for game dev only?

Any vector math — game dev, physics simulations, data viz, robotics. The calculator is generic; the output labeling targets game devs.