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.

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.

Game Math Calculator | DevTools Surf

DevTools Surf

Example: Game Math Calculator

A worked example, rendered from real sample data. Sign in to run the tool on your own input.

Input

distance 0,0 3,4
normalize 3,4
dot 1,0 0,1
lerp 0,0 10,10 0.5
angle 1,0 0,1
magnitude 5,12

Output

distance 0,0 3,4
  formula  |b − a| = √Σ(bᵢ − aᵢ)²
  = 5.0000

normalize 3,4
  formula  â = a / |a|
  = (0.6000, 0.8000)

dot 1,0 0,1
  formula  a·b = Σ aᵢbᵢ = |a||b|cosθ
  = 0.0000

lerp 0,0 10,10 0.5
  formula  lerp(a, b, t) = a + (b − a)·t
  = (5.0000, 5.0000)

angle 1,0 0,1
  formula  θ = acos( a·b / (|a||b|) )
  = 90.00°
  note     1.5708 rad

magnitude 5,12
  formula  |a| = √Σ aᵢ²
  = 13.0000

C# (Unity)
float d = Vector3.Distance(a, b);
Vector3 n = a.normalized;
float d = Vector3.Dot(a, b);
Vector3 p = Vector3.Lerp(a, b, t);
float deg = Vector3.Angle(a, b);
float m = a.magnitude;

About Game Math Calculator

$Game Math Calculator preview - Game Dev tool$

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.

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